EY_thesis.bib

@article{gurel_studies_1955,
	title = {Studies of the viscosity and sedimentation of suspensions: {Part} 3. - {The} sedimentation of isometric and compact particles},
	volume = {6},
	issn = {0508-3443},
	shorttitle = {Studies of the viscosity and sedimentation of suspensions},
	url = {https://doi.org/10.1088/0508-3443/6/3/304},
	doi = {10.1088/0508-3443/6/3/304},
	abstract = {Series of experiments on the sedimentation of a variety of isometrically-shaped bodies are described and it is shown that the resistance to motion R, of a body moving with velocity v, in an infinite extent of fluid in the region of streamline flow is given by R = vηK√(surface area of body), where η is the viscosity of the fluid and K a shape factor of the particle which varies from 3√π for spheres to 3√2.92 for tetrahedra. By using a value of 3√3 for K the equation may be applied to isometric and other compact shapes, where the axial ratio does not exceed about 1.4 to 1, with an error not greater than ±2\%. A more accurate, but less easily applied, empirical relationship for the settling rate of compact bodies is also given and an equation which satisfies the interference effects of the walls of a sedimentation vessel upon a falling body is developed experimentally.},
	language = {en},
	number = {3},
	urldate = {2021-01-13},
	journal = {British Journal of Applied Physics},
	author = {Gurel, S. and Ward, S. G. and Whitmore, R. L.},
	month = mar,
	year = {1955},
	note = {Publisher: IOP Publishing},
	pages = {83--87},
}

@book{trefethen_spectral_2000,
	series = {Software, {Environments} and {Tools}},
	title = {Spectral {Methods} in {MATLAB}},
	isbn = {978-0-89871-465-4},
	url = {https://epubs.siam.org/doi/book/10.1137/1.9780898719598},
	abstract = {The aim of this book is to teach you the essentials of spectral collocation methods with the aid of 40 short MATLAB® programs, or “M-files.”* The programs are available online at http://www.comlab.ox.ac.uk/oucl/work/nick.trefethen, and you will run them and modify them to solve all kinds of ordinary and partial differential equations (ODEs and PDEs) connected with problems in fluid mechanics, quantum mechanics, vibrations, linear and nonlinear waves, complex analysis, and other fields. Concerning prerequisites, it is assumed that the words just written have meaning for you, that you have some knowledge of numerical methods, and that you already know MATLAB. If you like computing and numerical mathematics, you will enjoy working through this book, whether alone or in the classroom—and if you learn a few new tricks of MATLAB along the way, that's OK too!},
	urldate = {2019-09-18},
	publisher = {Society for Industrial and Applied Mathematics},
	author = {Trefethen, L.},
	month = jan,
	year = {2000},
	doi = {10.1137/1.9780898719598},
	file = {Snapshot:/Users/eunji/Zotero/storage/KQIBY52P/1.html:text/html;Snapshot:/Users/eunji/Zotero/storage/4VL2RGBP/1.html:text/html},
}

@article{ying_kernel-independent_2004,
	title = {A kernel-independent adaptive fast multipole algorithm in two and three dimensions},
	volume = {196},
	issn = {0021-9991},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999103006090},
	doi = {10.1016/j.jcp.2003.11.021},
	abstract = {We present a new fast multipole method for particle simulations. The main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel, and it is based only on kernel evaluations. Instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical FMM tree, we use a continuous distribution of an equivalent density on a surface enclosing the box. To find this equivalent density, we match its potential to the potential of the original sources at a surface, in the far field, by solving local Dirichlet-type boundary value problems. The far-field evaluations are sparsified with singular value decomposition in 2D or fast Fourier transforms in 3D. We have tested the new method on the single and double layer operators for the Laplacian, the modified Laplacian, the Stokes, the modified Stokes, the Navier, and the modified Navier operators in two and three dimensions. Our numerical results indicate that our method compares very well with the best known implementations of the analytic FMM method for both the Laplacian and modified Laplacian kernels. Its advantage is the (relative) simplicity of the implementation and its immediate extension to more general kernels.},
	language = {en},
	number = {2},
	urldate = {2021-01-31},
	journal = {Journal of Computational Physics},
	author = {Ying, Lexing and Biros, George and Zorin, Denis},
	month = may,
	year = {2004},
	keywords = {-body problems, Double-layer potential, Fast multipole methods, Fast solvers, Integral equations, Particle methods, Single-layer potential},
	pages = {591--626},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/Y2VRC5HG/Ying et al. - 2004 - A kernel-independent adaptive fast multipole algor.pdf:application/pdf},
}

@article{tornberg_fast_2008,
	title = {A fast multipole method for the three-dimensional {Stokes} equations},
	volume = {227},
	issn = {0021-9991},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999107002744},
	doi = {10.1016/j.jcp.2007.06.029},
	abstract = {Many problems in Stokes flow (and linear elasticity) require the evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions. In the fluid mechanics setting, these are typically the Stokeslet (the kernel of the single layer potential) or the Stresslet (the kernel of the double layer potential). In this paper, we present a simple and efficient method for the rapid evaluation of such fields, using a decomposition into a small number of Coulombic N-body problems, following an approach similar to that of Fu and Rodin [Y. Fu, G.J. Rodin, Fast solution methods for three-dimensional Stokesian many-particle problems, Commun. Numer. Meth. En. 16 (2000) 145–149]. While any fast summation algorithm for Coulombic interactions can be employed, we present numerical results from a scheme based on the most modern version of the fast multipole method [H. Cheng, L. Greengard, V. Rokhlin, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys. 155 (1999) 468–498]. This approach should be of value in both the solution of boundary integral equations and multiparticle dynamics.},
	language = {en},
	number = {3},
	urldate = {2021-01-27},
	journal = {Journal of Computational Physics},
	author = {Tornberg, Anna-Karin and Greengard, Leslie},
	month = jan,
	year = {2008},
	pages = {1613--1619},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/ZDVXJXMS/Tornberg and Greengard - 2008 - A fast multipole method for the three-dimensional .pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/ZHECCUF8/S0021999107002744.html:text/html;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/YECWG2GY/S0021999107002744.html:text/html},
}

@article{king_yeung_yick_enhanced_2009,
	title = {Enhanced drag of a sphere settling in a stratified fluid at small {Reynolds} numbers},
	doi = {10.1017/s0022112009007332},
	abstract = {We present a combined experimental and numerical investigation of a sphere settling in a linearly stratified fluid at small Reynolds numbers. Using time-lapse photography and numerical modelling, we observed and quantified an increase in drag due to stratification. For a salt stratification, the normalized added drag coefficient scales as Ri 0.51 , where Ri=a 3 N 2 /(νU) is the viscous Richardson number, a the particle radius, U its speed, ν the kinematic fluid viscosity and N the buoyancy frequency. Microscale synthetic schlieren revealed that a settling sphere draws lighter fluid downwards, resulting in a density wake extending tens of particle radii. Analysis of the flow and density fields shows that the added drag results from the buoyancy of the fluid in a region of size (ν/N) 1/2  surrounding the sphere, while the bulk of the wake does not influence drag. A scaling argument is provided to rationalize the observations. The enhanced drag can increase settling times in natural aquatic environments, affecting retention of particles at density interfaces and vertical fluxes of organic matter.},
	journal = {Journal of Fluid Mechanics},
	author = {{King Yeung Yick} and {Carlos R. Torres} and {Thomas Peacock} and {Roman Stocker}},
	year = {2009},
	doi = {10.1017/s0022112009007332},
	note = {MAG ID: 1978200303},
}

@article{magdalena_m_mrokowska_influence_2020,
	title = {Influence of pycnocline on settling behaviour of non-spherical particle and wake evolution},
	doi = {10.1038/s41598-020-77682-y},
	abstract = {Settling of non-spherical particles in a stratified fluid exhibits complex dynamics in a low-to-moderate inertia regime. Although this process is involved in a wide variety of phenomena in natural fluid systems, its fundamental mechanisms are still unexplored. Understanding of particle settling in microscale is particularly important to explain challenging problems associated with ecological and biogeochemical processes in the ocean due to the delayed settling of particulate matter at pycnoclines. Here, I explore interactions between disk-shaped particles and a stratified fluid with a density transition. By laboratory experiments, I demonstrate that the settling dynamics of the disk crossing a density transition are tightly coupled with the wake structure evolution, and I observe for the first time in a two-layer ambient configuration a bell-shaped structure that forms on a jet after the wake has detached from the particle. Furthermore, I identify hydrodynamic conditions for the variations of settling velocity and particle orientation instabilities. These findings shed light on particle settling mechanisms necessary to explain dynamics of marine particles such as plankton, faecal pellets, and microplastics and may improve the estimation methods of sedimentation processes in various areas of earth sciences and engineering.},
	journal = {Scientific Reports},
	author = {{Magdalena M. Mrokowska}},
	year = {2020},
	doi = {10.1038/s41598-020-77682-y},
	pmcid = {7692520},
	pmid = {33244108},
	note = {MAG ID: 3109985030},
}

@article{arezoo_m_ardekani_stratlets_2010,
	title = {Stratlets: low {Reynolds} number point-force solutions in a stratified fluid.},
	doi = {10.1103/physrevlett.105.084502},
	abstract = {We present fundamental solutions of low Reynolds number flows in a stratified fluid, including the case of a point force (Stokeslet) and a doublet. Stratification dramatically alters the flow by creating toroidal eddies, and velocity decays much faster than in a homogeneous fluid. The fundamental length scale is set by the competition of buoyancy, diffusion and viscosity, and is O(100 μm―1 mm) in aquatic environments. Stratification can therefore affect the swimming of small organisms and the sinking of marine snow particles, and diminish the effectiveness of mechanosensing in the ocean.},
	journal = {Physical Review Letters},
	author = {{Arezoo M. Ardekani} and {Roman Stocker}},
	year = {2010},
	doi = {10.1103/physrevlett.105.084502},
	pmid = {20868101},
	note = {MAG ID: 2995510073},
}

@inproceedings{grengard_rapid_1988,
	address = {Berlin, Heidelberg},
	series = {Lecture {Notes} in {Mathematics}},
	title = {The rapid evaluation of potential fields in three dimensions},
	isbn = {978-3-540-46034-3},
	doi = {10.1007/BFb0089775},
	language = {en},
	booktitle = {Vortex {Methods}},
	publisher = {Springer},
	author = {Grengard, L. and Rokhlin, V.},
	editor = {Anderson, Christopher and Greengard, Claude},
	year = {1988},
	keywords = {Error Bound, Legendre Polynomial, Multipole Expansion, Potential Field, Translation Operator},
	pages = {121--141},
	file = {Springer Full Text PDF:/Users/eunji/Zotero/storage/VWXFLC6P/Grengard and Rokhlin - 1988 - The rapid evaluation of potential fields in three .pdf:application/pdf},
}

@book{guazzelli_physical_2011,
	address = {Cambridge},
	series = {Cambridge {Texts} in {Applied} {Mathematics}},
	title = {A {Physical} {Introduction} to {Suspension} {Dynamics}},
	isbn = {978-0-521-19319-1},
	url = {https://www.cambridge.org/core/books/physical-introduction-to-suspension-dynamics/B8EB2B34C3D3893D7E22884710AA7E7A},
	abstract = {Understanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book begins with the well-developed theory of particles in viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.},
	urldate = {2021-08-31},
	publisher = {Cambridge University Press},
	author = {Guazzelli, Élisabeth and Morris, Jeffrey F.},
	year = {2011},
	doi = {10.1017/CBO9780511894671},
	file = {Snapshot:/Users/eunji/Zotero/storage/SKFW3U57/B8EB2B34C3D3893D7E22884710AA7E7A.html:text/html},
}

@article{smithies_integral_1959,
	title = {Integral equations and their applications to certain problems in mechanics, mathematical physics and technology. {By} {S}. {G}. {Mikhlin}. {Translated} from the {Russian} by {A}. {H}. {Armstrong}. {Pp}. xii, 338. 80s. 1957. ({Pergamon} {Press})},
	volume = {43},
	issn = {0025-5572, 2056-6328},
	url = {https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/integral-equations-and-their-applications-to-certain-problems-in-mechanics-mathematical-physics-and-technology-by-s-g-mikhlin-translated-from-the-russian-by-a-h-armstrong-pp-xii-338-80s-1957-pergamon-press/4790BC73CCD508CBE7A21A630536BE74},
	doi = {10.2307/3610248},
	abstract = {//static.cambridge.org/content/id/urn\%3Acambridge.org\%3Aid\%3Aarticle\%3AS0025557200040717/resource/name/firstPage-S0025557200040717a.jpg},
	language = {en},
	number = {344},
	urldate = {2021-05-15},
	journal = {The Mathematical Gazette},
	author = {Smithies, F.},
	month = may,
	year = {1959},
	note = {Publisher: Cambridge University Press},
	pages = {156--156},
	file = {Snapshot:/Users/eunji/Zotero/storage/WX7NXMF4/4790BC73CCD508CBE7A21A630536BE74.html:text/html},
}

@article{mrokowska_dynamics_2020,
	title = {Dynamics of thin disk settling in two-layered fluid with density transition},
	volume = {68},
	issn = {1895-7455},
	url = {https://doi.org/10.1007/s11600-020-00455-8},
	doi = {10.1007/s11600-020-00455-8},
	abstract = {Settling of solid particles in a stratified ambient fluid is a process widely encountered in geophysical flows. A set of experiments demonstrating the settling behaviour (the pattern of trajectory, variation of particle orientation, and settling velocity with depth) of thin disks descending through a nonlinear density transition was performed. The results showed complex hydrodynamic interactions between a particle and a liquid causing settling orientation instabilities and unsteady particle descent in low to moderate Reynolds number regime. Five phases of settling were observed: two phases with stable horizontal, one with stable vertical disk position, and two reorientation phases; moreover, two local minima of settling velocity were identified. It was demonstrated that thresholds for local minima and the first reorientation depend on the settling dynamics in an upper layer, stratification conditions, and disk geometry. The comparison of settling behaviour of thin disks varying in diameter revealed that settling dynamics is sensitive to particle geometry mainly in the upper part of density transition with a non-obvious result that the first minimum velocity is smaller for a disk with a larger diameter than for a disk with a smaller diameter. The analysis of settling trajectory showed that two reorientations are accompanied with a horizontal drift, which may be important in the context of interactions between particles settling in a group.},
	language = {en},
	number = {4},
	urldate = {2021-04-20},
	journal = {Acta Geophysica},
	author = {Mrokowska, Magdalena M.},
	month = aug,
	year = {2020},
	pages = {1145--1160},
	file = {Springer Full Text PDF:/Users/eunji/Zotero/storage/MK53YGBM/Mrokowska - 2020 - Dynamics of thin disk settling in two-layered flui.pdf:application/pdf},
}

@book{kress_linear_2014,
	address = {New York},
	edition = {3},
	series = {Applied {Mathematical} {Sciences}},
	title = {Linear {Integral} {Equations}},
	isbn = {978-1-4614-9592-5},
	url = {https://www.springer.com/gp/book/9781461495925},
	abstract = {This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methodsReviews of earlier editions:"This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution."(Math. Reviews, 2000)"This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)},
	language = {en},
	urldate = {2021-03-23},
	publisher = {Springer-Verlag},
	author = {Kress, Rainer},
	year = {2014},
	doi = {10.1007/978-1-4614-9593-2},
	file = {Snapshot:/Users/eunji/Zotero/storage/T8FNU2GB/9781461495925.html:text/html},
}

@book{greengard_rapid_1988,
	title = {The {Rapid} {Evaluation} of {Potential} {Fields} in {Particle} {Systems}},
	isbn = {978-0-262-07110-9},
	abstract = {"The Rapid Evaluation of Potential Fields in Particle Systems" presents a group of algorithms for the computation of the potential and force fields in large-scale systems of particles that are likely to revolutionize a whole class of computer applications in science and engineering.In many areas of scientific computing, from studying the evolution of galaxies, to simulating the behavior of plasmas and fluids, to modeling chemical systems, a numerical scheme is used to follow the trajectories of a collection of particles moving in accordance with Newton's second law of motion in a field generated by the whole ensemble. Extending the earlier work of Rokhlin, Greengard has developed general, numerically stable methods for evaluating all pairwise interactions in linear time, a great improvement over the quadratic time required by the naive approach, and significantly better than any other proposed alternative.The "Rokhlin-Greengard" algorithm promises to make previously prohibitive simulations feasible, with speedups of three to four orders of magnitude in a system of a million particles. Moreover, the algorithm is well-suited for vector and parallel machines, and should make full use of their capabilities. The author presents his work with great clarity, and demonstrates the superiority of his methods both by mathematical analysis and by the results of numerical experiments."1987 ACM Distinguished Dissertation"},
	language = {en},
	publisher = {MIT Press},
	author = {Greengard, Leslie},
	year = {1988},
	note = {Google-Books-ID: pXjke29Ptc8C},
}

@article{cheng_fast_1999,
	title = {A {Fast} {Adaptive} {Multipole} {Algorithm} in {Three} {Dimensions}},
	volume = {155},
	issn = {0021-9991},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999199963556},
	doi = {10.1006/jcph.1999.6355},
	abstract = {We present an adaptive fast multipole method for the Laplace equation in three dimensions. It uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost.},
	language = {en},
	number = {2},
	urldate = {2021-01-27},
	journal = {Journal of Computational Physics},
	author = {Cheng, H. and Greengard, L. and Rokhlin, V.},
	month = nov,
	year = {1999},
	keywords = {adaptive algorithms, fast multipole method, Laplace equation, translation operators},
	pages = {468--498},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/E4QMW5BF/Cheng et al. - 1999 - A Fast Adaptive Multipole Algorithm in Three Dimen.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/5TK9D765/S0021999199963556.html:text/html},
}

@article{salmon_fast_1994,
	title = {Fast {Parallel} {Tree} {Codes} for {Gravitational} and {Fluid} {Dynamical} {N}-{Body} {Problems}},
	volume = {8},
	issn = {1078-3482},
	url = {https://doi.org/10.1177/109434209400800205},
	doi = {10.1177/109434209400800205},
	language = {en},
	number = {2},
	urldate = {2021-01-24},
	journal = {The International Journal of Supercomputer Applications and High Performance Computing},
	author = {Salmon, John K. and Warren, Michael S.},
	month = jun,
	year = {1994},
	note = {Publisher: SAGE Publications},
	pages = {129--142},
	file = {SAGE PDF Full Text:/Users/eunji/Zotero/storage/TF7K33SJ/Salmon and Warren - 1994 - Fast Parallel Tree Codes for Gravitational and Flu.pdf:application/pdf},
}

@article{sangani_on_1996,
	title = {An {O}({N}) algorithm for {Stokes} and {Laplace} interactions of particles},
	volume = {8},
	issn = {1070-6631},
	url = {https://aip.scitation.org/doi/abs/10.1063/1.869003},
	doi = {10.1063/1.869003},
	number = {8},
	urldate = {2021-01-24},
	journal = {Physics of Fluids},
	author = {Sangani, Ashok S. and Mo, Guobiao},
	month = aug,
	year = {1996},
	note = {Publisher: American Institute of Physics},
	pages = {1990--2010},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/6VNCKMGG/Sangani and Mo - 1996 - An O(N) algorithm for Stokes and Laplace interacti.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/WY98QSSP/1.html:text/html},
}

@article{fu_fast_2000,
	title = {Fast solution method for three-dimensional {Stokesian} many-particle problems},
	volume = {16},
	copyright = {Copyright © 2000 John Wiley \& Sons, Ltd.},
	issn = {1099-0887},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-0887%28200002%2916%3A2%3C145%3A%3AAID-CNM323%3E3.0.CO%3B2-E},
	doi = {https://doi.org/10.1002/(SICI)1099-0887(200002)16:2<145::AID-CNM323>3.0.CO;2-E},
	abstract = {It is demonstrated that three-dimensional single- and double-layer Stokesian potentials can be computed using fast solution methods for the N-body electrostatics problem. This allows one to develop fast iterative solution methods for a broad class of boundary integral equations corresponding to three-dimensional Stokesian many-particle problems. Copyright © 2000 John Wiley \& Sons, Ltd.},
	language = {en},
	number = {2},
	urldate = {2021-01-24},
	journal = {Communications in Numerical Methods in Engineering},
	author = {Fu, Yuhong and Rodin, Gregory J.},
	year = {2000},
	% note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/\%28SICI\%291099-0887\%28200002\%2916\%3A2\%3C145\%3A\%3AAID-CNM323\%3E3.0.CO\%3B2-E},
	keywords = {fast multipole method, boundary integral equation, many-particle problems},
	pages = {145--149},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/B76AIZQI/Fu and Rodin - 2000 - Fast solution method for three-dimensional Stokesi.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/MNISBWDX/(SICI)1099-0887(200002)162145AID-CNM3233.0.html:text/html},
}

@article{mammoli_stokes_1999,
	title = {Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods},
	volume = {44},
	copyright = {Copyright © 1999 John Wiley \& Sons, Ltd.},
	issn = {1097-0207},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819990310%2944%3A7%3C897%3A%3AAID-NME530%3E3.0.CO%3B2-S},
	doi = {https://doi.org/10.1002/(SICI)1097-0207(19990310)44:7<897::AID-NME530>3.0.CO;2-S},
	abstract = {The multipole technique has recently received attention in the field of boundary element analysis as a means of reducing the order of data storage and calculation time requirements from O(N2) (iterative solvers) or O(N3) (gaussian elimination) to O(N log N) or O(N), where N is the number of nodes in the discretized system. Such a reduction in the growth of the calculation time and data storage is crucial in applications where N is large, such as when modelling the macroscopic behaviour of suspensions of particles. In such cases, a minimum of 1000 particles is needed to obtain statistically meaningful results, leading to systems with N of the order of 10 000 for the smallest problems. When only boundary velocities are known, the indirect boundary element formulation for Stokes flow results in Fredholm equations of the second kind, which generally produce a well-posed set of equations when discretized, a necessary requirement for iterative solution methods. The direct boundary element formulation, on the other hand, results in Fredholm equations of the first kind, which, upon discretization, produce ill-conditioned systems of equations. The model system here is a two-dimensional wide-gap couette viscometer, where particles are suspended in the fluid between the cylinders. This is a typical system that is efficiently modelled using boundary element method simulations. The multipolar technique is applied to both direct and indirect formulations. It is found that the indirect approach is sufficiently well-conditioned to allow the use of fast multipole methods. The direct approach results in severe ill-conditioning, to a point where application of the multipole method leads to non-convergence of the solution iteration. Copyright © 1999 John Wiley \& Sons, Ltd.},
	language = {en},
	number = {7},
	urldate = {2021-01-22},
	journal = {International Journal for Numerical Methods in Engineering},
	author = {Mammoli, A. A. and Ingber, M. S.},
	year = {1999},
	% note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/\%28SICI\%291097-0207\%2819990310\%2944\%3A7\%3C897\%3A\%3AAID-NME530\%3E3.0.CO\%3B2-S},
	keywords = {BEM, multiphase flow, multipole acceleration},
	pages = {897--917},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/5734LU7I/Mammoli and Ingber - 1999 - Stokes flow around cylinders in a bounded two-dime.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/2H47SHX9/(SICI)1097-0207(19990310)447897AID-NME5303.0.html:text/html},
}

@article{yan_kernel_2020,
	title = {Kernel {Aggregated} {Fast} {Multipole} {Method}: {Efficient} summation of {Laplace} and {Stokes} kernel functions},
	shorttitle = {Kernel {Aggregated} {Fast} {Multipole} {Method}},
	url = {http://arxiv.org/abs/2010.15155},
	abstract = {Many different simulation methods for Stokes flow problems involve a common computationally intense task---the summation of a kernel function over \$O(N{\textasciicircum}2)\$ pairs of points. One popular technique is the Kernel Independent Fast Multipole Method (KIFMM), which constructs a spatial adaptive octree and places a small number of equivalent multipole and local points around each octree box, and completes the kernel sum with \$O(N)\$ performance. However, the KIFMM cannot be used directly with nonlinear kernels, can be inefficient for complicated linear kernels, and in general is difficult to implement compared to less-efficient alternatives such as Ewald-type methods. Here we present the Kernel Aggregated Fast Multipole Method (KAFMM), which overcomes these drawbacks by allowing different kernel functions to be used for specific stages of octree traversal. In many cases a simpler linear kernel suffices during the most extensive stage of octree traversal, even for nonlinear kernel summation problems. The KAFMM thereby improves computational efficiency in general and also allows efficient evaluation of some nonlinear kernel functions such as the regularized Stokeslet. We have implemented our method as an open-source software library STKFMM with support for Laplace kernels, the Stokeslet, regularized Stokeslet, Rotne-Prager-Yamakawa (RPY) tensor, and the Stokes double-layer and traction operators. Open and periodic boundary conditions are supported for all kernels, and the no-slip wall boundary condition is supported for the Stokeslet and RPY tensor. The package is designed to be ready-to-use as well as being readily extensible to additional kernels. Massive parallelism is supported with mixed OpenMP and MPI.},
	urldate = {2021-01-21},
	journal = {arXiv:2010.15155 [physics]},
	author = {Yan, Wen and Blackwell, Robert},
	month = oct,
	year = {2020},
	note = {arXiv: 2010.15155},
	keywords = {Mathematics - Numerical Analysis, Physics - Computational Physics, Physics - Fluid Dynamics},
	file = {arXiv Fulltext PDF:/Users/eunji/Zotero/storage/VT2SV8N2/Yan and Blackwell - 2020 - Kernel Aggregated Fast Multipole Method Efficient.pdf:application/pdf;arXiv.org Snapshot:/Users/eunji/Zotero/storage/NZPGLU3K/2010.html:text/html},
}

@article{qu_fast_2017,
	title = {Fast multipole singular boundary method for {Stokes} flow problems},
	volume = {146},
	doi = {10.1016/j.matcom.2017.10.001},
	abstract = {This paper firstly employs the fast multipole method (FMM) to accelerate the singular boundary method (SBM) solution of the Stokes equation. We present a fast multipole singular boundary method (FMSBM) based on the combination of the SBM and the FMM. The proposed FMSBM scheme reduces CPU operations and memory requirements by one order of magnitude, namely O(N) (where N is the number of boundary nodes). Thus, the strategy overcomes costly expenses of the SBM due to its dense interpolation matrix while keeping its major merits being free of mesh, boundary-only discretization, and high accuracy in the solution of the Stokes equation. The performance of this scheme is tested to a few benchmark problems. Numerical results demonstrate its efficiency, accuracy and applicability. © 2017 International Association for Mathematics and Computers in Simulation (IMACS).},
	journal = {Mathematics and Computers in Simulation},
	author = {Qu, Wenzhen and Chen, Wen and Fu, Zhuo-Jia and Gu, Yan},
	month = oct,
	year = {2017},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/7E5QFWBJ/Qu et al. - 2017 - Fast multipole singular boundary method for Stokes.pdf:application/pdf},
}

@article{henson_global_2012,
	title = {Global patterns in efficiency of particulate organic carbon export and transfer to the deep ocean},
	volume = {26},
	copyright = {Copyright 2012 by the American Geophysical Union},
	issn = {1944-9224},
	url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2011GB004099},
	doi = {https://doi.org/10.1029/2011GB004099},
	abstract = {The ocean's biological carbon pump is a key component of the global carbon cycle. Only a small fraction of the carbon fixed by primary production is exported to the deep ocean, yet this flux sets to first order the efficiency with which carbon is sequestered out of further contact with the atmosphere on long time scales. Here we examine global patterns in particle export efficiency (PEeff), the proportion of primary production that is exported from the surface ocean, and transfer efficiency (Teff), the fraction of exported organic matter that reaches the deep ocean. Previous studies have found a positive correlation between Teff and deep ocean calcite fluxes recovered from sediment traps, implying that ballasting by calcium carbonate may play an important role in regulating Teff. An alternative explanation is that this correlation is not causative, as regions where the dominant biomineral phase is calcite tend to be subtropical systems, which are hypothesized to produce sinking aggregates highly resistant to degradation. We attempt to distinguish between these alternative hypotheses on the control of Teff by examining the relationship between Teff and biomineral phases exported from the upper ocean, rather than those collected in deep traps. Global scale estimates derived from satellite data show, in keeping with earlier studies, that PEeff is high at high latitudes and low at low latitudes, but that Teff is low at high latitudes and high at low latitudes. However, in contrast to the relationship observed for deep biomineral fluxes in previous studies, we find that Teff is strongly negatively correlated with opal export flux from the upper ocean, but uncorrelated with calcium carbonate export flux. We hypothesize that the underlying factor governing the spatial patterns observed in Teff is ecosystem function, specifically the degree of recycling occurring in the upper ocean, rather than the availability of calcium carbonate for ballasting.},
	language = {en},
	number = {1},
	urldate = {2021-01-20},
	journal = {Global Biogeochemical Cycles},
	author = {Henson, Stephanie A. and Sanders, Richard and Madsen, Esben},
	year = {2012},
	% note = {\_eprint: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011GB004099},
	keywords = {carbon export, global, POC flux, satellite data},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/2LFZBVRG/Henson et al. - 2012 - Global patterns in efficiency of particulate organ.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/Z85DPA8C/2011GB004099.html:text/html},
}

@book{kaye_random_2008,
	title = {A {Random} {Walk} {Through} {Fractal} {Dimensions}},
	isbn = {978-3-527-61598-8},
	abstract = {Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin},
	language = {en},
	publisher = {John Wiley \& Sons},
	author = {Kaye, Brian H.},
	month = jul,
	year = {2008},
	keywords = {Science / Chemistry / General, Technology \& Engineering / Materials Science / General},
}

@article{witten_diffusion-limited_1981,
	title = {Diffusion-{Limited} {Aggregation}, a {Kinetic} {Critical} {Phenomenon}},
	volume = {47},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.47.1400},
	doi = {10.1103/PhysRevLett.47.1400},
	abstract = {A model for random aggregates is studied by computer simulation. The model is applicable to a metal-particle aggregation process whose correlations have been measured previously. Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates. The radius of gyration of the model aggregates has power-law behavior. The model is a limit of a model of dendritic growth.},
	number = {19},
	urldate = {2021-01-20},
	journal = {Physical Review Letters},
	author = {Witten, T. A. and Sander, L. M.},
	month = nov,
	year = {1981},
	note = {Publisher: American Physical Society},
	pages = {1400--1403},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/9UYPWB69/PhysRevLett.47.html:text/html},
}

@book{olver_introduction_2014,
	series = {Undergraduate {Texts} in {Mathematics}},
	title = {Introduction to {Partial} {Differential} {Equations}},
	isbn = {978-3-319-02098-3},
	url = {https://www.springer.com/gp/book/9783319020983},
	abstract = {This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.},
	language = {en},
	urldate = {2021-01-19},
	publisher = {Springer International Publishing},
	author = {Olver, Peter J.},
	year = {2014},
	doi = {10.1007/978-3-319-02099-0},
	file = {Snapshot:/Users/eunji/Zotero/storage/SD2M4WHY/9783319020983.html:text/html},
}

@book{hoffman_numerical_2018,
	title = {Numerical {Methods} for {Engineers} and {Scientists}},
	isbn = {978-1-4822-7060-0},
	abstract = {Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."},
	language = {en},
	publisher = {CRC Press},
	author = {Hoffman, Joe D. and Frankel, Steven},
	month = oct,
	year = {2018},
	note = {Google-Books-ID: F5K3DwAAQBAJ},
	keywords = {Mathematics / Applied, Mathematics / Number Systems},
}

@book{leveque_numerical_1992,
	edition = {2},
	series = {Lectures in {Mathematics}. {ETH} {Zürich}},
	title = {Numerical {Methods} for {Conservation} {Laws}},
	isbn = {978-3-7643-2723-1},
	url = {https://www.springer.com/gp/book/9783764327231},
	abstract = {These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de­ veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un­ derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present­ ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.},
	language = {en},
	urldate = {2021-01-19},
	publisher = {Birkhäuser Basel},
	author = {LeVeque, Randall J.},
	year = {1992},
	doi = {10.1007/978-3-0348-8629-1},
	file = {Snapshot:/Users/eunji/Zotero/storage/PISQETJP/9783764327231.html:text/html},
}

@article{alldredge_situ_1988,
	title = {In situ settling behavior of marine snow1},
	volume = {33},
	copyright = {© 1988, by the Association for the Sciences of Limnology and Oceanography, Inc.},
	issn = {1939-5590},
	url = {https://aslopubs.onlinelibrary.wiley.com/doi/abs/10.4319/lo.1988.33.3.0339},
	doi = {https://doi.org/10.4319/lo.1988.33.3.0339},
	abstract = {The settling velocities of undisturbed macroscopic aggregates known as marine snow were measured with SCUBA in surface waters off southern California and analyzed as a function of aggregate size, mass, and density. The mean settling velocity was 74±39 m d−1 for aggregates ranging from 2.4 to 75 mm in maximum length. Sinking rates in the field varied exponentially with aggregate size and dry weight and were consistently up to four times slower than rates measured in the laboratory. The excess densities of the 80 aggregates examined were calculated from volume and dry weight and ranged over four orders of magnitude with a median of 1.4 × 10−4 g cm−3. Aggregates of marine snow sank more slowly than predicted for either solid or porous spheres of equivalent volume and density, although their velocities were within the range expected for equivalent sinking prolate ellipsoids. No relationships between settling velocity and either excess density or particle shape were found. Drag coefficients of marine snow were also higher than predicted by theory for spheres of equivalent volume and density. These deviations from theoretical expectations may be partially explained by errors in the estimation of the excess densities of aggregates. Variability in the densities of the heterogeneous primary particles comprising marine snow (fecal pellets, clay-mineral particles, phytoplankton, molts, etc.) and the potential for buoyancy regulation by individual phytoplankton cells inhabiting aggregates make determination of excess density especially problematic.},
	language = {en},
	number = {3},
	urldate = {2021-01-19},
	journal = {Limnology and Oceanography},
	author = {Alldredge, Alice L. and Gotschalk, Chris},
	year = {1988},
	% note = {\_eprint: https://aslopubs.onlinelibrary.wiley.com/doi/pdf/10.4319/lo.1988.33.3.0339},
	pages = {339--351},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/M3JSGA3B/Alldredge and Gotschalk - 1988 - In situ settling behavior of marine snow1.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/UFP9NCAA/lo.1988.33.3.html:text/html},
}

@article{burd_particle_2009,
	title = {Particle {Aggregation}},
	volume = {1},
	issn = {1941-1405},
	url = {https://www.annualreviews.org/doi/10.1146/annurev.marine.010908.163904},
	doi = {10.1146/annurev.marine.010908.163904},
	abstract = {A basic problem in marine biogeochemistry is understanding material and elemental distributions and fluxes in the oceans, and a key part of this problem is understanding the processes that affect particulate material in the ocean. Aggregation of particulate material is a primary process because it alters the transport properties of particulate material and provides a mechanism for transferring material from the dissolved into the particulate pools. Aggregation theory not only provides a framework for understanding these processes, but it also provides a means for making predictions and has been successfully used to predict maximum particle concentrations in the oceans and the fate of diatom blooms (including those from iron fertilization), the size spectra of particles in the oceans, and the size distributions of trace metals. Here we review the basic theory involved, summarize recent developments, and explore unresolved issues.},
	number = {1},
	urldate = {2021-01-19},
	journal = {Annual Review of Marine Science},
	author = {Burd, Adrian B. and Jackson, George A.},
	month = jan,
	year = {2009},
	note = {Publisher: Annual Reviews},
	pages = {65--90},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/A7Q4KRMV/Burd and Jackson - 2009 - Particle Aggregation.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/HU7464T2/annurev.marine.010908.html:text/html},
}

@book{liu_fast_2009,
	address = {Cambridge},
	title = {Fast {Multipole} {Boundary} {Element} {Method}: {Theory} and {Applications} in {Engineering}},
	isbn = {978-0-521-11659-6},
	shorttitle = {Fast {Multipole} {Boundary} {Element} {Method}},
	url = {https://www.cambridge.org/core/books/fast-multipole-boundary-element-method/E522EB3361A4E033DCBD323F14F67ECE},
	abstract = {The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a single source.},
	urldate = {2021-01-19},
	publisher = {Cambridge University Press},
	author = {Liu, Yijun},
	year = {2009},
	doi = {10.1017/CBO9780511605345},
	file = {Liu - 2009 - Fast Multipole Boundary Element Method Theory and.pdf:/Users/eunji/Zotero/storage/QJQWUY9W/Liu - 2009 - Fast Multipole Boundary Element Method Theory and.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/RXQFYBKD/E522EB3361A4E033DCBD323F14F67ECE.html:text/html},
}

@article{greengard_fast_1987,
	title = {A fast algorithm for particle simulations},
	volume = {73},
	issn = {0021-9991},
	url = {http://www.sciencedirect.com/science/article/pii/0021999187901409},
	doi = {10.1016/0021-9991(87)90140-9},
	abstract = {An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature. For a system of N particles, an amount of work of the order O(N2) has traditionally been required to evaluate all pairwise interactions, unless some approximation or truncation method is used. The algorithm of the present paper requires an amount of work proportional to N to evaluate all interactions to within roundoff error, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.},
	language = {en},
	number = {2},
	urldate = {2021-01-19},
	journal = {Journal of Computational Physics},
	author = {Greengard, L and Rokhlin, V},
	month = dec,
	year = {1987},
	pages = {325--348},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/QPJ3U3W8/Greengard and Rokhlin - 1987 - A fast algorithm for particle simulations.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/BZSPSPF3/0021999187901409.html:text/html},
}

@article{mcnown_effects_1950,
	title = {Effects of particle shape on settling velocity at low {Reynolds} numbers},
	volume = {31},
	copyright = {©1950. American Geophysical Union. All Rights Reserved.},
	issn = {2324-9250},
	url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/TR031i001p00074},
	doi = {https://doi.org/10.1029/TR031i001p00074},
	abstract = {Extensive theoretical and experimental studies have been conducted at the Iowa Institute of Hydraulic Research in an investigation of the effect of shape on the settling velocity of particles. A number of representative axisymmetric shapes were used in the experiments, the Reynolds numbers of the particle motion ranging from 10−4 to 10+1. Stability of orientation was also investigated. Analytical results were obtained for the motion of ellipsoids within the Stokes range by solving Oberbeck's integral equation. The ratio of the principal-axis lengths was found to be by far the most significant of the various shape factors which have been proposed. In fact, the settling velocities of particles over a wide range of shape can be estimated within ten per cent from the theoretical results for ellipsoids.},
	language = {en},
	number = {1},
	urldate = {2021-01-13},
	journal = {Eos, Transactions American Geophysical Union},
	author = {McNown, John S. and Malaika, Jamil},
	year = {1950},
	% note = {\_eprint: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/TR031i001p00074},
	pages = {74--82},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/IM2V4N44/McNown and Malaika - 1950 - Effects of particle shape on settling velocity at .pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/YH35QSSC/TR031i001p00074.html:text/html},
}

@article{johnson_drag_1987,
	title = {Drag on non-spherical, orthotropic aerosol particles},
	volume = {18},
	issn = {0021-8502},
	url = {http://www.sciencedirect.com/science/article/pii/0021850287900139},
	doi = {10.1016/0021-8502(87)90013-9},
	abstract = {Inhaled particles have been implicated in many forms of respiratory disease. Mathematical lung deposition models have been developed for spheres and fibers, but not for non-spherical, noncylindrical particles because theory and experimental data have been unavailable. To satisfy this need, non-spherical, orthotropic particles settling in air were modeled under dynamically similar conditions using aluminum prisms settling in viscous oil. Twenty-five rectangular prisms, each with a different length: width: thickness ratio, were settled in each of their three primary orientations and the resulting drag forces determined. Linear regression using predictors related to prism geometry and orientation resulted in an empirical drag force equation. Equation drag predictions are in excellent agreement with published data for rectangular prisms and other orthotropic objects including cylinders, ellipsoids, and double-conicals. The equation was validated by settling a quasi-monodisperse aerosol of tungstic acid platelets in a Stöber spiral centrifuge, and comparing predicted with observed aerodynamic behavior. Using these results, lung deposition models for flakes and other non-spherical particles are now possible.},
	language = {en},
	number = {1},
	urldate = {2021-01-13},
	journal = {Journal of Aerosol Science},
	author = {Johnson, David L. and Leith, David and Reist, Parker C.},
	month = feb,
	year = {1987},
	pages = {87--97},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/ZJQQU7CW/Johnson et al. - 1987 - Drag on non-spherical, orthotropic aerosol particl.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/IUQMJZFH/0021850287900139.html:text/html},
}

@book{press_numerical_2007,
	title = {Numerical {Recipes} 3rd {Edition}: {The} {Art} of {Scientific} {Computing}},
	isbn = {978-0-521-88068-8},
	shorttitle = {Numerical {Recipes} 3rd {Edition}},
	abstract = {Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit www.nr.com or www.cambridge.org/us/numericalrecipes for more details. More information concerning licenses is available at: www.nr.com/licenses New key features:  2 new chapters, 25 new sections, 25\% longer than Second Edition Thorough upgrades throughout the text Over 100 completely new routines and upgrades of many more. New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector MachinesNew Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions An expanded treatment of ODEs with completely new routines  Plus comprehensive coverage of  linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory},
	language = {en},
	publisher = {Cambridge University Press},
	author = {Press, William H.},
	month = sep,
	year = {2007},
	note = {Google-Books-ID: 1aAOdzK3FegC},
	keywords = {Mathematics / Applied, Computers / Mathematical \& Statistical Software, Mathematics / General, Mathematics / Numerical Analysis},
}

@book{griffiths_numerical_2010,
	title = {Numerical {Methods} for {Ordinary} {Differential} {Equations}: {Initial} {Value} {Problems}},
	isbn = {978-0-85729-148-6},
	shorttitle = {Numerical {Methods} for {Ordinary} {Differential} {Equations}},
	abstract = {Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com},
	language = {en},
	publisher = {Springer Science \& Business Media},
	author = {Griffiths, David F. and Higham, Desmond J.},
	month = nov,
	year = {2010},
	note = {Google-Books-ID: HrrZop\_3bacC},
	keywords = {Mathematics / Number Systems, Mathematics / Numerical Analysis, Computers / Programming / Algorithms, Mathematics / Algebra / General, Mathematics / Discrete Mathematics},
}

@article{richard_slow_2005,
	title = {Slow relaxation and compaction of granular systems},
	volume = {4},
	copyright = {2005 Springer Nature Limited},
	issn = {1476-4660},
	url = {https://www.nature.com/articles/nmat1300},
	doi = {10.1038/nmat1300},
	abstract = {Granular materials are of substantial importance in many industrial and natural processes, yet their complex behaviours, ranging from mechanical properties of static packing to their dynamics, rheology and instabilities, are still poorly understood. Here we focus on the dynamics of compaction and its 'jamming' phenomena, outlining recent statistical mechanics approaches to describe it and their deep correspondence with thermal systems such as glass formers. In fact, granular media are often presented as ideal systems for studying complex relaxation towards equilibrium. Granular compaction is defined as an increase of the bulk density of a granular medium submitted to mechanical perturbation. This phenomenon, relevant in many industrial processes and widely studied by the soil mechanics community, is simple enough to be fully investigated and yet reveals all the complex nature of granular dynamics, attracting considerable attention in a broad range of disciplines ranging from chemical to physical sciences.},
	language = {en},
	number = {2},
	urldate = {2023-07-13},
	journal = {Nature Materials},
	author = {Richard, Patrick and Nicodemi, Mario and Delannay, Renaud and Ribière, Philippe and Bideau, Daniel},
	month = feb,
	year = {2005},
	note = {Number: 2
Publisher: Nature Publishing Group},
	keywords = {Biomaterials, Condensed Matter Physics, general, Materials Science, Nanotechnology, Optical and Electronic Materials},
	pages = {121--128},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/GUH3T4IN/Richard et al. - 2005 - Slow relaxation and compaction of granular systems.pdf:application/pdf},
}

@article{xie_summary_2021,
	title = {Summary and {Trend} {Analysis} of {Research} {Progress} on {Granular} {Slope} {Geological} {Hazards}},
	volume = {820},
	issn = {1755-1315},
	url = {https://dx.doi.org/10.1088/1755-1315/820/1/012022},
	doi = {10.1088/1755-1315/820/1/012022},
	abstract = {There are a large number of granular slope mixture geological disasters in the alpine mountainous areas in western China. Their structural characteristics are significantly different from the general slopes. They have the characteristics of poor self-stability, high suddenness and strong recurrence. With the continuous development of the western region of the country, such geological disasters have received close attention from scholars at home and abroad. This article first summarized and analyzed the basic characteristics of the typical domestic granular mixtures slope accidents, and understood the basic characteristics of disaster. Then the domestic and foreign research progress from the aspects of governance measures were summarized. Finally, based on the summary of typical granular mixtures slope disasters and research status, the existing problems in the current research were analyzed, and the key points and difficulties of future research had prospected. The research results have important theoretical significance for the treatment of granular slope.},
	language = {en},
	number = {1},
	urldate = {2023-07-13},
	journal = {IOP Conference Series: Earth and Environmental Science},
	author = {Xie, Liangfu and Wang, Bo and Zhu, Qingyang and Cui, Jianbin},
	month = jul,
	year = {2021},
	note = {Publisher: IOP Publishing},
	pages = {012022},
	file = {IOP Full Text PDF:/Users/eunji/Zotero/storage/UXIBUP5V/Xie et al. - 2021 - Summary and Trend Analysis of Research Progress on.pdf:application/pdf},
}

@article{senetakis_inter-particle_2013,
	title = {The inter-particle coefficient of friction at the contacts of {Leighton} {Buzzard} sand quartz minerals},
	volume = {53},
	issn = {0038-0806},
	url = {https://www.sciencedirect.com/science/article/pii/S0038080613000942},
	doi = {10.1016/j.sandf.2013.08.012},
	abstract = {A series of micro-mechanical tests was carried out in order to investigate the inter-particle coefficient of friction at the contacts of quartz minerals of Leighton Buzzard sand. For this purpose, a custom-built inter-particle loading apparatus was designed and constructed, the main features of which are described briefly in this paper. This apparatus is capable of performing shearing tests at the contacts of soil minerals of a particle–particle type in the range of very small displacements, from less than 1μm to about 300μm, and very small normal loads, between about less than 1N and 15N. The laboratory data showed that the effects of the normal force and the sliding velocity on the coefficient of dynamic friction are not significant, while dry and saturated surfaces had similar frictional characteristics. The steady state sliding was mobilized within a range of 0.5–3.0μm of horizontal displacement, and the coefficient of static friction was very similar to the corresponding coefficient during constant shearing. Repeating the inter-particle shearing tests on the same particles and following the same shearing track indicated a small reduction in the inter-particle coefficient of friction after the first shearing, which is possibly related to plastic deformation and damage to the asperities.},
	language = {en},
	number = {5},
	urldate = {2023-07-12},
	journal = {Soils and Foundations},
	author = {Senetakis, Kostas and Coop, Matthew R. and Todisco, M. Cristina},
	month = oct,
	year = {2013},
	pages = {746--755},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/HHHVKBML/Senetakis et al. - 2013 - The inter-particle coefficient of friction at the .pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/YXYZEZQ6/S0038080613000942.html:text/html},
}

@article{rajagopal_implicit_2006,
	title = {On implicit constitutive theories for fluids},
	volume = {550},
	issn = {1469-7645, 0022-1120},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-implicit-constitutive-theories-for-fluids/C9508E4F73761A1779F7F8F35FA88DA8},
	doi = {10.1017/S0022112005008025},
	abstract = {We consider generalizations of fluid models wherein the fluid is assumed to be incompressible, but with the viscosity depending on the pressure. We show that a natural setting for the development of such models is a class of implicit constitutive relations, which, in addition to the fluid model described here, provides a means for developing other complex models for viscoelastic fluids which cannot be set within the ambit of classical explicit constitutive relations for the stress in terms of the histories of appropriate kinematical variables.},
	language = {en},
	urldate = {2023-07-12},
	journal = {Journal of Fluid Mechanics},
	author = {Rajagopal, K. R.},
	month = mar,
	year = {2006},
	note = {Publisher: Cambridge University Press},
	pages = {243--249},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/ZECKPAV7/Rajagopal - 2006 - On implicit constitutive theories for fluids.pdf:application/pdf},
}

@article{almgren_conservative_1998,
	title = {A {Conservative} {Adaptive} {Projection} {Method} for the {Variable} {Density} {Incompressible} {Navier}–{Stokes} {Equations}},
	volume = {142},
	issn = {0021-9991},
	url = {https://www.sciencedirect.com/science/article/pii/S0021999198958909},
	doi = {10.1006/jcph.1998.5890},
	abstract = {In this paper we present a method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids. The method is based on a projection formulation in which we first solve advection–diffusion equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the first step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high Reynolds number flow. Density and other scalars are advected in such a way as to maintain conservation, if appropriate, and free-stream preservation. Our approach to adaptive refinement uses a nested hierarchy of logically-rectangular girds with simultaneous refinement of the girds in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithms's accuracy and convergence properties, and illustrate the behavior of the method. An additional example demonstrates the performance of the method on a more realistic problem, namely, a three-dimensional variable density shear layer.},
	language = {en},
	number = {1},
	urldate = {2023-07-11},
	journal = {Journal of Computational Physics},
	author = {Almgren, Ann S. and Bell, John B. and Colella, Phillip and Howell, Louis H. and Welcome, Michael L.},
	month = may,
	year = {1998},
	pages = {1--46},
	file = {Full Text:/Users/eunji/Zotero/storage/VPP2C9I3/Almgren et al. - 1998 - A Conservative Adaptive Projection Method for the .pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/R6KLJ2W5/S0021999198958909.html:text/html},
}

@article{papanastasiou_flows_1987,
	title = {Flows of {Materials} with {Yield}},
	volume = {31},
	issn = {0148-6055},
	url = {https://doi.org/10.1122/1.549926},
	doi = {10.1122/1.549926},
	abstract = {Steady, two‐dimensional flows of Bingham fluids are analyzed by means of a modified constitutive relation that applies everywhere in the flow field, in both yielded and practically unyielded regions. The conservation equations and the constitutive relation are solved simultaneously by Galerkin finite element and Newton iteration. This combination eliminates the necessity for tracking yield surfaces in the flow field. The analysis is applied to a one‐dimensional channel flow, a two‐dimensional boundary layer flow, and a two‐dimensional extrusion flow. The finite element predictions compare well with available analytic solutions for limiting cases.},
	number = {5},
	urldate = {2023-07-10},
	journal = {Journal of Rheology},
	author = {Papanastasiou, Tasos C.},
	month = jul,
	year = {1987},
	pages = {385--404},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/WIUYHN3C/Papanastasiou - 1987 - Flows of Materials with Yield.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/CD3AHRMU/Flows-of-Materials-with-Yield.html:text/html},
}

@book{bingham_investigation_1917,
	title = {An {Investigation} of the {Laws} of {Plastic} {Flow}},
	language = {en},
	publisher = {U.S. Government Printing Office},
	author = {Bingham, Eugene Cook},
	year = {1917},
	note = {Google-Books-ID: 0EhpNVCVShUC},
}

@article{herschel_konsistenzmessungen_1926,
	title = {Konsistenzmessungen von {Gummi}-{Benzollösungen}},
	volume = {39},
	issn = {1435-1536},
	url = {https://doi.org/10.1007/BF01432034},
	doi = {10.1007/BF01432034},
	abstract = {1.Von den Gleichungen, die die Strömung durch eine Kapillarröhre ausdrücken, ist\$\${\textbackslash}frac\{\{d{\textasciicircum}4 (P - k){\textasciicircum}n \}\}\{\{Lq\}\} = 1\$\$die für Lösungen von Rohgummi in Benzol bis zu einer Konzentration von 1,2 Proz. am besten anwendbare.2.Die Methode der Konsistenzbestimmung durch Benutzung dieser Gleichung hat den Vorteil, daß sie verwendbare Werte für alle praktischen Strömungsgeschwindigkeiten liefert und daß sie die Notwendigkeit, sehr hohe Drucke anzuwenden, vermeidet.3.Die Vermeidung der hohen Drucke gestattet die Verwendung einer einfacheren Versuchsanordnung und vermindert den Fehler, der durch die Unsicherheit in der Anwendung der kinetischen Energiekorrektion verursacht wird. Es würde dies also möglich machen, das Ostwald-Viskosimeter zu benutzen bei mäßigen äußeren Drucken, ohne Gefahr zu laufen, am Ende einer Messung Luft durch die Kapillare zu blasen.4.Bei der Benutzung des logarithmischen Strömung-Druckdiagramms können genauere Uebereinstimmungen für Kapillaren verschiedener Dimensionen erhalten werden als bei Bestimmung von Scherungsmodul, Steifigkeit oder Beweglichkeit.5.Die Materialkonstanten n und I werden aus der logarithmischen Kurve erhalten und nehmen beide mit der Konzentration zu. Verglichen mit Scherungsmodul und Bewegliċhkeit haben diese beiden Konstanten den Vorteil, daß sie beide die Strömung in demselben Sinne beeinflussen, also größere Plastizität eines Stoffes größere Werte für n und I bedingen würde.6.K verschwindet bei großen Kapillaren und geringen Konzentrationen oder ist zu klein, um ermittelt zu werden. Wenn K jedoch bestimmbar ist, wächst sein Wert mit Abnahme des Kapillarendurchmessers. K selbst ist keine Materialkonstante, aber weitere Untersuchungen sollen zeigen, daß aus ihm eine dritte Konstante berechnet werden kann.},
	language = {de},
	number = {4},
	urldate = {2023-07-10},
	journal = {Kolloid-Zeitschrift},
	author = {Herschel, Winslow H. and Bulkley, Ronald},
	month = aug,
	year = {1926},
	pages = {291--300},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/5DKIE6BV/Herschel and Bulkley - 1926 - Konsistenzmessungen von Gummi-Benzollösungen.pdf:application/pdf},
}

@book{barnes_introduction_1989,
	title = {An {Introduction} to {Rheology}},
	isbn = {978-0-444-87140-4},
	abstract = {Rheology is, by common consent, a difficult subject and some of the theoretical components are often viewed as being of prohibitive complexity by scientists without a strong mathematical background. There are also the difficulties inherent in any multidisciplinary science like rheology for those with a specific training. Therefore, newcomers to the field are sometimes discouraged, and for them the existing texts on the subject - some of which are outstanding - are of limited assistance because of their depth of detail and highly mathematical nature.This book introduces the subject of rheology in terms understandable to non-experts and describes the application of rheological principles to many industrial products and processes. It provides a simple but authoritative guide which shows clearly how mathematics, physics and chemistry have contributed to the development of rheology. The generic features of all liquid-like materials are summarised, i.e. viscosity, linear viscoelasticity, normal stresses and extensional viscosity. Particular systems are then discussed, i.e. polymeric liquids and suspensions. The final chapter gives an outline of the theoretical advances which have been made. Consistent notation and nomenclature have been used throughout the book, and the key textbooks and publications which will enable the reader to follow up particular topics are listed.},
	language = {en},
	publisher = {Elsevier},
	author = {Barnes, Howard A. and Hutton, John Fletcher and Walters, K.},
	month = jun,
	year = {1989},
	note = {Google-Books-ID: B1e0uxFg4oYC},
	keywords = {Science / Mechanics / Fluids},
}

@book{singh_introduction_2013,
	title = {Introduction to {Food} {Engineering}},
	isbn = {978-0-12-401675-0},
	abstract = {Long recognized as the bestselling textbook for teaching food engineering to food science students, this 5e transitions with today’s students from traditional textbook learning to integrated presentation of the key concepts of food engineering. Using carefully selected examples, Singh and Heldman demonstrate the relationship of engineering to the chemistry, microbiology, nutrition and processing of foods in a uniquely practical blend. This approach facilitates comprehensive learning that has proven valuable beyond the classroom as a lifetime professional reference.  Communicates key concepts using audio, video, and animations Integrates interactive tools to aid in understanding complex charts and graphs Features multimedia guide to setting up Excel spreadsheets and working with formulae Demonstrates key processes and engineering in practice through videos Shows the relationship of engineering to the chemistry, microbiology, nutrition and processing of foods via carefully selected examples Presents a practical, unique and challenging blend of principles and applications for comprehensive learning Ideal for classroom use, valuable as a lifetime professional reference},
	language = {en},
	publisher = {Academic Press},
	author = {Singh, R. Paul and Heldman, Dennis R.},
	month = jun,
	year = {2013},
	keywords = {Technology \& Engineering / Food Science / General},
}

@article{nguyen_measuring_1992,
	title = {Measuring the {Flow} {Properties} of {Yield} {Stress} {Fluids}},
	volume = {24},
	url = {https://doi.org/10.1146/annurev.fl.24.010192.000403},
	doi = {10.1146/annurev.fl.24.010192.000403},
	number = {1},
	urldate = {2023-07-06},
	journal = {Annual Review of Fluid Mechanics},
	author = {Nguyen, Q D and Boger, D V},
	year = {1992},
	% note = {\_eprint: https://doi.org/10.1146/annurev.fl.24.010192.000403},
	pages = {47--88},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/PCLGH6AT/Nguyen and Boger - 1992 - Measuring the Flow Properties of Yield Stress Flui.pdf:application/pdf},
}

@article{karrila_integral_1989,
	title = {Integral {Equations} of the {Second} {Kind} for {Stokes} {Flow}: {Direct} {Solution} for {Physical} {Variables} and {Removal} of {Inherent} {Accuracy} {Limitations}},
	volume = {82},
	issn = {0098-6445},
	shorttitle = {Integral {Equations} of the {Second} {Kind} for {Stokes} {Flow}},
	url = {https://doi.org/10.1080/00986448908940638},
	doi = {10.1080/00986448908940638},
	abstract = {Boundary integral methods offer the most attractive combination of generality and computational efficiency for a wide class of particulate Stokes flow problems. Integral equations of the first kind have been numerically applied for more than a decade, whereas those of the second kind are numerically better behaved but involve abstract nonphysical density distributions and have not gained much popularity in applications. We show how the latter may be used for the direct solution of mobility problems, and how the surface tractions corresponding to rigid body motion of a particle may be easily found, thus removing the major disadvantages of the second kind formulations. For the numerical examples we also show how Fourier analysis may be applied to non-axisymmetric problems with axisymmetric boundaries to yield one-dimensional Fredholm integral equations of the second kind. As an application we solve the resistance problem with a numerically efficient quadrature collocation method that avoids the complications of element methods and difficulties with the integrations near the kernel singularities.},
	number = {1},
	urldate = {2023-04-28},
	journal = {Chemical Engineering Communications},
	author = {Karrila, Seppo J. and Kim, Sangtae},
	month = aug,
	year = {1989},
	% note = {Publisher: Taylor \& Francis \_eprint: https://doi.org/10.1080/00986448908940638},
	keywords = {Accuracy Limitations, Equations, Integral, Physical variables, Stokes flow},
	pages = {123--161},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/GPMJNP8U/KARRILA and KIM - 1989 - Integral Equations of the Second Kind for Stokes F.pdf:application/pdf},
}

@incollection{coleman_special_1966,
	address = {Berlin, Heidelberg},
	series = {Springer {Tracts} in {Natural} {Philosophy}},
	title = {Special {Viscometric} {Flows}},
	isbn = {978-3-642-88655-3},
	url = {https://doi.org/10.1007/978-3-642-88655-3_4},
	abstract = {If the velocity field has the form14.1\$\$\{\{v\}{\textasciicircum}\{{\textbackslash}left{\textbackslash}langle x {\textbackslash}right{\textbackslash}rangle \}\}=0,{\textbackslash}text\{ \}\{\{v\}{\textasciicircum}\{{\textbackslash}left{\textbackslash}langle y {\textbackslash}right{\textbackslash}rangle \}\}=v{\textbackslash}left( x {\textbackslash}right),{\textbackslash}text\{ \}\{\{v\}{\textasciicircum}\{{\textbackslash}left{\textbackslash}langle x {\textbackslash}right{\textbackslash}rangle \}\}=0\$\$in a Cartesian coordinate system x, y, z, then we say that the motion is a steady shearing flow. Clearly, such a flow is a curvilineal flow with	\$\$u{\textbackslash}left( \{\{x\}{\textasciicircum}\{1\}\} {\textbackslash}right)=v{\textbackslash}left( x {\textbackslash}right),{\textbackslash}text\{ \}w{\textbackslash}left( \{\{x\}{\textasciicircum}\{1\}\} {\textbackslash}right)=0,{\textbackslash}text\{ \}\{\{e\}\_\{1\}\}{\textbackslash}equiv \{\{e\}\_\{2\}\}{\textbackslash}equiv \{\{e\}\_\{3\}\}{\textbackslash}equiv 1.\$\$Hence, by (13.4), the flow is a viscometric flow with a rate of shear x given by14.2\$\$x = v'{\textbackslash}left( x {\textbackslash}right) = {\textbackslash}frac\{\{dv{\textbackslash}left( x {\textbackslash}right)\}\}\{\{dx\}\}.\$\$The basis b{\textless}i{\textgreater} is now just the constant basis, e{\textless}x{\textgreater}, e{\textless}y{\textgreater}, e{\textless}z{\textgreater}, of unit vectors along the coordinate axis.},
	language = {en},
	urldate = {2023-06-27},
	booktitle = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}: {Theory} and {Experiment}},
	publisher = {Springer},
	author = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	editor = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	year = {1966},
	doi = {10.1007/978-3-642-88655-3_4},
	keywords = {Angular Velocity, Couette Flow, Helical Flow, Poiseuille Flow, Stress Function},
	pages = {34--55},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/67L6R3KR/Coleman et al. - 1966 - Special Viscometric Flows.pdf:application/pdf},
}

@incollection{coleman_experimental_1966,
	address = {Berlin, Heidelberg},
	series = {Springer {Tracts} in {Natural} {Philosophy}},
	title = {Experimental {Methods} and {Results}},
	isbn = {978-3-642-88655-3},
	url = {https://doi.org/10.1007/978-3-642-88655-3_5},
	abstract = {We saw in § 12 that three material functions, η, σ1, σ2, determine the behavior of an incompressible simple fluid in viscometric flows. In the previous chapter these material functions were related to measurable quantities such as velocities, volume discharges per unit time, angular velocities, applied forces and torques, differences of normal thrusts, etc. Without attempting an exhaustive summary, we here discuss practical methods of determining η, σ1, σ2.},
	language = {en},
	urldate = {2023-06-27},
	booktitle = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}: {Theory} and {Experiment}},
	publisher = {Springer},
	author = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	editor = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	year = {1966},
	doi = {10.1007/978-3-642-88655-3_5},
	keywords = {Angular Velocity, Couette Flow, Poiseuille Flow, Coaxial Cylinder, Ethylene Oxide},
	pages = {56--83},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/JX66S87K/Coleman et al. - 1966 - Experimental Methods and Results.pdf:application/pdf},
}

@book{coleman_viscometric_1966,
	address = {Berlin, Heidelberg},
	series = {Springer {Tracts} in {Natural} {Philosophy}},
	title = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}: {Theory} and {Experiment}},
	volume = {5},
	isbn = {978-3-642-88657-7 978-3-642-88655-3},
	shorttitle = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}},
	url = {http://link.springer.com/10.1007/978-3-642-88655-3},
	language = {en},
	urldate = {2023-06-27},
	publisher = {Springer},
	author = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	editor = {Truesdell, C. and Collatz, L. and Fichera, G. and Germain, P. and Keller, J. and Seeger, A.},
	year = {1966},
	doi = {10.1007/978-3-642-88655-3},
	keywords = {dynamics, flow, Flows, Flows of Non-Newtonian Fluids, material, Viskosität, Viskositätsmessung},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/4LBBYPLR/Coleman et al. - 1966 - Viscometric Flows of Non-Newtonian Fluids Theory .pdf:application/pdf},
}

@incollection{coleman_theory_1966,
	address = {Berlin, Heidelberg},
	series = {Springer {Tracts} in {Natural} {Philosophy}},
	title = {Theory of {Incompressible} {Simple} {Fluids}},
	isbn = {978-3-642-88655-3},
	url = {https://doi.org/10.1007/978-3-642-88655-3_2},
	abstract = {The mechanics of continuous media is concerned with the motion and deformation of bodies. A body consists of material points X, which in the course of a motion change their position in space. Let x be the position in Euclidean space ﻉ of the material point X at time t, which we interpret as the present time. Suppose that at time τ, say τ ≤ t, this same material point X occupied the position ξ in ﻉ. For the dependence of ξ on x, t,and τ, we write4.1\$\${\textbackslash}xi =\{\{{\textbackslash}chi \}\_\{t\}\}(x,{\textbackslash}tau ). \$\$},
	language = {en},
	urldate = {2023-06-27},
	booktitle = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}: {Theory} and {Experiment}},
	publisher = {Springer},
	author = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	editor = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	year = {1966},
	doi = {10.1007/978-3-642-88655-3_2},
	keywords = {Constitutive Equation, Contact Force, Material Objectivity, Material Point, Stress Tensor},
	pages = {10--20},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/SLWW4Y6J/Coleman et al. - 1966 - Theory of Incompressible Simple Fluids.pdf:application/pdf},
}

@incollection{coleman_general_1966,
	address = {Berlin, Heidelberg},
	series = {Springer {Tracts} in {Natural} {Philosophy}},
	title = {General {Theory} of {Viscometric} {Flows}},
	isbn = {978-3-642-88655-3},
	url = {https://doi.org/10.1007/978-3-642-88655-3_3},
	abstract = {A motion is called simple shearing flow if in some Cartesian coordinate system x, y, z the components of the velocity field v = v(x,t) have the form (9.1)\$\${\textbackslash}upsilon {\textasciicircum}\{{\textbackslash}left{\textbackslash}langle x {\textbackslash}right{\textbackslash}rangle \}  = 0,\{{\textbackslash}text\{ \}\}{\textbackslash}upsilon {\textasciicircum}\{{\textbackslash}left{\textbackslash}langle y {\textbackslash}right{\textbackslash}rangle \}  = xx,{\textbackslash},\{{\textbackslash}text\{ \}\}{\textbackslash}upsilon {\textasciicircum}\{{\textbackslash}left{\textbackslash}langle z {\textbackslash}right{\textbackslash}rangle \}  = 0,\$\$where ϰ is a constant called the rate of shear.},
	language = {en},
	urldate = {2023-06-27},
	booktitle = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}: {Theory} and {Experiment}},
	publisher = {Springer},
	author = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	editor = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	year = {1966},
	doi = {10.1007/978-3-642-88655-3_3},
	pages = {21--33},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/PHF7WHY8/Coleman et al. - 1966 - General Theory of Viscometric Flows.pdf:application/pdf},
}

@incollection{coleman_introduction_1966,
	address = {Berlin, Heidelberg},
	series = {Springer {Tracts} in {Natural} {Philosophy}},
	title = {Introduction},
	isbn = {978-3-642-88655-3},
	url = {https://doi.org/10.1007/978-3-642-88655-3_1},
	abstract = {The classical theory of incompressible viscous fluids is based upon the constitutive assumptions1 1.1\$\$ T=-p1+2\{\{{\textbackslash}eta \}\_\{0\}\}D,\$\$2.1\$\$\{{\textbackslash}text\{trace D = 0,\}\}\$\$where D is the stretching or rate of deformation tensor, T is the stress tensor, p is a pressure, and η0 is the viscosity, a material constant. The field equations which result from substitution of (1.1) into the dynamical equations are called the Navier-Stokes equations. Equation (1.2) expresses the assumption of incompressibility, i.e., constancy of mass density. More precise explanations of (1.1) and (1.2) will be given in the text.},
	language = {en},
	urldate = {2023-06-27},
	booktitle = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}: {Theory} and {Experiment}},
	publisher = {Springer},
	author = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	editor = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	year = {1966},
	doi = {10.1007/978-3-642-88655-3_1},
	keywords = {Couette Flow, Poiseuille Flow, Incompressible Viscous Fluid, Outer Cylinder, Steady Flow},
	pages = {1--9},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/VURT5A5W/Coleman et al. - 1966 - Introduction.pdf:application/pdf},
}

@incollection{coleman_historical_1966,
	address = {Berlin, Heidelberg},
	series = {Springer {Tracts} in {Natural} {Philosophy}},
	title = {Historical {Remarks}},
	isbn = {978-3-642-88655-3},
	url = {https://doi.org/10.1007/978-3-642-88655-3_6},
	abstract = {It is not our intent to chronicle in detail the history of the mechanics of fluids. Exposition of this history, in varying amount of detail and emphasis, can be found elsewhere.1 Here we outline the highlights of the theoretical developments that culminated in the theory of incompressible simple fluids.},
	language = {en},
	urldate = {2023-06-27},
	booktitle = {Viscometric {Flows} of {Non}-{Newtonian} {Fluids}: {Theory} and {Experiment}},
	publisher = {Springer},
	author = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	editor = {Coleman, Bernard D. and Markovitz, Hershel and Noll, Walter},
	year = {1966},
	doi = {10.1007/978-3-642-88655-3_6},
	keywords = {Couette Flow, Normal Stress, Normal Traction, Simple Fluid, Simple Shearing Flow},
	pages = {84--92},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/Q6L9UAIY/Coleman et al. - 1966 - Historical Remarks.pdf:application/pdf},
}

@book{irgens_rheology_2014,
	address = {Cham},
	title = {Rheology and {Non}-{Newtonian} {Fluids}},
	isbn = {978-3-319-01052-6 978-3-319-01053-3},
	url = {http://link.springer.com/10.1007/978-3-319-01053-3},
	language = {en},
	urldate = {2023-06-27},
	publisher = {Springer International Publishing},
	author = {Irgens, Fridtjov},
	year = {2014},
	doi = {10.1007/978-3-319-01053-3},
	keywords = {Deformation Kinematics, Extensional Flows, fluid- and aerodynamics, Generalized Newtonian Fluids, Kinematics of Shear Flows, Physics of Silly Putty, Viscoelastic Fluid Model, Viscoelastic Plastic Materials, Viscometric Flows},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/SS4TEMFQ/Irgens - 2014 - Rheology and Non-Newtonian Fluids.pdf:application/pdf},
}

@incollection{kundu_chapter_2016,
	address = {Boston},
	title = {Chapter 4 - {Conservation} {Laws}},
	isbn = {978-0-12-405935-1},
	url = {https://www.sciencedirect.com/science/article/pii/B9780124059351000046},
	abstract = {The laws governing fluid motion are based on conservation of mass, momentum, and energy. For the Eulerian description of fluid motion, these three conservation laws are coupled nonlinear partial differential equations. However, to produce a potentially solvable set of equations, a constitutive relationship must be specified. For many commonly encountered fluids, the simplest possible Newtonian viscosity law – a linear relationship between the stress and strain-rate tensors involving only two material constants – is appropriate. When supplemented by two thermodynamic relationships, such as caloric and thermal equations of state, the number of equations matches the number of unknown dependent field quantities. Thus, with the specification of appropriate boundary conditions, the overall system of equations can in principle be solved even in noninertial coordinate systems. When the equations of fluid motion are cast in dimensionless form, the dimensionless parameters (or numbers) commonly used to specify fluid flow conditions appear as coefficients of dimensionless terms in the equations. Although analytical solutions to the full set of equations are uncommon, the equations of fluid motion can be simplified, and are easier to solve, under certain circumstances.},
	language = {en},
	urldate = {2023-06-27},
	booktitle = {Fluid {Mechanics} ({Sixth} {Edition})},
	publisher = {Academic Press},
	author = {Kundu, Pijush K. and Cohen, Ira M. and Dowling, David R.},
	editor = {Kundu, Pijush K. and Cohen, Ira M. and Dowling, David R.},
	month = jan,
	year = {2016},
	doi = {10.1016/B978-0-12-405935-1.00004-6},
	keywords = {Bernoulli equation, Boundary condition, Boussinesq approximation, Conservation laws, Conservation of energy, Conservation of momentum, Continuity equation, Dynamic similarity, Frame of reference, Navier-Stokes equation, Newtonian fluid, Stream function, Surface tension},
	pages = {109--193},
	file = {ScienceDirect Snapshot:/Users/eunji/Zotero/storage/KYYLGI8T/fluid-mechanics.html:text/html},
}

@book{chorin_mathematical_1993,
	address = {New York, NY},
	series = {Texts in {Applied} {Mathematics}},
	title = {A {Mathematical} {Introduction} to {Fluid} {Mechanics}},
	volume = {4},
	isbn = {978-1-4612-6934-2 978-1-4612-0883-9},
	url = {http://link.springer.com/10.1007/978-1-4612-0883-9},
	urldate = {2023-06-25},
	publisher = {Springer},
	author = {Chorin, Alexandre J. and Marsden, Jerrold E.},
	editor = {Marsden, J. E. and Sirovich, L. and Golubitsky, M.},
	year = {1993},
	doi = {10.1007/978-1-4612-0883-9},
	keywords = {fluid- and aerodynamics, Navier-Stokes equation, fluid mechanics, mechanics, Potential, rotation, stability},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/S6IYYFK2/Chorin and Marsden - 1993 - A Mathematical Introduction to Fluid Mechanics.pdf:application/pdf},
}

@article{polimeno_toward_2022,
	title = {Toward a {Realistic} {Model} of {Diffusion}-{Limited} {Aggregation}: {Rotation}, {Size}-{Dependent} {Diffusivities}, and {Settling}},
	volume = {7},
	shorttitle = {Toward a {Realistic} {Model} of {Diffusion}-{Limited} {Aggregation}},
	url = {https://doi.org/10.1021/acsomega.2c03547},
	doi = {10.1021/acsomega.2c03547},
	abstract = {In this Brownian dynamics simulation study on the formation of aggregates made of spherical particles, we build on the well-established diffusion-limited cluster aggregation (DLCA) model. We include rotational effects, allow diffusivities to be size-dependent as is physically relevant, and incorporate settling under gravity. We numerically characterize the growth dynamics of aggregates and find that their radius of gyration, Rg, grows approximately as Rg ∼ t1.02 for classical DLCA but slows to an approximate growth rate of Rg ∼ t0.71 when diffusivity is size-dependent. We also analyze the fractal structure of the resulting aggregates and find that their fractal dimension, d, decreases from d ≈ 1.8 for classical DLCA to d ≈ 1.7 when size-dependent rotational diffusion is included. The addition of settling effects further reduces the fractal dimension observed to d ≈ 1.6 and appears to result in aggregates with a vertical extent marginally smaller than their horizontal extent.},
	number = {45},
	urldate = {2023-06-15},
	journal = {ACS Omega},
	author = {Polimeno, Matteo and Kim, Changho and Blanchette, François},
	month = nov,
	year = {2022},
	note = {Publisher: American Chemical Society},
	pages = {40826--40835},
	file = {ACS Full Text Snapshot:/Users/eunji/Zotero/storage/P7WDVFF5/acsomega.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/CZHC767G/Polimeno et al. - 2022 - Toward a Realistic Model of Diffusion-Limited Aggr.pdf:application/pdf},
}

@article{krishnaraj_dilation-driven_2016,
	title = {A dilation-driven vortex flow in sheared granular materials explains a rheometric anomaly},
	volume = {7},
	copyright = {2016 The Author(s)},
	issn = {2041-1723},
	url = {https://www.nature.com/articles/ncomms10630},
	doi = {10.1038/ncomms10630},
	abstract = {Granular flows occur widely in nature and industry, yet a continuum description that captures their important features is yet not at hand. Recent experiments on granular materials sheared in a cylindrical Couette device revealed a puzzling anomaly, wherein all components of the stress rise nearly exponentially with depth. Here we show, using particle dynamics simulations and imaging experiments, that the stress anomaly arises from a remarkable vortex flow. For the entire range of fill heights explored, we observe a single toroidal vortex that spans the entire Couette cell and whose sense is opposite to the uppermost Taylor vortex in a fluid. We show that the vortex is driven by a combination of shear-induced dilation, a phenomenon that has no analogue in fluids, and gravity flow. Dilatancy is an important feature of granular mechanics, but not adequately incorporated in existing models.},
	language = {en},
	number = {1},
	urldate = {2023-06-12},
	journal = {Nature Communications},
	author = {Krishnaraj, K. P. and Nott, Prabhu R.},
	month = feb,
	year = {2016},
	note = {Number: 1
Publisher: Nature Publishing Group},
	keywords = {Fluid dynamics, Condensed-matter physics},
	pages = {10630},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/K2XK9S97/Krishnaraj and Nott - 2016 - A dilation-driven vortex flow in sheared granular .pdf:application/pdf},
}

@article{coleman_approximation_1960,
	title = {An approximation theorem for functionals, with applications in continuum mechanics},
	volume = {6},
	issn = {1432-0673},
	url = {https://doi.org/10.1007/BF00276168},
	doi = {10.1007/BF00276168},
	language = {en},
	number = {1},
	urldate = {2023-06-12},
	journal = {Archive for Rational Mechanics and Analysis},
	author = {Coleman, Bernard D. and Noll, Walter},
	month = jan,
	year = {1960},
	keywords = {Approximation Theorem, Complex System, Electromagnetism, Neural Network, Nonlinear Dynamics},
	pages = {355--370},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/42J8SR4X/Coleman and Noll - 1960 - An approximation theorem for functionals, with app.pdf:application/pdf},
}

@article{boyer_dense_2011,
	title = {Dense suspensions in rotating-rod flows: normal stresses and particle migration},
	volume = {686},
	issn = {1469-7645, 0022-1120},
	shorttitle = {Dense suspensions in rotating-rod flows},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/dense-suspensions-in-rotatingrod-flows-normal-stresses-and-particle-migration/DB8EA123B630D3FE22DBBD4DFD287875},
	doi = {10.1017/jfm.2011.272},
	abstract = {Normal stress differences are measured in dense suspensions of neutrally buoyant non-Brownian spheres dispersed in a Newtonian fluid. Rotating-rod rheometry is used to characterize the suspension normal stresses which are responsible for a rod-dipping phenomenon. These normal stress differences are seen to strongly increase above a volume fraction of approximately 22 \%. During the course of the experiments, a new time-dependent behaviour is also observed: the dip is filled with increasing times. This time evolution is found to be related to particle migration from regions of high shear rate to regions of low shear rate. The behaviour is compared with the predictions of a suspension balance model in which the particle migration flux is related to the normal stresses of the suspension.},
	language = {en},
	urldate = {2023-06-12},
	journal = {Journal of Fluid Mechanics},
	author = {Boyer, François and Pouliquen, Olivier and Guazzelli, Élisabeth},
	month = nov,
	year = {2011},
	note = {Publisher: Cambridge University Press},
	keywords = {particle/fluid flow, rheology, suspensions},
	pages = {5--25},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/7CKLCWP6/Boyer et al. - 2011 - Dense suspensions in rotating-rod flows normal st.pdf:application/pdf},
}

@article{dai_viscometric_2013,
	title = {Viscometric functions for noncolloidal sphere suspensions with {Newtonian} matrices},
	volume = {57},
	issn = {0148-6055},
	url = {https://doi.org/10.1122/1.4774325},
	doi = {10.1122/1.4774325},
	abstract = {We present the results of measuring the three viscometric functions [the relative viscosity ηr, and the first (N1) and second (N2) normal stress differences] for nominally monosize sphere suspensions in a silicone fluid, which is nominally Newtonian. The measurements of ηr and N1−N2 were made with a parallel-plate rheometer, while we used the open semicircular trough method to give N2 directly. With the trough method measurements of N2 could be made down to a 10\% concentration (φ=0.1); measurements were continued up to 45\% concentration. The trough surface shows visually that N2 is directly proportional to the shear stress τ, and the measurements of N2 agree quite well with the results of Zarraga et al. [J. Rheol. 44, 185–220 (2000)] in the range where concentrations overlap (0.3–0.45) and with those of later investigators. The results for N1 show greater scatter. In the range 0.1≤φ≤0.45, our best estimate of N2/τ is −4.4φ3 and that of N1/τ is −0.8φ3. Hence, the magnitude of N2 is much greater than that of N1. Measurement uncertainties are given in the text—they depend on φ. We have also compared the new experiments with two sets of numerical simulations. There is considerable divergence, which remains to be explained, between some of the simulations and the experiments. However, agreement between experiment and some of the simulations of Bertevas et al. [Rheol. Acta 49, 53–73 (2010)] is reasonable.},
	number = {2},
	urldate = {2023-06-04},
	journal = {Journal of Rheology},
	author = {Dai, Shao-Cong and Bertevas, Erwan and Qi, Fuzhong and Tanner, Roger I.},
	month = mar,
	year = {2013},
	pages = {493--510},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/TCSHXEWX/Dai et al. - 2013 - Viscometric functions for noncolloidal sphere susp.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/8I84DHU9/Viscometric-functions-for-noncolloidal-sphere.html:text/html},
}

@article{rivlin_hydrodynamics_1997,
	title = {The hydrodynamics of non-{Newtonian} fluids. {I}},
	volume = {193},
	url = {https://royalsocietypublishing.org/doi/10.1098/rspa.1948.0044},
	doi = {10.1098/rspa.1948.0044},
	abstract = {The classical theory of the hydrodynamics of viscous fluids depends on the assumption of a particular law governing the relations between the components of stress in a fluid and those of the strain-velocity. This assumption limits its applicability to Newtonian fluids. Here, the most general possible relations between the stress and strain-velocity components, which can be obeyed by an incompressible, visco-inelastic fluid, are derived. These relations also apply to an incompressible, visco-elastic fluid in a steady state of laminar flow. It is shown how equations of motion and boundary conditions can be obtained if these relations are known. Two problems involving laminar flow are then discussed in some detail. These are: (i) the torsional motion of a cylindrical mass of fluid, produced by means of forces applied to its plane ends, and (ii) the laminar flow of a mass of fluid contained between two coaxial cylinders rotating with different angular velocities. It is found in case (i) that, in general, normal tractions must be applied to the plane surfaces of the fluid, in addition to the azimuthal tractions expected from the classical theory, in order to produce the specified motion. Analogous results are obtained in case (ii). These results apply even when centrifugal forces are neglected and so imply a qualitative difference between the behaviour of fluids in general and those for which the special case of classical hydrodynamics is valid.},
	number = {1033},
	urldate = {2023-06-04},
	journal = {Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
	author = {Rivlin, R. S. and Rideal, Eric Keightley},
	month = jan,
	year = {1997},
	note = {Publisher: Royal Society},
	pages = {260--281},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/3FKRJET9/Rivlin and Rideal - 1997 - The hydrodynamics of non-Newtonian fluids. I.pdf:application/pdf},
}

@article{reiner_mathematical_1945,
	title = {A {Mathematical} {Theory} of {Dilatancy}},
	volume = {67},
	issn = {0002-9327},
	url = {https://www.jstor.org/stable/2371950},
	doi = {10.2307/2371950},
	number = {3},
	urldate = {2023-06-04},
	journal = {American Journal of Mathematics},
	author = {Reiner, M.},
	year = {1945},
	note = {Publisher: Johns Hopkins University Press},
	pages = {350--362},
	file = {JSTOR Full Text PDF:/Users/eunji/Zotero/storage/FCU8NQKU/Reiner - 1945 - A Mathematical Theory of Dilatancy.pdf:application/pdf},
}

@article{vmore_rod-climbing_2023,
	title = {Rod-climbing rheometry revisited},
	url = {https://pubs.rsc.org/en/content/articlelanding/2023/sm/d3sm00181d},
	doi = {10.1039/D3SM00181D},
	language = {en},
	urldate = {2023-06-01},
	journal = {Soft Matter},
	author = {V. More, Rishabh and Patterson, Reid and Pashkovski, Eugene and H. McKinley, Gareth},
	year = {2023},
	note = {Publisher: Royal Society of Chemistry},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/QJSQBN98/V. More et al. - 2023 - Rod-climbing rheometry revisited.pdf:application/pdf},
}

@article{rivlin_stress-deformation_1955,
	title = {Stress-{Deformation} {Relations} for {Isotropic} {Materials}},
	volume = {4},
	issn = {1943-5282},
	url = {https://www.jstor.org/stable/24900365},
	urldate = {2023-06-01},
	journal = {Journal of Rational Mechanics and Analysis},
	author = {Rivlin, R. S. and Ericksen, J. L.},
	year = {1955},
	note = {Publisher: Indiana University Mathematics Department},
	pages = {323--425},
	file = {JSTOR Full Text PDF:/Users/eunji/Zotero/storage/KHXD2CCY/Rivlin and Ericksen - 1955 - Stress-Deformation Relations for Isotropic Materia.pdf:application/pdf},
}

@article{yadav_accurate_2023,
	title = {Accurate modeling of blood flow in a micro-channel as a non-homogeneous mixture using continuum approach-based diffusive flux model},
	volume = {35},
	issn = {1070-6631},
	url = {https://doi.org/10.1063/5.0144794},
	doi = {10.1063/5.0144794},
	abstract = {This paper presents a continuum approach for the blood flow simulation, inside the micro-channel of the few micrometers characteristics dimension, within the context of the finite volume method on unstructured grids. The velocity and pressure fields, for the blood flow, are obtained here by solving the Navier–Stokes equations. A particle transport equation, based on the diffusive flux model, provides the hematocrit distribution (i.e., the red blood cells volume-fraction). The momentum conservation equation for a non-Newtonian fluid model is coupled with the particle transport equation through the constitutive blood viscosity model, and this blood viscosity is dependent on hematocrit and shear rate. The continuum approach for blood flow inside the micro-channel of the length scale of a few micrometers to a few hundred micrometers is expected to break down. Interestingly, the present approach provides meaningful insights into biophysics with less computational cost and shows a good match with the experiments and mesoscale simulation with a maximum average deviation of 11\% even at the characteristic dimensions of 10–300 μm. A correlation is proposed for additional-local shear rate in terms of the hematocrit and the ratio of red blood cells diameter to the channel diameter, which helps us to demonstrate an increase in the accuracy and also eliminates the issues of unphysical hematocrit reported in the earlier studies available in the literature. The study is extended to provide new results inside a square and rectangular cross section micro-channels, under a range of inlet parameters.},
	number = {4},
	urldate = {2023-05-31},
	journal = {Physics of Fluids},
	author = {Yadav, Shivji Prasad and Sharma, Atul and Agrawal, Amit},
	month = apr,
	year = {2023},
	pages = {041905},
	file = {Snapshot:/Users/eunji/Zotero/storage/ZC7V2MIB/Accurate-modeling-of-blood-flow-in-a-micro-channel.html:text/html},
}

@article{greengard_new_2002,
	title = {A {New} {Version} of the {Fast} {Multipole} {Method} for {Screened} {Coulomb} {Interactions} in {Three} {Dimensions}},
	volume = {180},
	issn = {0021-9991},
	url = {https://www.sciencedirect.com/science/article/pii/S002199910297110X},
	doi = {10.1006/jcph.2002.7110},
	abstract = {We present a new version of the fast multipole method (FMM) for screened Coulomb interactions in three dimensions. Existing schemes can compute such interactions in O(N) time, where N denotes the number of particles. The constant implicit in the O(N) notation, however, is dominated by the expense of translating far-field spherical harmonic expansions to local ones. For each box in the FMM data structure, this requires 189p4 operations per box, where p is the order of the expansions used. The new formulation relies on an expansion in evanescent plane waves, with which the amount of work can be reduced to 40p2+6p3 operations per box.},
	language = {en},
	number = {2},
	urldate = {2023-05-30},
	journal = {Journal of Computational Physics},
	author = {Greengard, Leslie F. and Huang, Jingfang},
	month = aug,
	year = {2002},
	pages = {642--658},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/S6X96P9E/Greengard and Huang - 2002 - A New Version of the Fast Multipole Method for Scr.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/L6I2FHWB/S002199910297110X.html:text/html},
}

@article{greengard_new_1997,
	title = {A new version of the {Fast} {Multipole} {Method} for the {Laplace} equation in three dimensions},
	volume = {6},
	issn = {1474-0508, 0962-4929},
	url = {https://www.cambridge.org/core/journals/acta-numerica/article/new-version-of-the-fast-multipole-method-for-the-laplace-equation-in-three-dimensions/8D84CC50463A63C73A5E97A045F16B79},
	doi = {10.1017/S0962492900002725},
	abstract = {We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.},
	language = {en},
	urldate = {2023-05-30},
	journal = {Acta Numerica},
	author = {Greengard, Leslie and Rokhlin, Vladimir},
	month = jan,
	year = {1997},
	note = {Publisher: Cambridge University Press},
	pages = {229--269},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/PLF38ICZ/Greengard and Rokhlin - 1997 - A new version of the Fast Multipole Method for the.pdf:application/pdf},
}

@article{couturier_suspensions_2011,
	title = {Suspensions in a tilted trough: second normal stress difference},
	volume = {686},
	issn = {1469-7645, 0022-1120},
	shorttitle = {Suspensions in a tilted trough},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/suspensions-in-a-tilted-trough-second-normal-stress-difference/526B4DD50BEF1659882F91062B1AC288},
	doi = {10.1017/jfm.2011.315},
	abstract = {We measure the second normal-stress difference in suspensions of non-Brownian neutrally buoyant rigid spheres dispersed in a Newtonian fluid. We use a method inspired by Wineman \& Pipkin (Acta Mechanica, vol. 2, 1966, pp. 104–115) and Tanner (Trans. Soc. Rheol., vol. 14, 1970, pp. 483–507), which relies on the examination of the shape of the suspension free surface in a tilted trough flow. The second normal-stress difference is found to be negative and linear in shear stress. The ratio of the second normal-stress difference to shear stress increases with increasing volume fraction. A clear behavioural change exhibiting a strong (approximately linear) growth in the magnitude of this ratio with volume fraction is seen above a volume fraction of 0.22. By comparing our results with previous data obtained for the same batch of spheres by Boyer, Pouliquen \& Guazzeli (J. Fluid Mech., 2011, doi:10.1017/jfm.2011.272), the ratio of the first normal-stress difference to the shear stress is estimated and its magnitude is found to be very small.},
	language = {en},
	urldate = {2023-05-26},
	journal = {Journal of Fluid Mechanics},
	author = {Couturier, Étienne and Boyer, François and Pouliquen, Olivier and Guazzelli, Élisabeth},
	month = nov,
	year = {2011},
	note = {Publisher: Cambridge University Press},
	keywords = {particle/fluid flow, rheology, suspensions},
	pages = {26--39},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/Z2RTSRNP/Couturier et al. - 2011 - Suspensions in a tilted trough second normal stre.pdf:application/pdf},
}

@article{rokhlin_rapid_1985,
	title = {Rapid solution of integral equations of classical potential theory},
	volume = {60},
	issn = {0021-9991},
	url = {https://www.sciencedirect.com/science/article/pii/0021999185900026},
	doi = {10.1016/0021-9991(85)90002-6},
	abstract = {An algorithm is described for rapid solution of classical boundary value problems (Dirichlet an Neumann) for the Laplace equation based on iteratively solving integral equations of potential theory. CPU time requirements for previously published algorithms of this type are proportional to n2, where n is the number of nodes in the discretization of the boundary of the region. The CPU time requirements for the algorithm of the present paper are proportional to n, making it considerably more practical for large scale problems.},
	language = {en},
	number = {2},
	urldate = {2023-05-17},
	journal = {Journal of Computational Physics},
	author = {Rokhlin, V},
	month = sep,
	year = {1985},
	pages = {187--207},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/JT8HW72M/Rokhlin - 1985 - Rapid solution of integral equations of classical .pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/JUKYKY24/0021999185900026.html:text/html},
}

@article{kumar_lagrangian_2023,
	title = {Lagrangian stretching reveals stress topology in viscoelastic flows},
	volume = {120},
	url = {https://www.pnas.org/doi/10.1073/pnas.2211347120},
	doi = {10.1073/pnas.2211347120},
	abstract = {Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulates flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distribution of polymeric stress is lacking. In this work, we show that the topology of the polymeric stress field precisely mirrors the Lagrangian stretching field, where the latter depends solely on flow kinematics. We develop a general analytical expression that directly relates the polymeric stress and stretching in weakly viscoelastic fluids for both nonlinear and unsteady flows, which is also extended to special cases characterized by strong kinematics. Furthermore, numerical simulations reveal a clear correlation between the stress and stretching field topologies for unstable viscoelastic flows across a broad range of geometries. Ultimately, our results establish a connection between the Eulerian stress field and the Lagrangian structure of viscoelastic flows. This work provides a simple framework to determine the topology of polymeric stress directly from readily measurable flow field data and lays the foundation for directly linking the polymeric stress to flow transport properties.},
	number = {5},
	urldate = {2023-05-15},
	journal = {Proceedings of the National Academy of Sciences},
	author = {Kumar, Manish and Guasto, Jeffrey S. and Ardekani, Arezoo M.},
	month = jan,
	year = {2023},
	note = {Publisher: Proceedings of the National Academy of Sciences},
	pages = {e2211347120},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/R735REZM/Kumar et al. - 2023 - Lagrangian stretching reveals stress topology in v.pdf:application/pdf},
}

@article{tanner_review_2018,
	title = {Review {Article}: {Aspects} of non-colloidal suspension rheology},
	volume = {30},
	issn = {1070-6631},
	shorttitle = {Review {Article}},
	url = {https://doi.org/10.1063/1.5047535},
	doi = {10.1063/1.5047535},
	abstract = {This review deals with non-Brownian (non-colloidal) suspension rheology; experimental and computational studies are compared where possible. The matrix fluids are Newtonian, and the rigid particles have an aspect ratio close to one. Volume fractions up to and including 0.5 are considered. Shearing and extensional flows are discussed; the former are fairly well understood, but the latter are not prominent in the literature. Unsteady and oscillatory flows are surveyed; more work is needed in this area. Finally some attempts to find constitutive models are discussed, and an empirically based suggestion based on a modified Reiner-Rivlin model is described.},
	number = {10},
	urldate = {2023-05-15},
	journal = {Physics of Fluids},
	author = {Tanner, Roger I.},
	month = oct,
	year = {2018},
	pages = {101301},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/ZAR9EUQI/Tanner - 2018 - Review Article Aspects of non-colloidal suspensio.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/FGGPLN6D/Review-Article-Aspects-of-non-colloidal-suspension.html:text/html},
}

@article{bird_dynamics_1987,
	title = {Dynamics of polymeric liquids. {Vol}. 1, 2nd {Ed}. : {Fluid} mechanics},
	shorttitle = {Dynamics of polymeric liquids. {Vol}. 1, 2nd {Ed}.},
	url = {https://www.osti.gov/biblio/6164599},
	abstract = {This book examines Newtonian liquids and polymer fluid mechanics. It begins with a review of the main ideas of fluid dynamics as well as key points of Newtonian fluids. Major revisions include extensive updating of all material and a greater emphasis on fluid dynamics problem solving. It presents summaries of experiments describing the difference between polymeric and simple fluids. In addition, it traces, roughly in historical order, various methods for solving polymer fluid dynamics problems.},
	language = {English},
	urldate = {2023-05-15},
	author = {Bird, R. B. and Armstrong, R. C. and Hassager, O.},
	month = jan,
	year = {1987},
	note = {Publisher: John Wiley and Sons Inc.,New York, NY},
	file = {Bird et al. - 1987 - Dynamics of polymeric liquids. Vol. 1, 2nd Ed.  F.pdf:/Users/eunji/Zotero/storage/3H7CIZVV/Bird et al. - 1987 - Dynamics of polymeric liquids. Vol. 1, 2nd Ed.  F.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/QE7A37SZ/6164599.html:text/html},
}

@article{camassa_retention_2013,
	title = {Retention and entrainment effects: {Experiments} and theory for porous spheres settling in sharply stratified fluids},
	volume = {25},
	issn = {1070-6631},
	shorttitle = {Retention and entrainment effects},
	url = {https://doi.org/10.1063/1.4819407},
	doi = {10.1063/1.4819407},
	abstract = {We present an experimental study of single porous spheres settling in a near two-layer ambient density fluid. Data are compared with a first-principle model based on diffusive processes. The model correctly predicts accelerations of the sphere but does not capture the retention time at the density transition quantitatively. Entrainment of lighter fluid through a shell encapsulating the sphere is included in this model empirically. With this parametrization, which exhibits a power law dependence on Reynolds numbers, retention times are accurately captured. Extrapolating from our experimental data, model predictions are presented.},
	number = {8},
	urldate = {2023-05-05},
	journal = {Physics of Fluids},
	author = {Camassa, R. and Khatri, S. and McLaughlin, R. M. and Prairie, J. C. and White, B. L. and Yu, S.},
	month = aug,
	year = {2013},
	pages = {081701},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/LAY9L3YV/Camassa et al. - 2013 - Retention and entrainment effects Experiments and.pdf:application/pdf},
}

@article{alldredge_occurrence_2002,
	title = {Occurrence and mechanisms of formation of a dramatic thin layer of marine snow in a shallow {Pacific} fjord},
	volume = {233},
	issn = {0171-8630, 1616-1599},
	url = {https://www.int-res.com/abstracts/meps/v233/p1-12/},
	doi = {10.3354/meps233001},
	abstract = {Huge accumulations of diatom-dominated marine snow (aggregates {\textgreater}0.5 mm in diameter) were observed in a layer approximately 50 cm thick persisting over a 24 h period in a shallow fjord in the San Juan Islands, Washington, USA. The layer was
associated with the 22.4 σt density surface. A second thin layer of elevated phytoplankton concentration located at a density discontinuity 1.5 to 2 m above the marine snow layer occurred within a dense diatom bloom
near the surface. At the end of the study period, isopycnals shoaled and the 2 layers merged. More than 80\% of the diatom bloom consisted of Thalassiosira spp. (50 to 59\%), Odontella longicruris (5 to 14\%), Asterionellopsis glacialis,
and Thalassionema nitzschioides. A much higher proportion of O. longicruris occurred in marine snow (about 53\%) than among suspended cells suggesting that this species differentially aggregated. Most zooplankton avoided the mucus-rich
aggregate layer. The layer of marine snow was formed when sinking aggregated diatoms reached neutral buoyancy at the 22.4 isopycnal, probably due to the presence of low salinity mucus resistant to salt exchange in the interstices of the aggregates. Rates
of turbulent kinetic energy dissipation throughout the water column rarely exceeded 10-8 m2 s-3 and aggregates below the thin layer were largely detrital in composition indicating that small-scale shears due to turbulence
did not erode the layer of marine snow. The accumulation of marine snow and phytoplankton in persistent, discrete layers at density discontinuities results in habitat partitioning of the pelagic zone, impacts the distribution and interactions of
planktonic organisms as well as the intensity and location of biological processes in the water column, and helps maintain species diversity.},
	language = {en},
	urldate = {2023-05-05},
	journal = {Marine Ecology Progress Series},
	author = {Alldredge, Alice L. and Cowles, Timothy J. and MacIntyre, Sally and Rines, Jan E. B. and Donaghay, Percy L. and Greenlaw, Charles F. and Holliday, D. V. and Dekshenieks, Margaret M. and Sullivan, James M. and Zaneveld, J. Ronald V.},
	month = may,
	year = {2002},
	keywords = {Marine snow, Density discontinuity, Diatom bloom flocculation, Plankton distribution, Plankton patchiness, Thin layers},
	pages = {1--12},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/IS3ZMHSL/Alldredge et al. - 2002 - Occurrence and mechanisms of formation of a dramat.pdf:application/pdf},
}

@article{macintyre_accumulation_1995,
	title = {Accumulation of marines now at density discontinuities in the water column},
	volume = {40},
	issn = {1939-5590},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.4319/lo.1995.40.3.0449},
	doi = {10.4319/lo.1995.40.3.0449},
	abstract = {The vertical distribution of marine snow—aggregated particles {\textgreater}0.5 mm in diameter—was strongly correlated with density discontinuities in the upper 100 m of the water column at 33 stations off central California. Eighty-seven percent of peaks in aggregate abundance were associated with density discontinuities in which N2 (the Brunt-Väisälä frequency) exceeded 1.25 × 10−4 s−2 (N = 6 cph). For 56\% of the peaks, N2 exceeded 2.5 × 10−4 s−2 (N = 9 cph). Absolute abundances of aggregates increased from a mean of 38.7± 18.3 aggregates liter−1 above peaks to 59.3 ± 26.0 aggregates liter−1 within peaks. Accumulations of aggregates could result from sinking into denser water if sinking rates were reduced by at least 20\% due to slow equilibrium of either interstitial water or mucus within the flocs with the surrounding, higher density water. However, our observed increases in σt were insufficient to cause such slowing for flocs whose porosity was 99\% or less; such flocs comprised a significant proportion of aggregates in the observed peaks. However, larger flocs of moderate to high porosity were likely to decelerate as they encountered denser water and could even become neutrally or negatively buoyant for changes in σt such as we observed. Equilibration times of the interstitial water of these generally larger flocs ranged from hundreds of seconds up to 3 h. Results of a random walk simulation of particle motion indicated that turbulence was likely to cause localized accumulations of aggregates and to increase particle aggregation. Because we found subcritical values of the Richardson number (an indicator of turbulent mixing) at the top of regions of peak abundance but not at the base, for 68\% of the peaks observed, we infer that turbulence may contribute to the accumulation of the smaller flocs. Occurrence of strong shear and deviations of temperature and salinity profiles from typical patterns suggest that at least 23\% of these aggregate peaks were associated with horizontal intrusions.},
	language = {en},
	number = {3},
	urldate = {2023-05-05},
	journal = {Limnology and Oceanography},
	author = {MacIntyre, Sally and Alldredge, Alice L. and Gotschalk, Chris C.},
	year = {1995},
	% note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.4319/lo.1995.40.3.0449},
	pages = {449--468},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/9HYNDBK2/MacIntyre et al. - 1995 - Accumulation of marines now at density discontinui.pdf:application/pdf},
}

@article{jackson_model_1990,
	title = {A model of the formation of marine algal flocs by physical coagulation processes},
	volume = {37},
	issn = {0198-0149},
	url = {https://www.sciencedirect.com/science/article/pii/019801499090038W},
	doi = {10.1016/0198-0149(90)90038-W},
	abstract = {Aggregates of organic matter (“marine snow”) are highly visible phenomena oceanic waters which can control material fluxes to the deep sea. These aggregates take many forms and undoubtedly have many causes. One form frequently described is that composed of algae, usually diatoms, occurring after an algal bloom. A model combining kinetic coagulation theory and simple algal growth kinetics describes the dynamics of such an algal bloom. Results show this to be a two-state system in which coagulation processes are either unimportant when algal concentrations are low or dominant when they are high, with a rapid transition between the two states. Critical algal concentration for this transition is inversely related to fluid shear, algal size and stickiness, and is similar to values observed after a bloom. The role of coagulation in controlling particle dynamics for more complicated aquatic systems will depend on other biological particle production and consumption processes, such as zooplankton feeding and defecation. These results emphasize the importance of measuring algal sizes and abundances when studying floc formation.},
	language = {en},
	number = {8},
	urldate = {2023-05-05},
	journal = {Deep Sea Research Part A. Oceanographic Research Papers},
	author = {Jackson, George A.},
	month = aug,
	year = {1990},
	pages = {1197--1211},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/QUVPCUL9/Jackson - 1990 - A model of the formation of marine algal flocs by .pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/2DRT8DHA/019801499090038W.html:text/html},
}

@article{kiorboe_mechanisms_2002,
	title = {Mechanisms and {Rates} of {Bacterial} {Colonization} of {Sinking} {Aggregates}},
	volume = {68},
	url = {https://journals.asm.org/doi/10.1128/AEM.68.8.3996-4006.2002},
	doi = {10.1128/AEM.68.8.3996-4006.2002},
	abstract = {Quantifying the rate at which bacteria colonize aggregates is a key to understanding microbial turnover of aggregates. We used encounter models based on random walk and advection-diffusion considerations to predict colonization rates from the bacteria's motility patterns (swimming speed, tumbling frequency, and turn angles) and the hydrodynamic environment (stationary versus sinking aggregates). We then experimentally tested the models with 10 strains of bacteria isolated from marine particles: two strains were nonmotile; the rest were swimming at 20 to 60 μm s−1 with different tumbling frequency (0 to 2 s−1). The rates at which these bacteria colonized artificial aggregates (stationary and sinking) largely agreed with model predictions. We report several findings. (i) Motile bacteria rapidly colonize aggregates, whereas nonmotile bacteria do not. (ii) Flow enhances colonization rates. (iii) Tumbling strains colonize aggregates enriched with organic substrates faster than unenriched aggregates, while a nontumbling strain did not. (iv) Once on the aggregates, the bacteria may detach and typical residence time is about 3 h. Thus, there is a rapid exchange between attached and free bacteria. (v) With the motility patterns observed, freely swimming bacteria will encounter an aggregate in {\textless}1 day at typical upper-ocean aggregate concentrations. This is faster than even starving bacteria burn up their reserves, and bacteria may therefore rely solely on aggregates for food. (vi) The net result of colonization and detachment leads to a predicted equilibrium abundance of attached bacteria as a function of aggregate size, which is markedly different from field observations. This discrepancy suggests that inter- and intraspecific interactions among bacteria and between bacteria and their predators may be more important than colonization in governing the population dynamics of bacteria on natural aggregates.},
	number = {8},
	urldate = {2023-05-05},
	journal = {Applied and Environmental Microbiology},
	author = {Kiørboe, Thomas and Grossart, Hans-Peter and Ploug, Helle and Tang, Kam},
	month = aug,
	year = {2002},
	note = {Publisher: American Society for Microbiology},
	pages = {3996--4006},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/4VEDML3W/Kiørboe et al. - 2002 - Mechanisms and Rates of Bacterial Colonization of .pdf:application/pdf},
}

@article{eggersdorfer_multiparticle_2011,
	title = {Multiparticle {Sintering} {Dynamics}: {From} {Fractal}-{Like} {Aggregates} to {Compact} {Structures}},
	volume = {27},
	issn = {0743-7463},
	shorttitle = {Multiparticle {Sintering} {Dynamics}},
	url = {https://doi.org/10.1021/la200546g},
	doi = {10.1021/la200546g},
	abstract = {Multiparticle sintering is encountered in almost all high temperature processes for material synthesis (titania, silica, and nickel) and energy generation (e.g., fly ash formation) resulting in aggregates of primary particles (hard- or sinter-bonded agglomerates). This mechanism of particle growth is investigated quantitatively by mass and energy balances during viscous sintering of amorphous aerosol materials (e.g., SiO2 and polymers) that typically have a distribution of sizes and complex morphology. This model is validated at limited cases of sintering between two (equally or unequally sized) particles, and chains of particles. The evolution of morphology, surface area and radii of gyration of multiparticle aggregates are elucidated for various sizes and initial fractal dimension. For each of these structures that had been generated by diffusion limited (DLA), cluster–cluster (DLCA), and ballistic particle–cluster agglomeration (BPCA) the surface area evolution is monitored and found to scale differently than that of the radius of gyration (moment of inertia). Expressions are proposed for the evolution of fractal dimension and the surface area of aggregates undergoing viscous sintering. These expressions are important in design of aerosol processes with population balance equations (PBE) and/or fluid dynamic simulations for material synthesis or minimization and even suppression of particle formation.},
	number = {10},
	urldate = {2023-05-02},
	journal = {Langmuir},
	author = {Eggersdorfer, Max L. and Kadau, Dirk and Herrmann, Hans J. and Pratsinis, Sotiris E.},
	month = may,
	year = {2011},
	note = {Publisher: American Chemical Society},
	pages = {6358--6367},
	file = {ACS Full Text Snapshot:/Users/eunji/Zotero/storage/ZXQ6B5ST/la200546g.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/NDSGSLTU/Eggersdorfer et al. - 2011 - Multiparticle Sintering Dynamics From Fractal-Lik.pdf:application/pdf},
}

@article{jackson_aggregation_1998,
	title = {Aggregation in the {Marine} {Environment}},
	volume = {32},
	issn = {0013-936X},
	url = {https://doi.org/10.1021/es980251w},
	doi = {10.1021/es980251w},
	abstract = {The spatial distribution of chemical elements in the ocean is controlled by particles (including organisms); aggregation controls the particle properties. Coagulation is an important mechanism for controlling the size of marine particles and thereby their transport properties. Coagulation theory has provided a framework for the calculation of aggregation rates and size distributions. The use of fractal scaling to relate aggregate length to mass has been an important development that still needs to be fully incorporated into mathematical expressions for particle collision rates. In addition, disaggregation has emerged as an important process that is poorly described mathematically. Observations of particle spectra in the ocean are in general agreement with those expected for coagulation processes but tend to be for too small a size range to include the effects of particle disaggregation. Analysis of material caught in sediment traps suggests that aggregates are the dominant form of material falling through the ocean. An important aspect of the marine system is the presence of multiple particle sources that can confound fractal scaling based on single source particles. Coupled coagulation and chemical reaction models have become important tools in the interpretation of Th distributions. Further development of coagulation theory to describe marine systems promises to push the limits of our understanding of coagulation processes and their implications.},
	number = {19},
	urldate = {2023-05-02},
	journal = {Environmental Science \& Technology},
	author = {Jackson, George A. and Burd, Adrian B.},
	month = oct,
	year = {1998},
	note = {Publisher: American Chemical Society},
	pages = {2805--2814},
	file = {ACS Full Text Snapshot:/Users/eunji/Zotero/storage/F6DX5K6F/es980251w.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/2UUPE4XL/Jackson and Burd - 1998 - Aggregation in the Marine Environment.pdf:application/pdf},
}

@article{gmachowski_calculation_2002,
	title = {Calculation of the fractal dimension of aggregates},
	volume = {211},
	issn = {0927-7757},
	url = {https://www.sciencedirect.com/science/article/pii/S0927775702002789},
	doi = {10.1016/S0927-7757(02)00278-9},
	abstract = {Simple determination of the fractal dimension as the exponent in the mass-radius relation is possible only when the structure of growing aggregates is scale-invariant. If it is not the case, this method produces artifacts even if the slope in a log–log plot is nearly constant. It is shown that the difference between the fractal dimension and that determined from the slope is significant for diffusion limited particle–cluster aggregates. The fractal dimension of a given aggregate can be determined from its mass and radius of gyration using the proposed fractal dimension dependence of the structural coefficient, the prefactor in mass-radius relation.},
	language = {en},
	number = {2},
	urldate = {2023-05-02},
	journal = {Colloids and Surfaces A: Physicochemical and Engineering Aspects},
	author = {Gmachowski, Lech},
	month = dec,
	year = {2002},
	keywords = {Aggregates, Fractal dimension, Mass-radius relation, Particle–cluster aggregation, Structural coefficient},
	pages = {197--203},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/5PU8DEXA/Gmachowski - 2002 - Calculation of the fractal dimension of aggregates.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/Y76AEHR9/S0927775702002789.html:text/html},
}

@article{chan_second-order_1992,
	title = {Second-order boundary element method calculations of hydrodynamic interactions between particles in close proximity},
	volume = {14},
	issn = {1097-0363},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.1650140905},
	doi = {10.1002/fld.1650140905},
	abstract = {A second-order boundary element technique was developed to simulate the 3D hydrodynamic interactions between multiple particles of arbitrary shape. This paper reports the results of an extensive validation procedure aimed at demonstrating the convergence characteristics of the technique, especially in cases where the particles are in close proximity. The quadratic elements are superior to the lower-order elements in terms of accuracy, computer storage and CPU time required, thus resulting in a significant improvement in the overall computational efficiency. Superparametric discretization improves the accuracy over isoparametric discretization but lowers the convergence rate of the method. When the interparticle gap becomes very small (less than 1\% of the particle radius), the numerical solution diverges owing to inaccurate determination of the element contributions in the gap region. An adaptive subdomain integration scheme was developed that dramatically improved the integration accuracy and provided convergent solutions for problems of very small gaps down to 0–01\% of the particle diameter.},
	language = {en},
	number = {9},
	urldate = {2023-05-02},
	journal = {International Journal for Numerical Methods in Fluids},
	author = {Chan, Chiu Y. and Beris, Antony N. and Advani, Suresh G.},
	year = {1992},
	% note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.1650140905},
	keywords = {Adaptive subdomain integration, Boundary element method, Convergence, Local mesh refinement, Small interparticle gap, Superparametric},
	pages = {1063--1086},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/UH79Q66I/Chan et al. - 1992 - Second-order boundary element method calculations .pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/NCCDFN8P/fld.html:text/html},
}

@article{smith_nearest-neighbour_2018,
	title = {A nearest-neighbour discretisation of the regularized stokeslet boundary integral equation},
	volume = {358},
	issn = {0021-9991},
	url = {https://www.sciencedirect.com/science/article/pii/S0021999117308847},
	doi = {10.1016/j.jcp.2017.12.008},
	abstract = {The method of regularized stokeslets is extensively used in biological fluid dynamics due to its conceptual simplicity and meshlessness. This simplicity carries a degree of cost in computational expense and accuracy because the number of degrees of freedom used to discretise the unknown surface traction is generally significantly higher than that required by boundary element methods. We describe a meshless method based on nearest-neighbour interpolation that significantly reduces the number of degrees of freedom required to discretise the unknown traction, increasing the range of problems that can be practically solved, without excessively complicating the task of the modeller. The nearest-neighbour technique is tested against the classical problem of rigid body motion of a sphere immersed in very viscous fluid, then applied to the more complex biophysical problem of calculating the rotational diffusion timescales of a macromolecular structure modelled by three closely-spaced non-slender rods. A heuristic for finding the required density of force and quadrature points by numerical refinement is suggested. Matlab/GNU Octave code for the key steps of the algorithm is provided, which predominantly use basic linear algebra operations, with a full implementation being provided on github. Compared with the standard Nyström discretisation, more accurate and substantially more efficient results can be obtained by de-refining the force discretisation relative to the quadrature discretisation: a cost reduction of over 10 times with improved accuracy is observed. This improvement comes at minimal additional technical complexity. Future avenues to develop the algorithm are then discussed.},
	language = {en},
	urldate = {2023-05-02},
	journal = {Journal of Computational Physics},
	author = {Smith, David J.},
	month = apr,
	year = {2018},
	keywords = {Stokes flow, Boundary integral, Meshfree, Regularized stokeslet},
	pages = {88--102},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/NJE4CB9L/Smith - 2018 - A nearest-neighbour discretisation of the regulari.pdf:application/pdf},
}

@book{delves_computational_1985,
	address = {Cambridge},
	title = {Computational {Methods} for {Integral} {Equations}},
	isbn = {978-0-521-35796-8},
	url = {https://www.cambridge.org/core/books/computational-methods-for-integral-equations/451674F724F741E4FB674272F934B666},
	abstract = {Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides a readable account of techniques for their numerical solution. The authors devote their attention primarily to efficient techniques using high order approximations, taking particular account of situations where singularities are present. The classes of problems which arise frequently in practice, Fredholm of the first and second kind and eigenvalue problems, are dealt with in depth. Volterra equations, although attractive to treat theoretically, arise less often in practical problems and so have been given less emphasis. Some knowledge of numerical methods and linear algebra is assumed, but the book includes introductory sections on numerical quadrature and function space concepts. This book should serve as a valuable text for final year undergraduate or postgraduate courses, and as an introduction or reference work for practising computational mathematicians, scientists and engineers.},
	urldate = {2023-05-02},
	publisher = {Cambridge University Press},
	author = {Delves, L. M. and Mohamed, J. L.},
	year = {1985},
	doi = {10.1017/CBO9780511569609},
	file = {Snapshot:/Users/eunji/Zotero/storage/HVIW7VDE/451674F724F741E4FB674272F934B666.html:text/html},
}

@book{atkinson_numerical_1997,
	address = {Cambridge},
	series = {Cambridge {Monographs} on {Applied} and {Computational} {Mathematics}},
	title = {The {Numerical} {Solution} of {Integral} {Equations} of the {Second} {Kind}},
	isbn = {978-0-521-58391-6},
	url = {https://www.cambridge.org/core/books/numerical-solution-of-integral-equations-of-the-second-kind/91E77DDA93701D3B024830429043A037},
	abstract = {This book provides an extensive introduction to the numerical solution of a large class of integral equations. The initial chapters provide a general framework for the numerical analysis of Fredholm integral equations of the second kind, covering degenerate kernel, projection and Nystrom methods. Additional discussions of multivariable integral equations and iteration methods update the reader on the present state of the art in this area. The final chapters focus on the numerical solution of boundary integral equation (BIE) reformulations of Laplace's equation, in both two and three dimensions. Two chapters are devoted to planar BIE problems, which include both existing methods and remaining questions. Practical problems for BIE such as the set up and solution of the discretised BIE are also discussed. Each chapter concludes with a discussion of the literature and a large bibliography serves as an extended resource for students and researchers needing more information on solving particular integral equations.},
	urldate = {2023-05-02},
	publisher = {Cambridge University Press},
	author = {Atkinson, Kendall E.},
	year = {1997},
	doi = {10.1017/CBO9780511626340},
	file = {Snapshot:/Users/eunji/Zotero/storage/T3T54JNR/91E77DDA93701D3B024830429043A037.html:text/html},
}

@article{cortez_method_2001,
	title = {The {Method} of {Regularized} {Stokeslets}},
	volume = {23},
	issn = {1064-8275},
	url = {https://epubs.siam.org/doi/10.1137/S106482750038146X},
	doi = {10.1137/S106482750038146X},
	abstract = {A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed. The Stokes equations are then discretized using the second-order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper [SIAM J. Numer. Anal., 31(1994), pp. 1019--1044]. The resulting velocities are interpolated to the interface to determine the motion of the interface. An implicit quasi-Newton method is developed that allows reasonable time steps to be used.},
	number = {4},
	urldate = {2023-05-02},
	journal = {SIAM Journal on Scientific Computing},
	author = {Cortez, Ricardo},
	month = jan,
	year = {2001},
	note = {Publisher: Society for Industrial and Applied Mathematics},
	pages = {1204--1225},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/JY53QRTF/Cortez - 2001 - The Method of Regularized Stokeslets.pdf:application/pdf},
}

@article{bao_fluctuating_2018,
	title = {A fluctuating boundary integral method for {Brownian} suspensions},
	volume = {374},
	issn = {0021-9991},
	url = {https://www.sciencedirect.com/science/article/pii/S0021999118305448},
	doi = {10.1016/j.jcp.2018.08.021},
	abstract = {We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green's function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation–dissipation balance relation (DFDB). Based on a recently-developed Positively Split Ewald method Fiore et al. (2017) [24], near-field contributions to the Brownian displacements are efficiently approximated by iterative methods in real space, while far-field contributions are rapidly generated by fast Fourier-space methods based on fluctuating hydrodynamics. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator.},
	language = {en},
	urldate = {2023-05-02},
	journal = {Journal of Computational Physics},
	author = {Bao, Yuanxun and Rachh, Manas and Keaveny, Eric E. and Greengard, Leslie and Donev, Aleksandar},
	month = dec,
	year = {2018},
	keywords = {Stokes flow, Boundary integral equation, Brownian dynamics, Colloidal suspension, Fast algorithm, Fluctuating hydrodynamics},
	pages = {1094--1119},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/DCAZWYHD/Bao et al. - 2018 - A fluctuating boundary integral method for Brownia.pdf:application/pdf},
}

@article{bao_immersed_2017,
	title = {An {Immersed} {Boundary} method with divergence-free velocity interpolation and force spreading},
	volume = {347},
	issn = {0021-9991},
	url = {https://www.sciencedirect.com/science/article/pii/S0021999117304953},
	doi = {10.1016/j.jcp.2017.06.041},
	abstract = {The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.},
	language = {en},
	urldate = {2023-05-02},
	journal = {Journal of Computational Physics},
	author = {Bao, Yuanxun and Donev, Aleksandar and Griffith, Boyce E. and McQueen, David M. and Peskin, Charles S.},
	month = oct,
	year = {2017},
	keywords = {Fluid–structure interaction, Force spreading, Immersed Boundary method, Incompressible flow, Velocity interpolation, Volume conservation},
	pages = {183--206},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/CG7HNKL3/Bao et al. - 2017 - An Immersed Boundary method with divergence-free v.pdf:application/pdf},
}

@article{zinchenko_boundary-integral_2006,
	title = {A boundary-integral study of a drop squeezing through interparticle constrictions},
	volume = {564},
	issn = {1469-7645, 0022-1120},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/boundaryintegral-study-of-a-drop-squeezing-through-interparticle-constrictions/707D10028114EA18DCB4FA25586E0C7C},
	doi = {10.1017/S0022112006001479},
	abstract = {A three-dimensional boundary-integral algorithm is developed to study the squeezing of a deformable drop through a tight constriction formed by several solid particles rigidly held in space. The drop is freely suspended and driven by a flow that is uniform away from the solid obstacles. Particular emphasis is on the trapping mechanism and flow conditions close to critical, when the drop squeezes with high resistance. The problem is a close prototype of drop–solid interactions for emulsion flow through a granular material; such interactions are much more lubrication-sensitive than drop–drop interactions and require advanced numerical tools to succeed. The algorithm is based on the Hebeker representation for the solid–particle contribution, leading to a well-behaved system of second-kind integral equations, combined with novel regularization techniques for singular and near-singular boundary integrals; high-order near-singularity subtraction for the solid-to-drop double-layer contribution is the most crucial element. Simulations are performed for drop squeezing between (i) two close spheres, (ii) two parallel spheroidal disks, and (iii) three close spheres forming an equilateral triangle (including the case of close solid–solid contact). The drop non-deformed diameter is from two to several times larger than the inner constriction diameter and, in some simulations, the drop decelerates \$10{\textasciicircum}3\$–\$10{\textasciicircum}4\$ times in the throat before being able to pass through. The effects of the constriction type, capillary number, and viscosity ratio on the drop velocity in the throat, exit time, and drop–solid spacing (of the order of 1\% of the particle size) are explored in detail; critical capillary numbers (below which trapping occurs) are accurately determined. Even for a substantially supercritical capillary number, the drop has to nearly coat solid particles to be able to pass through a tight constriction. The ability of the algorithm to simulate both supercritical and subcritical conditions (when the drop is trapped, with a small but non-zero drop–solid spacing) is vital for future applications to large-scale simulations of emulsion flow through granular media.},
	language = {en},
	urldate = {2023-05-02},
	journal = {Journal of Fluid Mechanics},
	author = {Zinchenko, Alexander Z. and Davis, Robert H.},
	month = oct,
	year = {2006},
	note = {Publisher: Cambridge University Press},
	pages = {227--266},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/TERMVDEP/Zinchenko and Davis - 2006 - A boundary-integral study of a drop squeezing thro.pdf:application/pdf},
}

@article{vanni_accurate_2015,
	title = {Accurate modelling of flow induced stresses in rigid colloidal aggregates},
	volume = {192},
	issn = {0010-4655},
	url = {https://www.sciencedirect.com/science/article/pii/S0010465515000806},
	doi = {10.1016/j.cpc.2015.02.022},
	abstract = {A method has been developed to estimate the motion and the internal stresses induced by a fluid flow on a rigid aggregate. The approach couples Stokesian dynamics and structural mechanics in order to take into account accurately the effect of the complex geometry of the aggregates on hydrodynamic forces and the internal redistribution of stresses. The intrinsic error of the method, due to the low-order truncation of the multipole expansion of the Stokes solution, has been assessed by comparison with the analytical solution for the case of a doublet in a shear flow. In addition, it has been shown that the error becomes smaller as the number of primary particles in the aggregate increases and hence it is expected to be negligible for realistic reproductions of large aggregates. The evaluation of internal forces is performed by an adaptation of the matrix methods of structural mechanics to the geometric features of the aggregates and to the particular stress–strain relationship that occurs at intermonomer contacts. A preliminary investigation on the stress distribution in rigid aggregates and their mode of breakup has been performed by studying the response to an elongational flow of both realistic reproductions of colloidal aggregates (made of several hundreds monomers) and highly simplified structures. A very different behaviour has been evidenced between low-density aggregates with isostatic or weakly hyperstatic structures and compact aggregates with highly hyperstatic configuration. In low-density clusters breakup is caused directly by the failure of the most stressed intermonomer contact, which is typically located in the inner region of the aggregate and hence originates the birth of fragments of similar size. On the contrary, breakup of compact and highly cross-linked clusters is seldom caused by the failure of a single bond. When this happens, it proceeds through the removal of a tiny fragment from the external part of the structure. More commonly, however, breakup takes place through a sequence of bond failures that start at the periphery of the aggregates and then moves toward the interior according to a crack propagation mechanism. A gradual transition between these two modes of breakup has been found as the density of the aggregates increases.},
	language = {en},
	urldate = {2023-05-02},
	journal = {Computer Physics Communications},
	author = {Vanni, Marco},
	month = jul,
	year = {2015},
	keywords = {Breakup, Colloidal aggregates, Colloids, Computer simulation of molecular and particle dynamics, Emulsions and suspensions, Stress distribution},
	pages = {70--90},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/3RTQ459R/Vanni - 2015 - Accurate modelling of flow induced stresses in rig.pdf:application/pdf},
}

@article{gastaldi_distribution_2011,
	title = {The distribution of stresses in rigid fractal-like aggregates in a uniform flow field},
	volume = {357},
	issn = {0021-9797},
	url = {https://www.sciencedirect.com/science/article/pii/S0021979711001111},
	doi = {10.1016/j.jcis.2011.01.080},
	abstract = {The distribution of stresses in rigid fractal-like aggregates moving in a uniform flow field was investigated for particle–cluster and cluster–cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. The method of reflections was used to calculate the drag force on each monomer, while the internal inter-monomer interactions were calculated by applying force and torque balances on each primary particle. The stress distribution was found to be very dissimilar from that of the applied external forces. Although the highest external forces act on the monomers located at the periphery of the aggregate where the drag is more intense, the most stressed inter-monomer bonds are always located in the internal part of the aggregate. This phenomenon is a consequence of the structure of the studied fractal aggregates, which are made mainly of filaments of monomers: the stress generated by the external forces is propagated and progressively accumulated by such filaments up to their roots, which are situated in the inner part of the cluster. Such a behaviour is different from that exhibited by highly connected structures, in which the loads are absorbed locally by the structure and the largest stresses are normally found in the proximity of the highest applied external forces.},
	language = {en},
	number = {1},
	urldate = {2023-05-02},
	journal = {Journal of Colloid and Interface Science},
	author = {Gastaldi, Andrea and Vanni, Marco},
	month = may,
	year = {2011},
	keywords = {Colloidal aggregates, Stress distribution, Breakage, Dispersion},
	pages = {18--30},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/FRPQGSY5/Gastaldi and Vanni - 2011 - The distribution of stresses in rigid fractal-like.pdf:application/pdf},
}

@article{binder_structural_2009,
	title = {Structural dependent drag force and orientation prediction for small fractal aggregates},
	volume = {331},
	issn = {0021-9797},
	url = {https://www.sciencedirect.com/science/article/pii/S0021979708015014},
	doi = {10.1016/j.jcis.2008.11.021},
	abstract = {Aggregates settle in viscous fluids in specific directions depending on their morphology. We investigated the settling behavior of fractal aggregates with Df=1.85 in fluids using the Accelerated Stokesian Dynamics method. The results have been compared with experimental data. A simple equation is proposed which gives the drag force in dependence on the radius of gyration rgyr, the projection area Ap and the aggregate orientation during settling. This equation reproduces the data from ASD within ±10\% for Re {\textless}1. Additionally, a new algorithm has been developed which allows a prediction of the orientation of such fractal aggregates provided that they have time enough to orient in the fluid. Moreover, the drag force acting on them can be predicted in a narrow range (maximum error 15\%). This algorithm allows a very fast evaluation of the orienting behavior with small deviations.},
	language = {en},
	number = {1},
	urldate = {2023-05-02},
	journal = {Journal of Colloid and Interface Science},
	author = {Binder, Christian and Hartig, Martin A. J. and Peukert, Wolfgang},
	month = mar,
	year = {2009},
	keywords = {Aggregate behavior, Drag force, Fractal aggregates, Hydrodynamics, Stokesian Dynamics},
	pages = {243--250},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/VT6BQ8QP/Binder et al. - 2009 - Structural dependent drag force and orientation pr.pdf:application/pdf},
}

@article{bossis_hydrodynamic_1991,
	title = {Hydrodynamic stress on fractal aggregates of spheres},
	volume = {94},
	issn = {0021-9606},
	url = {https://doi.org/10.1063/1.460543},
	doi = {10.1063/1.460543},
	abstract = {We calculate the average hydrodynamic stress on fractal aggregates of spheres using Stokesian dynamics. We find that for fractal aggregates of force‐free particles, the stress does not grow as the cube of the radius of gyration, but rather as the number of particles in the aggregate. This behavior is only found for random aggregates of force‐free particles held together by hydrodynamic lubrication forces. The stress on aggregates of particles rigidly connected by interparticle forces grows as the radius of gyration cubed. We explain this behavior by examining the transmission of the tension along connecting lines in an aggregate and use the concept of a persistance length in order to characterize this stress transmission within an aggregate.},
	number = {7},
	urldate = {2023-05-02},
	journal = {The Journal of Chemical Physics},
	author = {Bossis, G. and Meunier, A. and Brady, J. F.},
	month = apr,
	year = {1991},
	pages = {5064--5070},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/HCH3TZRD/Bossis et al. - 1991 - Hydrodynamic stress on fractal aggregates of spher.pdf:application/pdf},
}

@article{rogak_stokes_1990,
	title = {Stokes drag on self-similar clusters of spheres},
	volume = {134},
	issn = {0021-9797},
	url = {https://www.sciencedirect.com/science/article/pii/002197979090268S},
	doi = {10.1016/0021-9797(90)90268-S},
	abstract = {Aggregation phenomena in gas and liquid phases often produce agglomerates that appear to be fractals in the sense that the cluster mass varies with the radius of gyration to a fractional power. The creeping (Stokes) flow around the cluster may be represented by the superposition of k single-sphere velocity fields chosen to satisfy the boundary conditions at k points on the cluster. Computations can be performed for large self-similar clusters of Kn monomers by decomposing the cluster n times into smaller clusters which may be replaced by hydrodynamically equivalent spheres. The method recovers the correct results for chains, disks, and compact clusters. Computations done on random, connected clusters similar to real aggregates show that both the primary particle diameter and the cluster radius influence the drag. The influence of the primary particle size and other small-scale structure features is lost very rapidly as the fractal dimension increases above 1.3 and the number of monomers in the cluster increases above 100.},
	language = {en},
	number = {1},
	urldate = {2023-05-02},
	journal = {Journal of Colloid and Interface Science},
	author = {Rogak, Steven N and Flagan, Richard C},
	month = jan,
	year = {1990},
	pages = {206--218},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/4X7AT2VE/Rogak and Flagan - 1990 - Stokes drag on self-similar clusters of spheres.pdf:application/pdf},
}

@article{brady_stokesian_1988,
	title = {Stokesian {Dynamics}},
	volume = {20},
	url = {https://doi.org/10.1146/annurev.fl.20.010188.000551},
	doi = {10.1146/annurev.fl.20.010188.000551},
	number = {1},
	urldate = {2023-05-02},
	journal = {Annual Review of Fluid Mechanics},
	author = {Brady, J F and Bossis, G},
	year = {1988},
	% note = {\_eprint: https://doi.org/10.1146/annurev.fl.20.010188.000551},
	pages = {111--157},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/DCBH6R6G/Brady and Bossis - 1988 - Stokesian Dynamics.pdf:application/pdf},
}

@article{chen_translational_1984,
	title = {Translational friction coefficient of diffusion limited aggregates},
	volume = {80},
	issn = {0021-9606},
	url = {https://doi.org/10.1063/1.447012},
	doi = {10.1063/1.447012},
	number = {6},
	urldate = {2023-05-02},
	journal = {The Journal of Chemical Physics},
	author = {Chen, Zhong‐Ying and Deutch, J. M. and Meakin, Paul},
	month = mar,
	year = {1984},
	pages = {2982--2983},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/XWI7KFXR/Chen et al. - 1984 - Translational friction coefficient of diffusion li.pdf:application/pdf},
}

@article{johnson_settling_1996,
	title = {Settling {Velocities} of {Fractal} {Aggregates}},
	volume = {30},
	issn = {0013-936X},
	url = {https://doi.org/10.1021/es950604g},
	doi = {10.1021/es950604g},
	abstract = {Aggregates generated in water and wastewater treatment systems and those found in natural systems are fractal and therefore have different scaling properties than assumed in settling velocity calculations using Stokes' law. In order to demonstrate that settling velocity models based on impermeable spheres do not accurately relate aggregate size, porosity and settling velocity for highly porous fractal aggregates, we generated fractal aggregates by coagulation of latex microspheres in paddle mixers and analyzed each aggregate individually for its size, porosity, and settling velocity. Settling velocities of these aggregates were on average 4−8.3 times higher than those predicted using either an impermeable sphere model (Stokes' law) or a permeable sphere model that specified aggregate permeability for a homogeneous distribution of particles within an aggregate. Fractal dimensions (D) derived from size−porosity relationships for the three batches of aggregates were 1.78 ± 0.10, 2.19 ± 0.12 and 2.25 ± 0.10. These fractal dimensions were used to predict power law relationships between aggregate size and settling velocity based on Stokes' law. When it was assumed that the the drag coefficient, CD, was constant and fixed at its value of CD = 24/Re for the creeping flow region (Re ≪ 1), predicted slopes of size and settling velocity were in agreement with only the data sets where D {\textgreater} 2. As a result, when D {\textless} 2, aggregate porosities will be overestimated and fractal dimensions will be calculated incorrectly from settling velocity data and Stokes' law.},
	number = {6},
	urldate = {2023-05-02},
	journal = {Environmental Science \& Technology},
	author = {Johnson, Clifford P. and Li, Xiaoyan and Logan, Bruce E.},
	month = may,
	year = {1996},
	note = {Publisher: American Chemical Society},
	pages = {1911--1918},
	file = {ACS Full Text Snapshot:/Users/eunji/Zotero/storage/DNZRNM5X/es950604g.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/JW6Z857N/Johnson et al. - 1996 - Settling Velocities of Fractal Aggregates.pdf:application/pdf},
}

@article{takayasu_determination_1998,
	title = {Determination of the {Equivalent} {Radii} and {Fractal} {Dimension} of {Polystyrene} {Latex} {Aggregates} from {Sedimentation} {Coefficients}},
	volume = {202},
	issn = {0021-9797},
	url = {https://www.sciencedirect.com/science/article/pii/S0021979798954285},
	doi = {10.1006/jcis.1998.5428},
	abstract = {Sedimentation coefficients of small polystyrene latex aggregates (n= 2, 3, 4) were determined by centrifugation of a coagulated latex sample within a density gradient and fitted to theR* =ncrequation, whereR* is the equivalent radius of the aggregate,ris the radius of each individual sphere, andc= 0.58. This equation was also satisfactorily used to fit latex aggregate diffusion data, previously published by other authors. The constantcagrees with the value calculated from the fractal dimensionDfreported for larger aggregates in the literature, usingc= 1/Df. As a conclusion, aggregate sedimentation and diffusion coefficients can be obtained from light-scattering and microscopical data, and vice versa, using a scaling factor which is related to the aggregate fractal dimension.},
	language = {en},
	number = {1},
	urldate = {2023-05-02},
	journal = {Journal of Colloid and Interface Science},
	author = {Takayasu, Miriam Michiyo and Galembeck, Fernando},
	month = jun,
	year = {1998},
	keywords = {aggregates, diffusion of aggregates, equivalent radii, fractal dimension of aggregates, PS latex aggregates, sedimentation of aggregates},
	pages = {84--88},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/TF6GU27I/Takayasu and Galembeck - 1998 - Determination of the Equivalent Radii and Fractal .pdf:application/pdf},
}

@article{wiltzius_hydrodynamic_1987,
	title = {Hydrodynamic behavior of fractal aggregates},
	volume = {58},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.58.710},
	doi = {10.1103/PhysRevLett.58.710},
	abstract = {Measurements of the radius of gyration RG and the hydrodynamic radius RH of colloidal silica aggregates are reported. These aggregates have fractal geometry and RH is proportional to RG for 500 Å≤RH≤7000 Å, with a ratio RH/RG=0.72±0.02. The results are compared with predictions for macromolecules of various shapes. The proportionality of the two radii can be understood with use of the pair correlation function of fractal objects and hydrodynamic interactions on the Oseen level. The value of the ratio remains to be explained.},
	number = {7},
	urldate = {2023-05-02},
	journal = {Physical Review Letters},
	author = {Wiltzius, Pierre},
	month = feb,
	year = {1987},
	note = {Publisher: American Physical Society},
	pages = {710--713},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/4PRMW4QP/PhysRevLett.58.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/HR5HEZI2/Wiltzius - 1987 - Hydrodynamic behavior of fractal aggregates.pdf:application/pdf},
}

@article{kolb_anisotropic_1987,
	title = {Anisotropic {Diffusion} {Limited} {Aggregation}: {From} {Self}-{Similarity} to {Self}-{Affinity}},
	volume = {4},
	issn = {0295-5075},
	shorttitle = {Anisotropic {Diffusion} {Limited} {Aggregation}},
	url = {https://dx.doi.org/10.1209/0295-5075/4/1/014},
	doi = {10.1209/0295-5075/4/1/014},
	abstract = {Diffusion-limited particle aggregation is simulated with a modified growth rule. By means of a parameter the growth anisotropy along the axes of symmetry can be varied continually from isotropic to strongly anisotropic. For weak anisotropy one initially observes an isotropic structure with a fractal dimension D = 1.7 which crosses over to an anisotropic structure with two different scaling exponents Daxial = 1.5 and Ddiagonal = 2.0 along the axes, respectively, along the diagonals, on a square lattice. One can understand the growth in the anisotropic regime in terms of classical aggregation, where the fluctuations are neglected.},
	language = {en},
	number = {1},
	urldate = {2023-05-02},
	journal = {Europhysics Letters},
	author = {Kolb, M.},
	month = jul,
	year = {1987},
	pages = {85},
	file = {IOP Full Text PDF:/Users/eunji/Zotero/storage/UITDHL7S/Kolb - 1987 - Anisotropic Diffusion Limited Aggregation From Se.pdf:application/pdf},
}

@article{witten_tenuous_1986,
	title = {Tenuous {Structures} from {Disorderly} {Growth} {Processes}},
	volume = {232},
	url = {https://www.science.org/doi/10.1126/science.232.4758.1607},
	doi = {10.1126/science.232.4758.1607},
	abstract = {Colloidal aggregation and other random growth processes produce structures that behave differently from ordinary bulk matter. Much of this behavior can be described in terms of the invariance of the aggregates under changes of spatial length scale: they appear to be fractals. There are two types of basic mechanisms for producing fractal aggregates. Those in which aggregation proceeds cluster by cluster can be understood qualitatively in terms of a solvable schematic model. The diffusion-limited aggregation or deposition of individual particles to make a large cluster is not as well understood. It is closely related to several irreversible processes in other areas of physics, such as two-fluid displacement in porous materials and the dielectric breakdown of insulators. More generally, disorderly growth mechanisms provide structures having unique properties, many of which can be understood by using simple statistical principles.},
	number = {4758},
	urldate = {2023-05-02},
	journal = {Science},
	author = {Witten, T. A. and Cates, M. E.},
	month = jun,
	year = {1986},
	note = {Publisher: American Association for the Advancement of Science},
	pages = {1607--1612},
}

@article{rosenstock_cluster_1980,
	title = {Cluster formation in two-dimensional random walks: {Application} to photolysis of silver halides},
	volume = {22},
	shorttitle = {Cluster formation in two-dimensional random walks},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.22.5797},
	doi = {10.1103/PhysRevB.22.5797},
	abstract = {As a model for the growth of silver aggregates on the surface of silver halide crystallites, we have studied the following problem: Independent ions perform random walks on a closed two-dimensional lattice containing, initially, one trap; when a walker reaches a site adjacent to a trap, that site itself becomes a trap. Several simplifications are necessary and justifiable to enable us to use standard random-walk theory: they include replacing the actual crystallite surface by a toroidal one, averaging over all starting points at an early stage, and replacing the irregularly growing cluster by a simply shaped one. Upper and lower limits on the rate of cluster growth are obtained, and results are fitted to experimental observations.},
	number = {12},
	urldate = {2023-05-02},
	journal = {Physical Review B},
	author = {Rosenstock, Herbert B. and Marquardt, Charles L.},
	month = dec,
	year = {1980},
	note = {Publisher: American Physical Society},
	pages = {5797--5809},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/357W77SU/PhysRevB.22.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/JB999JMJ/Rosenstock and Marquardt - 1980 - Cluster formation in two-dimensional random walks.pdf:application/pdf},
}

@article{park_performance_2020,
	title = {The {Performance} of {Low}-{Pressure} {Seawater} as a {CO2} {Solvent} in {Underwater} {Air}-{Independent} {Propulsion} {Systems}},
	volume = {8},
	copyright = {http://creativecommons.org/licenses/by/3.0/},
	issn = {2077-1312},
	url = {https://www.mdpi.com/2077-1312/8/1/22},
	doi = {10.3390/jmse8010022},
	abstract = {Air-independent propulsion systems have improved the performance and decreased the vulnerability of underwater weapon systems. Reforming systems, however, generates large amounts of water and CO2. The recovery or separation of CO2, a residual gas component generated in vessels, entails considerable cost and energy consumption. It is necessary to understand the characteristics of the interaction between CO2 and seawater under the conditions experienced by underwater weapon systems to design and optimize a CO2 treatment process for dissolving CO2 in seawater. In this study, numerical analysis was conducted using the derived experimental concentration and MATLAB. The diffusion coefficient was derived as a function of temperature according to the CO2 dissolution time. Experiments on CO2 dissolution in seawater were conducted. The concentration of CO2 according to the reaction pressure and experimental temperature was obtained. The diffusion coefficient between CO2 and seawater was found to be 6.3 × 10−5 cm2/s at 25 °C and 7.24 × 10−5 cm2/s at 32 °C. CO2 concentration could be estimated accurately under vessel operating conditions using the derived CO2 diffusion coefficients. Optimal design of the residual gas treatment process will be possible using the derived seawater–CO2 diffusion coefficients under the actual operating conditions experienced by underwater weapon systems.},
	language = {en},
	number = {1},
	urldate = {2023-05-01},
	journal = {Journal of Marine Science and Engineering},
	author = {Park, Eun-Young and Choi, Jungho},
	month = jan,
	year = {2020},
	note = {Number: 1
Publisher: Multidisciplinary Digital Publishing Institute},
	keywords = {carbon dioxide, CO$_{\textrm{2}}$ dissolution, diffusion, diffusion coefficient, underwater weapon systems},
	pages = {22},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/LIRMBJFC/Park and Choi - 2020 - The Performance of Low-Pressure Seawater as a CO2 .pdf:application/pdf},
}

@article{zhang_modeling_2015,
	series = {The assessment of {CO2} utilization technology in {China}},
	title = {The modeling and experimental studies on the diffusion coefficient of {CO2} in saline water},
	volume = {11},
	issn = {2212-9820},
	url = {https://www.sciencedirect.com/science/article/pii/S2212982015000025},
	doi = {10.1016/j.jcou.2014.12.009},
	abstract = {In order to study the law of migration and diffusion of CO2 in brine and promote large-scale CO2 gas sequestration projects in saline aquifers, this thesis commits a series of experiments to explore the diffusion coefficient of CO2 in saline water and the factors which may have an impact on it. Thus a set of innovative diffusion experimental installations to measure the diffusion properties of CO2 in the brine under different conditions are designed and manufactured, building a diffusion coefficient prediction mathematical model. This thesis acquires the diffusion coefficient of CO2 in the saline water under different conditions by means of laboratory experiments and analysis of the results, analyzing the influence that the factors such as temperature, injection pressure, salinity have on the diffusion coefficient of CO2 in saline water, calculating different diffusion coefficient of CO2. And thesis also applies a method which uses pH value to calculate diffusion coefficient of CO2 and acquires the result.},
	language = {en},
	urldate = {2023-05-01},
	journal = {Journal of CO2 Utilization},
	author = {Zhang, Weidong and Wu, Shuangliang and Ren, Shaoran and Zhang, Liang and Li, Juntao},
	month = sep,
	year = {2015},
	keywords = {CO geological storage, Diffusion coefficient, Experimental research, Model},
	pages = {49--53},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/DJFVE2J4/Zhang et al. - 2015 - The modeling and experimental studies on the diffu.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/5YYGWQYU/S2212982015000025.html:text/html},
}

@article{prairie_delayed_2013,
	title = {Delayed settling of marine snow at sharp density transitions driven by fluid entrainment and diffusion-limited retention},
	volume = {487},
	issn = {0171-8630, 1616-1599},
	url = {https://www.int-res.com/abstracts/meps/v487/p185-200/},
	doi = {10.3354/meps10387},
	abstract = {Marine snow is central to the marine carbon cycle, and quantifying its small-scale settling dynamics in different physical environments is essential to understanding its role in biogeochemical cycles. Previous field observations of marine aggregate thin layers associated with sharp density gradients have led to the hypothesis that these layers may be caused by a decrease in aggregate settling speed at density interfaces. Here, we present experimental data on aggregate settling behavior, showing that these particles can dramatically decrease their settling velocity when passing through sharp density transitions. This delayed settling can be caused by 2 potential mechanisms: (1) entrainment of lighter fluid from above as the particle passes through the density gradient, and (2) retention at the transition driven by changes in the density of the particle due to its porosity. The aggregates observed in this study exhibited 2 distinct settling behaviors when passing through the density transition. Quantitatively comparing these different behaviors with predictions from 2 models allow us to infer that the delayed settling of the first group of aggregates was primarily driven by diffusion-limited retention, whereas entrainment of lighter fluid was the dominant mechanism for the second group. Coupled with theory, our experimental results demonstrate that both entrainment and diffusion-limited retention can play an important role in determining particle settling dynamics through density transitions. This study thus provides insight into ways that delayed settling can lead to the formation of aggregate thin layers, important biological hotspots that affect trophic dynamics, and biogeochemical cycling in the ocean.},
	language = {en},
	urldate = {2023-05-01},
	journal = {Marine Ecology Progress Series},
	author = {Prairie, Jennifer C. and Ziervogel, Kai and Arnosti, Carol and Camassa, Roberto and Falcon, Claudia and Khatri, Shilpa and McLaughlin, Richard M. and White, Brian L. and Yu, Sungduk},
	month = jul,
	year = {2013},
	keywords = {Accumulation, Aggregation, Biophysical coupling, Hotspots, Thin layer},
	pages = {185--200},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/5NWB99SX/Prairie et al. - 2013 - Delayed settling of marine snow at sharp density t.pdf:application/pdf},
}

@article{zhang_direct_2015,
	title = {Direct {Simulation} of {Drag} {Force} on {Fractal} {Flocs} during {Settling}},
	volume = {73},
	issn = {0749-0208, 1551-5036},
	url = {https://bioone.org/journals/journal-of-coastal-research/volume-73/issue-sp1/SI73-129.1/Direct-Simulation-of-Drag-Force-on-Fractal-Flocs-during-Settling/10.2112/SI73-129.1.full},
	doi = {10.2112/SI73-129.1},
	abstract = {Zhang, J. and Zhang, Q., 2015. Direct simulation of drag force on fractal flocs during settling.The hydrodynamic drag force of fractal flocs during settling is examined by the Lattice Boltzmann method. Fractal flocs formed by Diffusion-Limited Aggregation (DLA) and diffusion-limited-cluster-cluster aggregation (DLCCA) models settle down in the quiescent water and drag forces are directly calculated. The numerical simulations are consistent with the analytical results. The ratio of drag force on fractal flocs and floc size shows a linear relationship with the floc settling velocity when the flow filed around the flocs is Stokes flow. The drag coefficient experienced by flocs is significantly different from the spheres. Moreover, drag forces on flocs formed by DLCCA are larger than flocs formed by DLA, when the flocs are composed of the same primary particles.},
	number = {sp1},
	urldate = {2023-05-01},
	journal = {Journal of Coastal Research},
	author = {Zhang, Jinfeng and Zhang, Qinghe},
	month = jan,
	year = {2015},
	note = {Publisher: Coastal Education and Research Foundation},
	pages = {753--757},
}

@article{tang_model_2002,
	title = {A {Model} to {Describe} the {Settling} {Behavior} of {Fractal} {Aggregates}},
	volume = {247},
	issn = {0021-9797},
	url = {https://www.sciencedirect.com/science/article/pii/S0021979701980282},
	doi = {10.1006/jcis.2001.8028},
	abstract = {A model to predict fractal dimension from sedimentating fractal aggregates has been successfully developed. This model was developed using the settling rate and size data of fractal aggregates. In order to test the validity of the model, a purpose-built settling rig, equipped with lens with magnification of 1200×, which can capture images of particles/flocs down to 2 μm in diameter was used. The performace and technique of the settling rig were validated by comparing the measured settling rates of 30- and 50.7-μm standard particles with their theoretical settling rates calculated using Stokes' law. The measured settling rates were within 10\% agreement with the calculated Stokes' velocities. The settling rates and sizes of the particles/flocs were analyzed using image analysis software called WiT 5.3. The maximum temperature gradient across the settling column was 0.1°C, which effectively eliminated convective currents due to temperature differences in the settling column. A total of 1000 calcium phosphate flocs were anaylzed. Calcium phosphate flocs with fractal dimensions varying from 2.3 to 2.8 were generated via orthokinetic aggregation. Measurements of fractal dimensions, using light scattering, were done simultaneously with the settling experiments and they were found to be constant. The fractal dimensions calculated using the model agreed with those obtained by light scattering to within 12\%.},
	language = {en},
	number = {1},
	urldate = {2023-05-01},
	journal = {Journal of Colloid and Interface Science},
	author = {Tang, P. and Greenwood, J. and Raper, J. A.},
	month = mar,
	year = {2002},
	keywords = {fractal aggregates, fractal dimension, sedimentation, Stokes' law},
	pages = {210--219},
	file = {ScienceDirect Snapshot:/Users/eunji/Zotero/storage/WDBFM2CG/S0021979701980282.html:text/html},
}

@book{delves_numerical_1974,
	title = {Numerical {Solution} of {Integral} {Equations}},
	url = {https://books.google.com/books?id=tuqQwgEACAAJ},
	publisher = {Clarendon Press},
	author = {Delves, L.M. and Walsh, J. and Mathematics, University of Manchester Department of and Computational, University of Liverpool Department of and Science, Statistical},
	year = {1974},
	lccn = {10094267},
}

@article{youngren_stokes_1975,
	title = {Stokes flow past a particle of arbitrary shape: a numerical method of solution},
	volume = {69},
	issn = {1469-7645, 0022-1120},
	shorttitle = {Stokes flow past a particle of arbitrary shape},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/stokes-flow-past-a-particle-of-arbitrary-shape-a-numerical-method-of-solution/1DD984501FDD52C7F88811182CD4D286},
	doi = {10.1017/S0022112075001486},
	abstract = {The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear integral equations of the first kind for a distribution of Stokeslets over the particle surface. The unknown density of Stokeslets is identical with the surface-stress force and can be obtained numerically by reducing the integral equations to a system of linear algebraic equations. This appears to be an efficient way of determining solutions for several external flows past a particle, since it requires that the matrix of the algebraic system be inverted only once for a given particle.The technique was tested successfully against the analytic solutions for spheroids in uniform and simple shear flows, and was then applied to two problems involving the motion of finite circular cylinders: (i) a cylinder translating parallel to its axis, for which the local stress force distribution and the drag were determined; and (ii) the equivalent axis ratio of a freely suspended cylinder, which was calculated by determining the couple on a stationary cylinder placed symmetrically in two different simple shear flows. The numerical results were found to be consistent with the asymptotic analysis of Cox (1970, 1971) and in excellent agreement with the experiments of Anczurowski \& Mason (1968), but not with those of Harris \& Pittman (1975).},
	language = {en},
	number = {2},
	urldate = {2023-04-28},
	journal = {Journal of Fluid Mechanics},
	author = {Youngren, G. K. and Acrivos, A.},
	month = may,
	year = {1975},
	note = {Publisher: Cambridge University Press},
	pages = {377--403},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/K456XKBK/Youngren and Acrivos - 1975 - Stokes flow past a particle of arbitrary shape a .pdf:application/pdf},
}

@book{stakgold_boundary_2000,
	series = {Classics in {Applied} {Mathematics}},
	title = {Boundary {Value} {Problems} of {Mathematical} {Physics}: {Volume} 1},
	isbn = {978-0-89871-456-2},
	shorttitle = {Boundary {Value} {Problems} of {Mathematical} {Physics}},
	url = {https://epubs.siam.org/doi/book/10.1137/1.9780898719888},
	urldate = {2023-04-28},
	publisher = {Society for Industrial and Applied Mathematics},
	author = {Stakgold, Ivar},
	month = jan,
	year = {2000},
	doi = {10.1137/1.9780898719888},
	keywords = {potential theory, boundary value problems, mathematical physics},
}

@article{honjo_understanding_2014,
	title = {Understanding the {Role} of the {Biological} {Pump} in the {Global} {Carbon} {Cycle}: {An} {Imperative} for {Ocean} {Science}},
	volume = {27},
	issn = {10428275},
	shorttitle = {Understanding the {Role} of the {Biological} {Pump} in the {Global} {Carbon} {Cycle}},
	url = {https://tos.org/oceanography/article/understanding-the-role-of-the-biological-pump-in-the-globalcarbon-cycle-an-},
	doi = {10.5670/oceanog.2014.78},
	number = {3},
	urldate = {2023-04-26},
	journal = {Oceanography},
	author = {Honjo, Susumu and Eglinton, Timothy and Taylor, Craig and Ulmer, Kevin and Sievert, Stefan and Bracher, Astrid and German, Christopher and Edgcomb, Virginia and Francois, Roger and Iglesias-Rodriguez, M. Debora and Van Mooy, Benjamin and Rapeta, Daniel},
	month = sep,
	year = {2014},
	pages = {10--16},
	file = {Full Text:/Users/eunji/Zotero/storage/W9W2J8WJ/Honjo et al. - 2014 - Understanding the Role of the Biological Pump in t.pdf:application/pdf},
}

@article{alldredge_occurrence_2002-1,
	title = {Occurrence and mechanisms of formation of a dramatic thin layer of marine snow in a shallow {Pacific} fjord},
	volume = {233},
	issn = {0171-8630, 1616-1599},
	url = {https://www.int-res.com/abstracts/meps/v233/p1-12/},
	doi = {10.3354/meps233001},
	abstract = {Huge accumulations of diatom-dominated marine snow (aggregates {\textgreater}0.5 mm in diameter) were observed in a layer approximately 50 cm thick persisting over a 24 h period in a shallow fjord in the San Juan Islands, Washington, USA. The layer was
associated with the 22.4 σt density surface. A second thin layer of elevated phytoplankton concentration located at a density discontinuity 1.5 to 2 m above the marine snow layer occurred within a dense diatom bloom
near the surface. At the end of the study period, isopycnals shoaled and the 2 layers merged. More than 80\% of the diatom bloom consisted of Thalassiosira spp. (50 to 59\%), Odontella longicruris (5 to 14\%), Asterionellopsis glacialis,
and Thalassionema nitzschioides. A much higher proportion of O. longicruris occurred in marine snow (about 53\%) than among suspended cells suggesting that this species differentially aggregated. Most zooplankton avoided the mucus-rich
aggregate layer. The layer of marine snow was formed when sinking aggregated diatoms reached neutral buoyancy at the 22.4 isopycnal, probably due to the presence of low salinity mucus resistant to salt exchange in the interstices of the aggregates. Rates
of turbulent kinetic energy dissipation throughout the water column rarely exceeded 10-8 m2 s-3 and aggregates below the thin layer were largely detrital in composition indicating that small-scale shears due to turbulence
did not erode the layer of marine snow. The accumulation of marine snow and phytoplankton in persistent, discrete layers at density discontinuities results in habitat partitioning of the pelagic zone, impacts the distribution and interactions of
planktonic organisms as well as the intensity and location of biological processes in the water column, and helps maintain species diversity.},
	language = {en},
	urldate = {2023-04-24},
	journal = {Marine Ecology Progress Series},
	author = {Alldredge, Alice L. and Cowles, Timothy J. and MacIntyre, Sally and Rines, Jan E. B. and Donaghay, Percy L. and Greenlaw, Charles F. and Holliday, D. V. and Dekshenieks, Margaret M. and Sullivan, James M. and Zaneveld, J. Ronald V.},
	month = may,
	year = {2002},
	keywords = {Marine snow, Density discontinuity, Diatom bloom flocculation, Plankton distribution, Plankton patchiness, Thin layers},
	pages = {1--12},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/7GMQV7DR/Alldredge et al. - 2002 - Occurrence and mechanisms of formation of a dramat.pdf:application/pdf},
}

@article{jackson_simulation_1989,
	title = {Simulation of bacterial attraction and adhesion to falling particles in an aquatic environment},
	volume = {34},
	issn = {1939-5590},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.4319/lo.1989.34.3.0514},
	doi = {10.4319/lo.1989.34.3.0514},
	abstract = {Chemosensory movement of bacteria toward the cloud of leaked material around planktonic algae has been suggested as an important aspect of bacterial nutrition in aquatic ecosystems. Inability of bacteria to keep pace with falling algae has been suggested as inhibiting such interactions. The interaction between bacteria and falling particles, including microalgae, is explored with a simulation model of bacterial chemotaxis that incorporates low Reynolds number fluid flow and resulting substrate spatial distributions. Results show that although bacteria cannot maintain a position relative to a falling particle unless the particle is extremely large, such as a marine snow aggregate, chemosensory response does allow them to stay in the high substrate environment of the leaky particle longer than if they did not have it. The ecological significance for bacterial metabolism depends on several factors, including the frequency of contact between algae and bacteria and the relative concentrations of substrate at the cell surface and in the background. Optimal enhancement should occur in eutrophic conditions of large algal cells present in high abundances. Presently available values for the ratio of substrate concentration next to the algal cell relative to that in solution are not large enough to suggest that the microzones around algal cells provide significant enhancement of bacterial nutrition. Chemotaxis should enhance interactions with large marine snow aggregates, both by allowing bacteria to stay for significant periods around them and by enhancing the rates at which bacteria attach to the aggregate surfaces. This enhancement is greater for surfaces in which there is a lower probability of sticking.},
	language = {en},
	number = {3},
	urldate = {2023-04-24},
	journal = {Limnology and Oceanography},
	author = {Jackson, George A.},
	year = {1989},
	% note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.4319/lo.1989.34.3.0514},
	pages = {514--530},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/28WGKL6F/Jackson - 1989 - Simulation of bacterial attraction and adhesion to.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/L5GXZ796/lo.1989.34.3.html:text/html},
}

@article{sharqawy_thermophysical_2010,
	title = {Thermophysical properties of seawater: a review of existing correlations and data},
	volume = {16},
	issn = {1944-3994},
	shorttitle = {Thermophysical properties of seawater},
	url = {https://doi.org/10.5004/dwt.2010.1079},
	doi = {10.5004/dwt.2010.1079},
	abstract = {Correlations and data for the thermophysical properties of seawater are reviewed. Properties examined include density, specific heat capacity, thermal conductivity, dynamic viscosity, surface tension, vapor pressure, boiling point elevation, latent heat of vaporization, specifi c enthalpy, specific entropy and osmotic coefficient. These properties include those needed for design of thermal and membrane desalination processes. Results are presented in terms of regression equations as functions of temperature and salinity. The available correlations for each property are summarized with their range of validity and accuracy. Best-fi tted new correlations are obtained from available data for density, dynamic viscosity, surface tension, boiling point elevation, specifi c enthalpy, specific entropy and osmotic coefficient after appropriate conversion of temperature and salinity scales to the most recent standards. In addition, a model for latent heat of vaporization is suggested. Comparisons are carried out among these correlations, and recommendations are provided for each property, particularly over the ranges of temperature and salinity common in thermal and/or reverse osmosis seawater desalination applications.},
	number = {1-3},
	urldate = {2023-02-09},
	journal = {Desalination and Water Treatment},
	author = {Sharqawy, Mostafa H. and Lienhard, John H. and Zubair, Syed M.},
	month = apr,
	year = {2010},
	% note = {Publisher: Taylor \& Francis\_eprint: https://doi.org/10.5004/dwt.2010.1079},
	keywords = {Surface tension, Boiling point elevation, Density, Enthalpy, Entropy, Latent heat, Osmotic coefficient, Seawater, Specific heat, Thermal conductivity, Thermophysical properties, Vapor pressure, Viscosity},
	pages = {354--380},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/MRAM83A2/Sharqawy et al. - 2010 - Thermophysical properties of seawater a review of.pdf:application/pdf},
}

@article{nayar_thermophysical_2016,
	title = {Thermophysical properties of seawater: {A} review and new correlations that include pressure dependence},
	volume = {390},
	issn = {0011-9164},
	shorttitle = {Thermophysical properties of seawater},
	url = {https://www.sciencedirect.com/science/article/pii/S0011916416300807},
	doi = {10.1016/j.desal.2016.02.024},
	abstract = {In a previous paper, the authors have given correlations for seawater thermophysical properties as functions of temperature and salinity, but only for near atmospheric pressures. Seawater reverse osmosis (SWRO) systems operate routinely at pressures of 6MPa or more; however, experimental data for seawater properties at elevated pressures (P=0.1–12MPa) are limited to a salinity of 56g/kg. To accurately model and design SWRO and thermal desalination systems, a reliable method of estimating the effect of pressure on seawater properties is required. In this work, we present this method and new correlations for seawater thermophysical properties that are valid within the range: t=0–120°C, S=0–120g/kg, and P=0–12MPa. Seawater isothermal compressibility data, available until a salinity of 56g/kg, were used to develop a correlation for compressibility that is extrapolated to 160g/kg. Thermodynamic identities were then used to develop accurate pressure dependent correlations for seawater: density, isobaric expansivity, specific heat capacity, enthalpy, entropy and Gibbs energy. New correlations were proposed for seawater: vapor pressure, thermal conductivity and activity of water. Recent work on seawater surface tension and osmotic coefficient were reviewed. Uncertainty bounds were calculated for each correlation.},
	language = {en},
	urldate = {2023-02-09},
	journal = {Desalination},
	author = {Nayar, Kishor G. and Sharqawy, Mostafa H. and Banchik, Leonardo D. and Lienhard V, John H.},
	month = jul,
	year = {2016},
	keywords = {Surface tension, Density, Enthalpy, Entropy, Osmotic coefficient, Seawater, Thermal conductivity, Thermophysical properties, Activity, Gibbs energy, Isobaric thermal expansivity, Isothermal compressibility, Specific heat capacity},
	pages = {1--24},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/5KG5ZBSH/Nayar et al. - 2016 - Thermophysical properties of seawater A review an.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/M4Y2SI6J/S0011916416300807.html:text/html},
}

@article{wollast_diffusion_1971,
	title = {Diffusion {Coefficient} of {Silica} in {Seawater}},
	volume = {229},
	copyright = {1971 Nature Publishing Group},
	issn = {2058-1106},
	url = {https://www.nature.com/articles/physci229094a0},
	doi = {10.1038/physci229094a0},
	abstract = {THE diffusion coefficient of dissolved monomeric silica in seawater of 36.1\% salinity has been determined at 25° C by the diaphragm cell method. The value of the coefficient D is 1.0±0.05×10−5 cm2 s−1. The value at seafloor temperatures is probably about 0.5×10−5 cm2 s−1 and is consistent with empirical diffusion coefficients of silica in pore water-sediment systems of the order of 0.1 to 0.3×10−5 cm2 s−1, when corrections for porosity are made.},
	language = {en},
	number = {3},
	urldate = {2023-02-09},
	journal = {Nature Physical Science},
	author = {Wollast, Roland and Garrels, Robert M.},
	month = jan,
	year = {1971},
	note = {Number: 3
Publisher: Nature Publishing Group},
	keywords = {general, Physics},
	pages = {94--94},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/PBHQS7DG/Wollast and Garrels - 1971 - Diffusion Coefficient of Silica in Seawater.pdf:application/pdf},
}

@article{omand_sinking_2020,
	title = {Sinking flux of particulate organic matter in the oceans: {Sensitivity} to particle characteristics},
	volume = {10},
	copyright = {2020 The Author(s)},
	issn = {2045-2322},
	shorttitle = {Sinking flux of particulate organic matter in the oceans},
	url = {https://www.nature.com/articles/s41598-020-60424-5},
	doi = {10.1038/s41598-020-60424-5},
	abstract = {The sinking of organic particles produced in the upper sunlit layers of the ocean forms an important limb of the oceanic biological pump, which impacts the sequestration of carbon and resupply of nutrients in the mesopelagic ocean. Particles raining out from the upper ocean undergo remineralization by bacteria colonized on their surface and interior, leading to an attenuation in the sinking flux of organic matter with depth. Here, we formulate a mechanistic model for the depth-dependent, sinking, particulate mass flux constituted by a range of sinking, remineralizing particles. Like previous studies, we find that the model does not achieve the characteristic ‘Martin curve’ flux profile with a single type of particle, but instead requires a distribution of particle sizes and/or properties. We consider various functional forms of remineralization appropriate for solid/compact particles, and aggregates with an anoxic or oxic interior. We explore the sensitivity of the shape of the flux vs. depth profile to the choice of remineralization function, relative particle density, particle size distribution, and water column density stratification, and find that neither a power-law nor exponential function provides a definitively superior fit to the modeled profiles. The profiles are also sensitive to the time history of the particle source. Varying surface particle size distribution (via the slope of the particle number spectrum) over 3 days to represent a transient phytoplankton bloom results in transient subsurface maxima or pulses in the sinking mass flux. This work contributes to a growing body of mechanistic export flux models that offer scope to incorporate underlying dynamical and biological processes into global carbon cycle models.},
	language = {en},
	number = {1},
	urldate = {2023-02-09},
	journal = {Scientific Reports},
	author = {Omand, Melissa M. and Govindarajan, Rama and He, Jing and Mahadevan, Amala},
	month = mar,
	year = {2020},
	note = {Number: 1
Publisher: Nature Publishing Group},
	keywords = {Biogeochemistry, Physical oceanography},
	pages = {5582},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/5SQCMB9N/Omand et al. - 2020 - Sinking flux of particulate organic matter in the .pdf:application/pdf},
}

@article{henson_global_2012-1,
	title = {Global patterns in efficiency of particulate organic carbon export and transfer to the deep ocean},
	volume = {26},
	issn = {1944-9224},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1029/2011GB004099},
	doi = {10.1029/2011GB004099},
	abstract = {The ocean's biological carbon pump is a key component of the global carbon cycle. Only a small fraction of the carbon fixed by primary production is exported to the deep ocean, yet this flux sets to first order the efficiency with which carbon is sequestered out of further contact with the atmosphere on long time scales. Here we examine global patterns in particle export efficiency (PEeff), the proportion of primary production that is exported from the surface ocean, and transfer efficiency (Teff), the fraction of exported organic matter that reaches the deep ocean. Previous studies have found a positive correlation between Teff and deep ocean calcite fluxes recovered from sediment traps, implying that ballasting by calcium carbonate may play an important role in regulating Teff. An alternative explanation is that this correlation is not causative, as regions where the dominant biomineral phase is calcite tend to be subtropical systems, which are hypothesized to produce sinking aggregates highly resistant to degradation. We attempt to distinguish between these alternative hypotheses on the control of Teff by examining the relationship between Teff and biomineral phases exported from the upper ocean, rather than those collected in deep traps. Global scale estimates derived from satellite data show, in keeping with earlier studies, that PEeff is high at high latitudes and low at low latitudes, but that Teff is low at high latitudes and high at low latitudes. However, in contrast to the relationship observed for deep biomineral fluxes in previous studies, we find that Teff is strongly negatively correlated with opal export flux from the upper ocean, but uncorrelated with calcium carbonate export flux. We hypothesize that the underlying factor governing the spatial patterns observed in Teff is ecosystem function, specifically the degree of recycling occurring in the upper ocean, rather than the availability of calcium carbonate for ballasting.},
	language = {en},
	number = {1},
	urldate = {2023-02-09},
	journal = {Global Biogeochemical Cycles},
	author = {Henson, Stephanie A. and Sanders, Richard and Madsen, Esben},
	year = {2012},
	% note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2011GB004099},
	keywords = {carbon export, global, POC flux, satellite data},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/3SS7BZWY/Henson et al. - 2012 - Global patterns in efficiency of particulate organ.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/JGNEGH65/2011GB004099.html:text/html},
}

@article{xue_modelling_2011,
	title = {Modelling and simulation of the behaviour of a biofluid in a microchannel biochip separator.},
	volume = {14},
	doi = {10.1080/10255842.2010.485570},
	abstract = {This paper reports an investigation into the flow behaviour of a biofluid in a microchannel systems through conceptual analysis and modelling. The application is the design of a microfluidic chip developed for the separation of plasma from blood. The effect of key design features of the microchannels on the flow behaviour of the biofluid is explored. These include geometric features such as the constriction, bending channel, bifurcation and the channel length ratio between the main and side channels. The performance of each design is discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. Particular phenomena such as the Fahraeus and Fahraeus–Lindqvist effects, the Zweifach–Fung bifurcation law and the cell-free layer are discussed. In this paper, the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviour to investigate the effect of the fluid viscosity on both flow and separation efficiency. For a flow rate-controll...},
	number = {6},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	author = {Xue, Xiangdong and Patel, Mayur and Kersaudy-Kerhoas, Maïwenn and Bailey, Chris and Desmulliez, Marc P.Y.},
	month = feb,
	year = {2011},
	doi = {10.1080/10255842.2010.485570},
	pmid = {21331958},
	note = {MAG ID: 2155686705
S2ID: 92060881d1f595c42e3aaa2d8ea695859036579e},
	pages = {549--560},
	file = {Xue et al. - 2011 - Modelling and simulation of the behaviour of a bio.pdf:/Users/eunji/Zotero/storage/9BTV3YZL/Xue et al. - 2011 - Modelling and simulation of the behaviour of a bio.pdf:application/pdf},
}

@article{naillon_dynamics_2019,
	title = {Dynamics of particle migration in confined viscoelastic {Poiseuille} flows},
	volume = {4},
	url = {https://link.aps.org/doi/10.1103/PhysRevFluids.4.053301},
	doi = {10.1103/PhysRevFluids.4.053301},
	abstract = {Particles migrate in the transverse direction of the flow due to the existence of normal stress anisotropy in weakly viscoelastic liquids. We test the ability of theoretical predictions to predict the transverse velocity migration of particles in a confined Poiseuille flow according to the viscoelastic constitutive parameters of dilute polymer solutions. First, we carefully characterize the viscoelastic properties of two families of dilute polymer solutions at various concentrations using shear rheometry and capillary breakup experiments. Second, we develop a specific three-dimensional particle tracking velocimetry method to measure with a high accuracy the dynamics of particles focusing in flow for Weissenberg numbers Wi ranging from 10−2 to 10−1 and particle confinement β of 0.1 and 0.2. The results show unambiguously that the migration velocity scales as Wiβ2, as expected theoretically for weakly elastic flows of an Oldroyd-B liquid. We conclude that classic constitutive viscoelastic laws are relevant to predict particle migration in dilute polymer solutions whereas detailed analysis of our results reveals that theoretical models overestimate by a few tenths the efficiency of particle focusing.},
	number = {5},
	urldate = {2022-10-31},
	journal = {Physical Review Fluids},
	author = {Naillon, Antoine and de Loubens, Clément and Chèvremont, William and Rouze, Samuel and Leonetti, Marc and Bodiguel, Hugues},
	month = may,
	year = {2019},
	note = {Publisher: American Physical Society},
	pages = {053301},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/BPCWYRPF/PhysRevFluids.4.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/GUP82FB2/Naillon et al. - 2019 - Dynamics of particle migration in confined viscoel.pdf:application/pdf},
}

@article{sverdrup_embedded_2019,
	title = {An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions},
	volume = {31},
	issn = {1070-6631},
	url = {https://aip.scitation.org/doi/10.1063/1.5110654},
	doi = {10.1063/1.5110654},
	abstract = {We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modeled by generalized Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelizable computations on block-structured grids. In this context, geometric features are handled by the embedded boundary approach, which requires specialized treatment only in cells intersecting or adjacent to the boundary. This constitutes the first published implementation of an embedded boundary algorithm for simulating flow of viscoplastic fluids on structured grids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretization, in which viscous terms are treated semi-implicitly and projection methods are utilized to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since the viscosity depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After performing convergence analysis and validating the code against standard test cases, we present the first ever fully three-dimensional simulations of creeping flow of Bingham plastics around translating objects. Our results shed new light on the flow fields around these objects.},
	number = {9},
	urldate = {2022-10-03},
	journal = {Physics of Fluids},
	author = {Sverdrup, Knut and Almgren, Ann and Nikiforakis, Nikolaos},
	month = sep,
	year = {2019},
	note = {Publisher: American Institute of Physics},
	pages = {093102},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/LGRF938L/Sverdrup et al. - 2019 - An embedded boundary approach for efficient simula.pdf:application/pdf},
}

@article{panah_simulations_2017,
	title = {Simulations of a porous particle settling in a density-stratified ambient fluid},
	volume = {2},
	url = {https://link.aps.org/doi/10.1103/PhysRevFluids.2.114303},
	doi = {10.1103/PhysRevFluids.2.114303},
	abstract = {We study numerically the settling of a porous sphere in a density-stratified ambient fluid. Simulations are validated against prior laboratory experiments and compared to two mathematical models. Two main effects cause the particle to slow down as it enters a density gradient: lighter fluid within the particle and entrainment of the density-stratified ambient fluid. The numerical simulations accurately capture the particle retention time. We quantify the delay in settling due to ambient fluid entrainment and lighter internal fluid becoming denser through diffusion as a function of the Reynolds, Péclet, and Darcy numbers, as well as the thickness of the transition layer and the ratio of the density difference between the lower and upper fluid layers to the density difference between the particle and the upper layer. A simple fitting formula is presented to describe the settling time delay as a function of each of those five nondimensional parameters.},
	number = {11},
	urldate = {2022-09-13},
	journal = {Physical Review Fluids},
	author = {Panah, Mac and Blanchette, François and Khatri, Shilpa},
	month = nov,
	year = {2017},
	note = {Publisher: American Physical Society},
	pages = {114303},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/V3VDYIS5/PhysRevFluids.2.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/ELUXZNDD/Panah et al. - 2017 - Simulations of a porous particle settling in a den.pdf:application/pdf},
}

@article{yoo_hydrodynamic_2020,
	title = {Hydrodynamic forces on randomly formed marine aggregates},
	volume = {5},
	url = {https://link.aps.org/doi/10.1103/PhysRevFluids.5.044305},
	doi = {10.1103/PhysRevFluids.5.044305},
	abstract = {We study numerically the fluid forces acting on aggregates formed by a collation of cubic particles as a model of marine aggregates in the ocean. The flow around the aggregates and the resulting stresses on the surface of the aggregates are computed in the limit of zero Reynolds number using a boundary integral method, resulting in an accurate evaluation of the flow around fractal objects. We compare a single- and double-layer integral method to compute the velocity, and we determine that the single-layer approach is more suitable to capturing the flow around aggregates. We then characterize the drag of translation flows, the torque of rotational flows, and the straining force of extensional flows acting on aggregates as a function of their size and mode of formation. We determine that the force and torque are best characterized using the gyration radius of the aggregates, and the straining force is better characterized by the maximal radius.},
	number = {4},
	urldate = {2022-09-13},
	journal = {Physical Review Fluids},
	author = {Yoo, Eunji and Khatri, Shilpa and Blanchette, François},
	month = apr,
	year = {2020},
	note = {Publisher: American Physical Society},
	pages = {044305},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/BLKR2IR2/Yoo et al. - 2020 - Hydrodynamic forces on randomly formed marine aggr.pdf:application/pdf},
}

@article{jop_constitutive_2006,
	title = {A constitutive law for dense granular flows},
	volume = {441},
	copyright = {2006 Nature Publishing Group},
	issn = {1476-4687},
	url = {https://www.nature.com/articles/nature04801},
	doi = {10.1038/nature04801},
	abstract = {Equations describing how granular materials move under shear are still a matter of debate. Jop et al. now propose a new model for dense granular flows in three dimensions, inspired by the behaviour of visco-plastic fluids such as toothpaste. The results could serve as a basic tool for modelling complex flows in geophysical or industrial applications.},
	language = {en},
	number = {7094},
	urldate = {2022-06-08},
	journal = {Nature},
	author = {Jop, Pierre and Forterre, Yoël and Pouliquen, Olivier},
	month = jun,
	year = {2006},
	note = {Number: 7094
Publisher: Nature Publishing Group},
	keywords = {rheology, granular flow, Humanities and Social Sciences, multidisciplinary, Science, surface flow},
	pages = {727--730},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/7KMEKVDT/Jop et al. - 2006 - A constitutive law for dense granular flows.pdf:application/pdf;HAL PDF Full Text:/Users/eunji/Zotero/storage/K6DYABUG/Jop et al. - 2006 - A constitutive law for dense granular flows.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/28A2ZJI3/nature04801.html:text/html},
}

@article{ingber_comparison_1999,
	title = {A comparison of integral formulations for the analysis of low {Reynolds} number flows},
	volume = {23},
	issn = {0955-7997},
	url = {https://www.sciencedirect.com/science/article/pii/S0955799798000903},
	doi = {10.1016/S0955-7997(98)00090-3},
	abstract = {Integral formulations for the analysis of low Reynolds number flows have been developed over the past 25 years. These formulations can typically be categorized as being either direct or indirect and either velocity integral equations or traction integral equations. Depending on the boundary conditions imposed for a given problem, the resulting integral formulation will result in either a Fredholm integral equation of the first kind, second kind or mixed. In general, Fredholm integral equations of the first kind lead to unstable numerical schemes based upon discretization and can result in low-order accuracy. For most practical problems, the direct velocity integral equation results in a Fredholm equation of the first kind. Nevertheless, many researchers have used this integral formulation with great success and any potential matrix ill-conditioning seems to have little influence on the accuracy of the numerical solutions. In this research, three integral formulations are compared, namely, the direct velocity integral equation, the indirect velocity integral equation, and the direct traction integral equation. Three benchmark problems are chosen for which there are analytic solutions. Although the discretized matrix condition numbers are in some cases orders of magnitude larger for the direct velocity integral formulation, there is little to distinguish between the three methods in terms of accuracy. In fact, the results for the direct velocity integral equation were slightly more accurate in most cases for the three benchmark problems considered in this research.},
	language = {en},
	number = {4},
	urldate = {2021-09-13},
	journal = {Engineering Analysis with Boundary Elements},
	author = {Ingber, M. S. and Mammoli, A. A.},
	month = apr,
	year = {1999},
	keywords = {Fredholm integral equations, Indirect and direct boundary element methods, Low Reynolds number flows, Suspension flows},
	pages = {307--315},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/HVMKS345/Ingber and Mammoli - 1999 - A comparison of integral formulations for the anal.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/YGZSMVJL/S0955799798000903.html:text/html},
}

@book{pozrikidis_boundary_1992,
	address = {Cambridge},
	series = {Cambridge {Texts} in {Applied} {Mathematics}},
	title = {Boundary {Integral} and {Singularity} {Methods} for {Linearized} {Viscous} {Flow}},
	isbn = {978-0-521-40502-7},
	url = {https://www.cambridge.org/core/books/boundary-integral-and-singularity-methods-for-linearized-viscous-flow/219AA1CE5DE05AE67096EA59692E25B3},
	abstract = {This book presents a coherent introduction to boundary integral, boundary element and singularity methods for steady and unsteady flow at zero Reynolds number. The focus of the discussion is not only on the theoretical foundation, but also on the practical application and computer implementation. The text is supplemented with a number of examples and unsolved problems, many drawn from the field of particulate creeping flows. The material is selected so that the book may serve both as a reference monograph and as a textbook in a graduate course on fluid mechanics or computational fluid mechanics.},
	urldate = {2021-01-13},
	publisher = {Cambridge University Press},
	author = {Pozrikidis, C.},
	year = {1992},
	doi = {10.1017/CBO9780511624124},
	file = {Pozrikidis - 1992 - Boundary Integral and Singularity Methods for Line.pdf:/Users/eunji/Zotero/storage/JQIMNNK8/Pozrikidis - 1992 - Boundary Integral and Singularity Methods for Line.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/LJ42HHMP/219AA1CE5DE05AE67096EA59692E25B3.html:text/html},
}

@article{power_second_1987,
	title = {Second {Kind} {Integral} {Equation} {Formulation} of {Stokes}’ {Flows} {Past} a {Particle} of {Arbitrary} {Shape}},
	volume = {47},
	issn = {0036-1399},
	url = {https://epubs.siam.org/doi/abs/10.1137/0147047},
	doi = {10.1137/0147047},
	abstract = {The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a distribution of Stresslets over the particle surface plus a pair of singularities (Stokeslet and Rotlet) located in the interior of the particle, singularities which give rise to a force and torque with magnitude depending linearly upon the unknown density of the surface Stresslets. It is shown that this integral equation possesses a unique continuous solution when the particle boundary is a Lyapunov surface and the velocity data on the boundary surface is continuous.},
	number = {4},
	urldate = {2019-09-18},
	journal = {SIAM Journal on Applied Mathematics},
	author = {Power, H. and Miranda, G.},
	month = aug,
	year = {1987},
	keywords = {35G15, 45F05, 45L10, 76D99, boundary value problem, second kind integral equations, Stokes’ flow},
	pages = {689--698},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/4KY3ABLM/Power and Miranda - 1987 - Second Kind Integral Equation Formulation of Stoke.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/MISDR7AM/0147047.html:text/html},
}

@article{camassa_retention_2013-1,
	title = {Retention and entrainment effects: {Experiments} and theory for porous spheres settling in sharply stratified fluids},
	volume = {25},
	issn = {1070-6631},
	shorttitle = {Retention and entrainment effects},
	url = {https://aip.scitation.org/doi/10.1063/1.4819407},
	doi = {10.1063/1.4819407},
	abstract = {We present an experimental study of single porous spheres settling in a near two-layer ambient density fluid. Data are compared with a first-principle model based on diffusive processes. The model correctly predicts accelerations of the sphere but does not capture the retention time at the density transition quantitatively. Entrainment of lighter fluid through a shell encapsulating the sphere is included in this model empirically. With this parametrization, which exhibits a power law dependence on Reynolds numbers, retention times are accurately captured. Extrapolating from our experimental data, model predictions are presented.},
	number = {8},
	urldate = {2022-08-30},
	journal = {Physics of Fluids},
	author = {Camassa, R. and Khatri, S. and McLaughlin, R. M. and Prairie, J. C. and White, B. L. and Yu, S.},
	month = aug,
	year = {2013},
	note = {Publisher: American Institute of Physics},
	pages = {081701},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/RAALKBXF/Camassa et al. - 2013 - Retention and entrainment effects Experiments and.pdf:application/pdf},
}

@article{prairie_delayed_2015,
	series = {Particles in aquatic environments: from invisible exopolymers to sinking aggregates},
	title = {Delayed settling of marine snow: {Effects} of density gradient and particle properties and implications for carbon cycling},
	volume = {175},
	issn = {0304-4203},
	shorttitle = {Delayed settling of marine snow},
	url = {https://www.sciencedirect.com/science/article/pii/S0304420315001000},
	doi = {10.1016/j.marchem.2015.04.006},
	abstract = {Marine snow aggregates are often a dominant component of carbon flux and are sites of high bacterial activity; thus, small-scale changes in the settling behavior of marine snow can affect the vertical locations of carbon export and remineralization in the surface ocean. In this study, we experimentally investigated the sinking velocities of marine snow aggregates formed in roller tanks as they settled through sharp density gradients. We observed between 8 and 10 aggregates in 3 different experiments, each of which displayed delayed settling behavior — that is, a settling velocity minimum — as they crossed the density transitions. Characteristics of delayed settling behavior were also compared to density stratification and aggregate density and size; aggregate settling velocity decreased more, and for longer periods of time, when density gradients were sharper and when aggregates were less dense. The observed relationships between non-dimensional parameters and aggregate settling allow for direct application of our results to the field, providing insight into the conditions under which strong delayed settling behavior is likely to occur. Activities of extracellular enzymes (the initial step in microbial remineralization of organic matter) were more than an order of magnitude higher in the aggregates compared to the surrounding water from which the aggregates were derived. Coupling measured enzyme activities with observations of delayed settling behavior demonstrates that the extent as well as the vertical location of enzyme activity is strongly affected by aggregate settling behavior: total enzyme activity within the region of the density transition increased by a factor of 18 with increasing stratification. This study, which combines direct measurements of small-scale aggregate settling and microbial enzyme activity, offers an opportunity to determine the potential implications of delayed settling behavior for local and larger-scale carbon cycling in the ocean.},
	language = {en},
	urldate = {2022-09-12},
	journal = {Marine Chemistry},
	author = {Prairie, Jennifer C. and Ziervogel, Kai and Camassa, Roberto and McLaughlin, Richard M. and White, Brian L. and Dewald, Carolin and Arnosti, Carol},
	month = oct,
	year = {2015},
	keywords = {Fluid dynamics, Marine snow, Aggregates, Biogeochemistry, Density gradients, Density interfaces},
	pages = {28--38},
	file = {1-s2.0-S0304420315001000-main.pdf:/Users/eunji/Zotero/storage/YTU6Y67H/1-s2.0-S0304420315001000-main.pdf:application/pdf;ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/PDXSSXAW/Prairie et al. - 2015 - Delayed settling of marine snow Effects of densit.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/X7TRANTE/S0304420315001000.html:text/html},
}

@article{singh_role_2015,
	title = {The role of gravity or pressure and contact stiffness in granular rheology},
	volume = {17},
	issn = {1367-2630},
	url = {https://doi.org/10.1088/1367-2630/17/4/043028},
	doi = {10.1088/1367-2630/17/4/043028},
	abstract = {The steady-state shear rheology of granular materials is investigated in slow quasistatic and inertial flows. The effect of gravity (thus the local pressure) and the often-neglected contact stiffness are the focus of this study. A series of particle simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various magnitudes of gravity and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate time scales, is used to describe the flow rheology, we report that a second dimensionless number, the ratio of softness and stress time scales, must also be included to characterize the bulk flow behavior. For slow, quasistatic flows, the density increases while the effective (macroscopic) friction decreases with increase in either particle softness or local pressure. This trend is added to the rheology and can be traced back to the anisotropy in the contact network, displaying a linear correlation between the effective friction coefficient and deviatoric fabric in the steady state. When the external rotation rate is increased towards the inertial regime, for a given gravity field and contact stiffness, the effective friction increases faster than linearly with the deviatoric fabric.},
	language = {en},
	number = {4},
	urldate = {2022-09-08},
	journal = {New Journal of Physics},
	author = {Singh, Abhinendra and Magnanimo, Vanessa and Saitoh, Kuniyasu and Luding, Stefan},
	month = apr,
	year = {2015},
	note = {Publisher: IOP Publishing},
	pages = {043028},
	file = {IOP Full Text PDF:/Users/eunji/Zotero/storage/RCXW22F6/Singh et al. - 2015 - The role of gravity or pressure and contact stiffn.pdf:application/pdf},
}

@article{xue_numerical_1995,
	title = {Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method},
	volume = {59},
	issn = {0377-0257},
	url = {https://www.sciencedirect.com/science/article/pii/0377025795013653},
	doi = {10.1016/0377-0257(95)01365-3},
	abstract = {In this paper, a general class of viscoelastic model is used to investigate numerically the pattern and strength of the secondary flows in rectangular pipes as well as the influence of material parameters on them. To solve the coupled governing equation system, an implicit finite volume method based on the SIMPLEST algorithm, which is applicable for both time-dependent and steady-state flow computations, has been developed and extended for viscoelastic flow computations by applying the decoupled techniques. The main feature of the method is to split the solution process into a series of steps in which the continuity of the flow field is enforced by solving a Poisson's equation for the pressure, and at the end of the steps, both the pressure and velocity fields are made to satisfy one and the same momentum equation. For viscoelastic flow computations, artificial diffusion terms are introduced on both sides of the discretized constitutive equations to improve numerical stability. It is found that there are in total two vortices in each quadrant of the pipe at different aspect ratios (from 1 to 16), and at each ratio the pattern of secondary flows takes the same form for different material parameters, but their strength is very sensitive to the viscoelastic material parameters. Numerical results indicate that the presence of secondary flow strongly depends on the primary flow rate and the elasticity of the fluid, namely, the first and the second normal stress differences as well as their functional departure from the constant multiple viscosity.},
	language = {en},
	number = {2},
	urldate = {2022-09-02},
	journal = {Journal of Non-Newtonian Fluid Mechanics},
	author = {Xue, S. -C. and Phan-Thien, N. and Tanner, R. I.},
	month = sep,
	year = {1995},
	keywords = {Implicit finite volume method, Secondary flows, Straight pipes, Viscoelastic fluid},
	pages = {191--213},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/Y2ZLGE28/Xue et al. - 1995 - Numerical study of secondary flows of viscoelastic.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/XKC3EYHS/0377025795013653.html:text/html},
}

@inproceedings{siginer_review_2009,
	title = {Review of the {Secondary} {Flows} of {Complex} {Fluids}},
	url = {https://www.asmedigitalcollection.asme.org/FEDSM/proceedings/FEDSM2003/36975/1843/303421},
	doi = {10.1115/FEDSM2003-45327},
	language = {en},
	urldate = {2022-09-02},
	publisher = {American Society of Mechanical Engineers Digital Collection},
	author = {Siginer, Dennis A.},
	month = feb,
	year = {2009},
	pages = {1843--1854},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/A7XY68PB/1843_1.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/8FRBBGKJ/303421.html:text/html},
}

@article{da_cruz_rheophysics_2005,
	title = {Rheophysics of dense granular materials: {Discrete} simulation of plane shear flows},
	volume = {72},
	shorttitle = {Rheophysics of dense granular materials},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.72.021309},
	doi = {10.1103/PhysRevE.72.021309},
	abstract = {We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.},
	number = {2},
	urldate = {2022-09-01},
	journal = {Physical Review E},
	author = {da Cruz, Frédéric and Emam, Sacha and Prochnow, Michaël and Roux, Jean-Noël and Chevoir, François},
	month = aug,
	year = {2005},
	note = {Publisher: American Physical Society},
	pages = {021309},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/5BBR5A3M/PhysRevE.72.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/H7ZJR4AB/da Cruz et al. - 2005 - Rheophysics of dense granular materials Discrete .pdf:application/pdf},
}

@article{srdic-mitrovic_gravitational_1999,
	title = {Gravitational settling of particles through density interfaces},
	volume = {381},
	issn = {1469-7645, 0022-1120},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/gravitational-settling-of-particles-through-density-interfaces/BE91E7365C5674995D668B2812566EF2},
	doi = {10.1017/S0022112098003590},
	abstract = {Gravitational settling of dense particles through density interfaces
 is common in 
many environmental and engineering flow situations, yet very little research
 has been 
done to understand the mechanics of particle–stratification interactions.
 To this end, 
a detailed experimental study was carried out to investigate the settling
 of solid 
spherical particles through density interfaces. In these experiments, the
 solid particles 
first descended through a deep homogeneous layer, entered a thick pycnocline
 and then 
descended to another denser homogeneous layer. It was found that the stratification
 
has a significant impact on the settling of particles in the approximate
 parameter 
range 1.5{\textless}Re1{\textless}15, where 
Re1=U1dp/v
 
is the Reynolds number based on the 
particle entry velocity U1 to the stratified layer,
 
dp is the particle diameter and v
 is 
the kinematic viscosity of the fluid. In the above parameter range, the
 particles tend 
to drag lighter fluid from the upper layer into the stratified region,
 thus increasing the drag 
on them substantially and decelerating them within the stratified layer.
 In the Froude number 
Fr1=U1/Ndp
 range 
investigated, 3{\textless}Fr1{\textless}10, where N is the
 
buoyancy frequency of the stratified layer, the drag coefficient was found
 to be an 
order of magnitude larger than its homogeneous-fluid counterpart. The internal-wave
 
contribution to the drag was small compared to that of fluid dragged into
 the stratified 
layer, but substantial internal-wave activity could be detected after the
 fluid dragged 
from the lighter layer (the caudal fluid) detached from the particle.The minimum velocity of the solid particle within the stratified layer
 was found to be given 
by Umin/U1=
5.5×10−2Fr9/101,
 occurring on a 
time scale tmin/
(d2p/v)=
1.4×102Re−1.71, where
 
tmin was measured relative to the time of
 the particle's 
entry into the stratified region. Outside the parameter range 
1.5{\textless}Re1{\textless}15, the drag on the 
sphere in the density-stratified layer could be approximated to that in
 a homogeneous 
fluid, whence the bringing of lighter fluid into the stratified layer as
 a tail behind the 
descending particle was found to be negligible.},
	language = {en},
	urldate = {2022-08-30},
	journal = {Journal of Fluid Mechanics},
	author = {Srdić-Mitrović, A. N. and Mohamed, N. A. and Fernando, H. J. S.},
	month = feb,
	year = {1999},
	note = {Publisher: Cambridge University Press},
	pages = {175--198},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/YCLT27UC/Srdić-Mitrović et al. - 1999 - Gravitational settling of particles through densit.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/NBKKI7X6/BE91E7365C5674995D668B2812566EF2.html:text/html},
}

@article{sverdrup_highly_2018,
	title = {Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement},
	volume = {30},
	issn = {1070-6631},
	url = {https://link.springer.com/book/10.1007/b98904},
	doi = {10.1063/1.5049202},
	abstract = {We present the extension of an efficient and highly parallelisable framework for incompressible fluid flow simulations to viscoplastic fluids. The system is governed by incompressible conservation of mass, the Cauchy momentum equation, and a generalised Newtonian constitutive law. In order to simulate a wide range of viscoplastic fluids, we employ the Herschel-Bulkley model for yield-stress fluids with nonlinear stress-strain dependency above the yield limit. We utilise Papanastasiou regularisation in our algorithm to deal with the singularity in apparent viscosity. The resulting system of partial differential equations is solved using the IAMR (Incompressible Adaptive Mesh Refinement) code, which uses second-order Godunov methodology for the advective terms and semi-implicit diffusion in the context of an approximate projection method to solve adaptively refined meshes. By augmenting the IAMR code with the ability to simulate regularised Herschel-Bulkley fluids, we obtain efficient numerical software for time-dependent viscoplastic flow in three dimensions, which can be used to investigate systems not considered previously due to computational expense. We validate results from simulations using this new capability against previously published data for Bingham plastics and power-law fluids in the two-dimensional lid-driven cavity. In doing so, we expand the range of Bingham and Reynolds numbers which have been considered in the benchmark tests. Moreover, extensions to time-dependent flow of Herschel-Bulkley fluids and three spatial dimensions offer new insights into the flow of viscoplastic fluids in this test case, and we provide missing benchmark results for these extensions.},
	number = {9},
	urldate = {2022-06-01},
	journal = {Physics of Fluids},
	author = {Sverdrup, Knut and Nikiforakis, Nikolaos and Almgren, Ann},
	month = sep,
	year = {2018},
	note = {Publisher: American Institute of Physics},
	pages = {093102},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/VWR5ERZN/Sverdrup et al. - 2018 - Highly parallelisable simulations of time-dependen.pdf:application/pdf;Submitted Version:/Users/eunji/Zotero/storage/B58GTA4F/Sverdrup et al. - 2018 - Highly parallelisable simulations of time-dependen.pdf:application/pdf},
}

@article{cates_jamming_1998,
	title = {Jamming, {Force} {Chains}, and {Fragile} {Matter}},
	volume = {81},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.81.1841},
	doi = {10.1103/PhysRevLett.81.1841},
	abstract = {We consider materials whose mechanical integrity is the result of a jamming process. We argue that such media are generically “fragile,” unable to support certain types of incremental loading without plastic rearrangement. Fragility is linked to the marginal stability of force chain networks within the material. It can lead to novel mechanical responses that may be relevant to (a) jammed colloids and (b) poured sand. The crossover from fragile to elastoplastic behavior is explored.},
	number = {9},
	urldate = {2022-08-22},
	journal = {Physical Review Letters},
	author = {Cates, M. E. and Wittmer, J. P. and Bouchaud, J.-P. and Claudin, P.},
	month = aug,
	year = {1998},
	note = {Publisher: American Physical Society},
	pages = {1841--1844},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/YCYHG5EA/PhysRevLett.81.html:text/html},
}

@article{maklad_review_2021,
	title = {A review of the second normal-stress difference; its importance in various flows, measurement techniques, results for various complex fluids and theoretical predictions},
	volume = {292},
	issn = {0377-0257},
	url = {https://www.sciencedirect.com/science/article/pii/S0377025721000458},
	doi = {10.1016/j.jnnfm.2021.104522},
	abstract = {Shear flow is ubiquitous. Not only is it arguably the most widely-used deformation type to characterise complex fluids in rheological studies but also, in practice, the deformation most likely to occur in the great majority of flows, e.g. involving fluid transport through pipes or conduits. In steady simple shear flow the rheological properties of a complex fluid are completely characterised in just three material functions; the variation with shear rate of the shear viscosity and the so-called first and second normal-stress differences. Despite requiring only three material functions to be completely characterised, most shear-flow rheological characterisations are usually restricted simply to the shear viscosity and, at best, the variation of the first normal-stress difference N1 with shear rate. The second normal-stress difference N2 remains very much neglected. For dilute polymer solutions where this quantity may be negligibly small in comparison to the first normal-stress difference, such neglect is justified but for a whole range of complex fluids – indeed even polymer solutions outside of the dilute regime and especially melts – it is not clear that N2 may be safely disregarded. Indeed, in this review article we spotlight a number of flows where second normal-stress differences are of importance and potentially major consequence. Following this attention, we review the many experimental techniques which have been proposed for its measurement and survey the available literature for measurements of this quantity for various complex fluids including the aforementioned polymeric solutions, melts, liquid crystals, dense non-Brownian suspensions (both with Newtonian and complex fluid bases), semi-dilute wormlike micellar fluids and magnetorheological fluids. Theoretical predictions for N2 from various commonly-used continuum constitutive equations – primarily from the polymer literature – are also given and their asymptotic predictions at low and high shear rates compared. Finally, we end with a brief summary and outlook.},
	language = {en},
	urldate = {2022-08-05},
	journal = {Journal of Non-Newtonian Fluid Mechanics},
	author = {Maklad, O. and Poole, R. J.},
	month = jun,
	year = {2021},
	keywords = {Normal-stresses, Secondary flow, Shear flow, Viscoelastic fluids},
	pages = {104522},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/Z5YXYBMW/Maklad and Poole - 2021 - A review of the second normal-stress difference\; i.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/76AZKT5A/S0377025721000458.html:text/html},
}

@article{mcelwaine_surface_2012,
	title = {Surface curvature of steady granular flows},
	volume = {14},
	issn = {1434-7636},
	url = {https://doi.org/10.1007/s10035-012-0339-y},
	doi = {10.1007/s10035-012-0339-y},
	abstract = {Laboratory experiments have shown that the steady flow of granular material down a rough inclined plane has a surface that is not parallel to the plane, but has a curvature across the slope with the height increasing toward the middle of the flow. We study this observation by postulating a new granular rheology, similar to that of a second order fluid. This model is applied to the experiments using a shallow water approximation, given that the depth of the flow is much smaller than the width. The model predicts that a second normal stress difference allows cross-slope height variations to develop in regions with considerable cross-slope velocity shear, consistent with the experiments. The model also predicts the development of lateral eddies, which are yet to be observed.},
	language = {en},
	number = {2},
	urldate = {2022-07-05},
	journal = {Granular Matter},
	author = {McElwaine, Jim N. and Takagi, Daisuke and Huppert, Herbert E.},
	month = apr,
	year = {2012},
	keywords = {Levée formation, Normal stress difference, Shallow granular flow},
	pages = {229--234},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/6M6BZGRF/McElwaine et al. - 2012 - Surface curvature of steady granular flows.pdf:application/pdf},
}

@article{artoni_effective_2014,
	title = {Effective wall slip in chutes and channels: experiments and discrete element simulations},
	volume = {16},
	issn = {1434-7636},
	shorttitle = {Effective wall slip in chutes and channels},
	url = {https://doi.org/10.1007/s10035-013-0431-y},
	doi = {10.1007/s10035-013-0431-y},
	abstract = {Wall slip is an important phenomenon for the flow of granular materials in chutes and channels. The appearance of a slip velocity at the wall critically affects wall stresses and flow profiles, and particularly the total flowrate. In this work we show, through numerical simulations and experiments, that the global slip phenomenon at a wall has peculiar features which deviate significantly from simple sliding behavior. At first we present experimental data for the vertical chute flow which highlight that wall slip depends on many operating and system variables such as flow rate, material properties, wall properties. Secondly, we resume a large campaign of numerical data performed in 2D with polygonal particles, and try to analyse the effect of material properties, contact parameters, operating variables, different flow configurations, on the slip phenomenon. The numerical campaign allowed to identify the main parameters affecting the wall slip behavior of a numerical model of granular flow, providing the ingredients for the creation of a framework for the description of wall slip.},
	language = {en},
	number = {3},
	urldate = {2022-07-05},
	journal = {Granular Matter},
	author = {Artoni, Riccardo and Santomaso, Andrea},
	month = jun,
	year = {2014},
	keywords = {Dense granular flows, Discrete numerical simulations, Experiments, Scaling laws, Wall slip},
	pages = {377--382},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/H25X7A3A/Artoni and Santomaso - 2014 - Effective wall slip in chutes and channels experi.pdf:application/pdf},
}

@article{kim_power-law_2020,
	title = {Power-{Law} {Scaling} in {Granular} {Rheology} across {Flow} {Geometries}},
	volume = {125},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.088002},
	doi = {10.1103/PhysRevLett.125.088002},
	abstract = {Based on discrete element method simulations, we propose a new form of the constitutive equation for granular flows independent of packing fraction. Rescaling the stress ratio μ by a power of dimensionless temperature Θ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number I. The basic power-law structure appears robust to varying particle properties (e.g., surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the nonlocal granular fluidity model.},
	number = {8},
	urldate = {2022-07-05},
	journal = {Physical Review Letters},
	author = {Kim, Seongmin and Kamrin, Ken},
	month = aug,
	year = {2020},
	note = {Publisher: American Physical Society},
	pages = {088002},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/K3C5CC6X/PhysRevLett.125.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/NHBZNQJG/Kim and Kamrin - 2020 - Power-Law Scaling in Granular Rheology across Flow.pdf:application/pdf},
}

@article{chauchat_three-dimensional_2014,
	title = {A three-dimensional numerical model for dense granular flows based on the μ({I}) rheology},
	volume = {256},
	issn = {0021-9991},
	url = {https://www.sciencedirect.com/science/article/pii/S0021999113006098},
	doi = {10.1016/j.jcp.2013.09.004},
	abstract = {This paper presents a three-dimensional implementation of the so-called μ(I) rheology to accurately and efficiently compute steady-state dense granular flows. The tricky pressure dependent visco-plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the Newton–Raphson algorithm. The computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution. Then, two application examples dealing with actual lab experiments have also been considered: the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder. In both configurations the obtained computational results are in good agreement with available experimental data.},
	language = {en},
	urldate = {2022-06-10},
	journal = {Journal of Computational Physics},
	author = {Chauchat, Julien and Médale, Marc},
	month = jan,
	year = {2014},
	keywords = {Dense granular flows, Finite element method, Regularisation techniques, Visco-plastic flows},
	pages = {696--712},
	file = {ScienceDirect Snapshot:/Users/eunji/Zotero/storage/VXEGN2LK/S0021999113006098.html:text/html;Submitted Version:/Users/eunji/Zotero/storage/P3YM4JYG/Chauchat and Médale - 2014 - A three-dimensional numerical model for dense gran.pdf:application/pdf},
}

@article{forterre_flows_2008,
	title = {Flows of {Dense} {Granular} {Media}},
	volume = {40},
	issn = {0066-4189, 1545-4479},
	url = {https://www.annualreviews.org/doi/10.1146/annurev.fluid.40.111406.102142},
	doi = {10.1146/annurev.fluid.40.111406.102142},
	abstract = {We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally, we briefly present depth-averaged methods developed for free surface granular flows.},
	language = {en},
	number = {1},
	urldate = {2022-06-08},
	journal = {Annual Review of Fluid Mechanics},
	author = {Forterre, Yoël and Pouliquen, Olivier},
	month = jan,
	year = {2008},
	pages = {1--24},
	file = {Forterre and Pouliquen - 2008 - Flows of Dense Granular Media.pdf:/Users/eunji/Zotero/storage/PLZBE9SZ/Forterre and Pouliquen - 2008 - Flows of Dense Granular Media.pdf:application/pdf},
}

@book{simo_computational_2000,
	title = {Computational {Inelasticity}},
	isbn = {978-0-387-97520-7},
	url = {https://link.springer.com/book/10.1007/b98904},
	abstract = {This book goes back a long way. There is a tradition of research and teaching in inelasticity at Stanford that goes back at least to Wilhelm Flugge ̈ and Erastus Lee. I joined the faculty in 1980, and shortly thereafter the Chairman of the Applied Mechanics Division, George Herrmann, asked me to present a course in plasticity. I decided to develop a new two-quarter sequence entitled “Theoretical and C- putational Plasticity” which combined the basic theory I had learned as a graduate student at the University of California at Berkeley from David Bogy, James Kelly, Jacob Lubliner, and Paul Naghdi with new computational techniques from the ?nite-element literature and my personal research. I taught the course a couple of times and developed a set of notes that I passed on to Juan Simo when he joined thefacultyin1985. IwasChairmanatthattimeandIaskedJuantofurtherdevelop the course into a full year covering inelasticity from a more comprehensive p- spective. Juan embarked on this path creating what was to become his signature course. He eventually renamed it “Computational and Theoretical Inelasticity” and it covered much of the material that was the basis of his research in material modeling and simulation for which he achieved international recognition. At the outset we decided to write a book that would cover the material in the course.},
	language = {en},
	publisher = {Springer New York},
	author = {Simo, J. C. and Hughes, T. J. R.},
	month = aug,
	year = {2000},
	keywords = {Mathematics / General, Mathematics / Numerical Analysis, Computers / Programming / Algorithms, Science / Physics / Mathematical \& Computational},
}

@article{srivastava_viscometric_2021,
	title = {Viscometric flow of dense granular materials under controlled pressure and shear stress},
	volume = {907},
	issn = {0022-1120, 1469-7645},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/viscometric-flow-of-dense-granular-materials-under-controlled-pressure-and-shear-stress/416296B44B0F3C9CDAD6FE8BDD0B93AB},
	doi = {10.1017/jfm.2020.811},
	abstract = {, This study examines the flow of dense granular materials under external shear stress and pressure using discrete element method simulations. In this method, the material is allowed to strain along all periodic directions and adapt its solid volume fraction in response to an imbalance between the internal state of stress and the external applied stress. By systematically varying the external shear stress and pressure, the steady rheological response is simulated for: (1) rate-independent quasi-static flow; and (2) rate-dependent inertial flow. The simulated flow is viscometric with non-negligible first and second normal stress differences. While both normal stress differences are negative in inertial flows, the first normal stress difference switches from negative to slightly positive, and second normal stress difference tends to zero in quasi-static flows. The first normal stress difference emerges from a lack of coaxiality between a second-rank contact fabric tensor and strain rate tensor in the flow plane, while the second normal stress difference is linked to an excess of contacts in the shear plane compared with the vorticity direction. A general rheological model of second order (in terms of strain rate tensor) is proposed to describe the two types of flow, and the model is calibrated for various values of interparticle friction from simulations on nearly monodisperse spheres. The model incorporates normal stress differences in both regimes of flow and provides a complete viscometric description of steady dense granular flows.},
	language = {en},
	urldate = {2022-06-01},
	journal = {Journal of Fluid Mechanics},
	author = {Srivastava, Ishan and Silbert, Leonardo E. and Grest, Gary S. and Lechman, Jeremy B.},
	month = jan,
	year = {2021},
	note = {Publisher: Cambridge University Press},
	keywords = {rheology, granular media},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/3EWKQ3W3/Srivastava et al. - 2021 - Viscometric flow of dense granular materials under.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/CGD9GGCU/416296B44B0F3C9CDAD6FE8BDD0B93AB.html:text/html},
}

@article{arun_kumar_varanasi_rotation_2021,
	title = {The rotation of a sedimenting spheroidal particle in a linearly stratified fluid},
	doi = {10.1017/jfm.2021.1016},
	abstract = {We derive analytically the angular velocity of a spheroid, of an arbitrary aspect ratio \${\textbackslash}{\textbackslash}kappa\$ , sedimenting in a linearly stratified fluid. The analysis demarcates regions in parameter space corresponding to broadside-on and edgewise settling in the limit \$Re, Ri\_v {\textbackslash}{\textbackslash}ll 1\$ , where \$Re = {\textbackslash}{\textbackslash}rho \_0UL/{\textbackslash}{\textbackslash}mu\$ and \$Ri\_v ={\textbackslash}{\textbackslash}gamma L{\textasciicircum}3{\textbackslash}{\textbackslash},g/{\textbackslash}{\textbackslash}mu U\$ , the Reynolds and viscous Richardson numbers, respectively, are dimensionless measures of the importance of inertial and buoyancy forces relative to viscous ones. Here, \$L\$ is the spheroid semi-major axis, \$U\$ an appropriate settling velocity scale, \${\textbackslash}{\textbackslash}mu\$ the fluid viscosity and \${\textbackslash}{\textbackslash}gamma {\textbackslash}{\textbackslash} (\&gt;0)\$ the (constant) density gradient characterizing the stably stratified ambient, with the fluid density \${\textbackslash}{\textbackslash}rho\_0\$ taken to be a constant within the Boussinesq framework. A reciprocal theorem formulation identifies three contributions to the angular velocity: (1) an \$O(Re)\$ inertial contribution that already exists in a homogeneous ambient, and orients the spheroid broadside-on; (2) an \$O(Ri\_v)\$ hydrostatic contribution due to the ambient stratification that also orients the spheroid broadside-on; and (3) a hydrodynamic contribution arising from the perturbation of the ambient stratification whose nature depends on \$Pe\$ ; \$Pe = UL/D\$ being the Péclet number with \$D\$ the diffusivity of the stratifying agent. For \$Pe {\textbackslash}{\textbackslash}ll 1\$ , this contribution is \$O(Ri\_v)\$ and orients prolate spheroids edgewise for all \${\textbackslash}{\textbackslash}kappa {\textbackslash}{\textbackslash} (\&gt;1)\$ . For oblate spheroids, it changes sign across a critical aspect ratio \${\textbackslash}{\textbackslash}kappa \_c {\textbackslash}{\textbackslash}approx 0.41\$ , orienting oblate spheroids with \${\textbackslash}{\textbackslash}kappa \_c \&lt; {\textbackslash}{\textbackslash}kappa \&lt; 1\$ edgewise and those with \${\textbackslash}{\textbackslash}kappa \&lt; {\textbackslash}{\textbackslash}kappa \_c\$ broadside-on. For \$Pe {\textbackslash}{\textbackslash}ll 1\$ , the hydrodynamic component is always smaller in magnitude than the hydrostatic one, so a sedimenting spheroid in this limit always orients broadside-on. For \$Pe {\textbackslash}{\textbackslash}gg 1\$ , the hydrodynamic contribution is dominant, being \$O(Ri\_v{\textasciicircum}\{\{2\}/\{3\}\}\$ ) in the Stokes stratification regime characterized by \$Re {\textbackslash}{\textbackslash}ll Ri\_v{\textasciicircum}\{\{1\}/\{3\}\}\$ , and orients the spheroid edgewise regardless of \${\textbackslash}{\textbackslash}kappa\$ . Consideration of the inertial and large- \$Pe\$ stratification-induced angular velocities leads to two critical curves which separate the broadside-on and edgewise settling regimes in the \$Ri\_v/Re{\textasciicircum}\{\{3\}/\{2\}\}\$ – \${\textbackslash}{\textbackslash}kappa\$ plane, with the region between the curves corresponding to stable intermediate equilibrium orientations. The predictions for large \$Pe\$ are broadly consistent with observations.},
	journal = {Journal of Fluid Mechanics},
	author = {{Arun Kumar Varanasi} and Marath, Navaneeth K. and Subramanian, Ganesh},
	year = {2021},
	doi = {10.1017/jfm.2021.1016},
	note = {MAG ID: 4200054348},
}

@article{prairie_ephemeral_2017,
	title = {Ephemeral aggregate layers in the water column leave lasting footprints in the carbon cycle},
	volume = {2},
	doi = {10.1002/lol2.10053},
	abstract = {Marine aggregates play a critical role in the biological pump, both as a dominant component of carbon flux and as hotspots for organic matter remineralization by microbial communities. In this study, we used laboratory experiments to investigate how aggregate thin layers, such as those commonly found in the coastal ocean, affect the distribution of bacteria and their activity. Diatom aggregates were added to a stratified water column, forming layers within which both microbial concentration and extracellular enzyme activity were substantially increased relative to background levels. Importantly, this enhancement of bacterial concentration and activity persisted long after the marine snow aggregates settled through the tank—that is, 10 times longer than the duration of the aggregate layer at the density interface. Thus, these small-scale microbial interactions within aggregate layers leave behind considerable “carbon processing footprints” in the water column that may affect biogeochemical cycles at much larger temporal and spatial scales.},
	number = {6},
	journal = {Limnology and Oceanography},
	author = {Prairie, Jennifer C. and Ziervogel, Kai and Camassa, Roberto and McLaughlin, Richard and White, Brian L. and Johnson, Zackary I. and Arnosti, Carol},
	month = dec,
	year = {2017},
	doi = {10.1002/lol2.10053},
	note = {MAG ID: 2766183202},
	pages = {202--209},
}

@article{rajat_dandekar_motion_2020,
	title = {Motion of an arbitrarily shaped particle in a density stratified fluid},
	doi = {10.1017/jfm.2020.81},
	abstract = {In this work, we theoretically investigate the motion of an arbitrarily shaped particle in a linear density stratified fluid with weak stratification and negligible inertia. We calculate the hydrodynamic force and torque experienced by the particle using the method of matched asymptotic expansions. We analyse our results for two classes of particles (non-skew and skew) depending on whether the particle possesses a centre of hydrodynamic stress. For both classes, we derive general expressions for the modified resistance tensors in the presence of stratification. We demonstrate the application of our results by considering some specific examples of particles settling in a direction parallel to the density gradient by considering both the limits of high (                                                                 \$Pe{\textbackslash}gg 1\$
                                        ) and low (                                                                 \$Pe{\textbackslash}ll 1\$
                                        ) Peclet numbers. We find that presence of stratification causes a slender body to rotate and settle along the broader side due to the contribution of the hydrostatic torque. Our work sheds light on the impact of stratification on the transport of arbitrarily shaped particles in density stratified environments in low-Reynolds-number regimes.},
	journal = {Journal of Fluid Mechanics},
	author = {{Rajat Dandekar} and {Rajat Dandekar} and {Vaseem A. Shaik} and {Vaseem A. Shaik} and {Arezoo M. Ardekani}},
	year = {2020},
	doi = {10.1017/jfm.2020.81},
	note = {MAG ID: 3010904670},
}

@article{david_deepwell_settling_2021,
	title = {Settling of a particle pair through a sharp, miscible density interface},
	doi = {10.1103/physrevfluids.6.044304},
	abstract = {The settling of a pair of particles through a density interface is analyzed for various particle positions and stratifications. The particles decelerate through the interface as surface fluid remains attached to the particles. Heightened transport is found to occur for vertically aligned particles.},
	author = {{David Deepwell} and {David Deepwell} and {Raphael Ouillon} and {Eckart Meiburg} and {Eckart Meiburg} and {Bruce R. Sutherland}},
	year = {2021},
	doi = {10.1103/physrevfluids.6.044304},
	note = {MAG ID: 3153969668},
}