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A Physical Introduction to Suspension Dynamics
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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.


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Ackerson, B. J. 1990. Shear induced order and shear processing of model hardsphere suspensions. J. Rheol., 34, 553–590.
Aris, R. 1962. Vectors, Tensors and the Basic Equations of Fluid Mechanics. Prentice-Hall. Reprinted by Dover Publications, New York.
Asmolov, E. S. 1999. The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech., 381, 63–87.
Baker, G. L. and Gollub, J. P. 1996. Chaotic Dynamics: An Introduction. 2nd ed. Cambridge University Press.
Batchelor, G. K. 1967. An Introduction to Fluid Dynamics. Cambridge University Press.
Batchelor, G. K. 1970a. The stress system in a suspension of force-free particles. J. Fluid Mech., 41, 545–570.
Batchelor, G. K. 1970b. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech., 44, 419–440.
Batchelor, G. K. 1972. Sedimentation in a dilute dispersion of spheres. J. Fluid Mech., 52, 245–268.
Batchelor, G. K. 1977. The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech., 83, 97–117.
Batchelor, G. K. 1982. Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory. J. Fluid Mech., 119, 379–408. Corrigendum. 1983. J. Fluid Mech., 137, 467–469.
Batchelor, G. K. and Green, J. T. 1972a. The hydrodynamic interactions of two small freely-moving spheres in a linear flow field. J. Fluid Mech., 56, 375–400.
Batchelor, G. K. and Green, J. T. 1972b. The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech., 56, 401–427.
Batchelor, G. K. and Janse Van Rensburg, R. W. 1986. Structure formation in bidisperse sedimentation. J. Fluid Mech., 166, 379–407.
Batchelor, G. K. and Wen, C.-S. 1982. Sedimentation in a dilute polydisperse system of interacting spheres. Part 2. Numerical results. J. Fluid Mech., 124, 495–528. Corrigendum. 1983. J. Fluid Mech., 137, 467–469.
Beenakker, C. W. J. and Mazur, P. 1985. Is sedimentation container-shape dependent? Phys. Fluids, 28, 3203–3206.
Berg, H. C. 1983. Random Walks in Biology, New, expanded edition. Princeton University Press.
Bergenholtz, J., Brady, J. F., and Vicic, M. A. 2002. The non-Newtonian rheology of dilute colloidal suspensions. J. Fluid Mech., 456, 239–275.
Bird, R. B., Armstrong, R. C., and Hassager, O. 1987. Dynamics of Polymeric Liquids, Vol 1, 2nd ed. John Wiley, New York.
Bracewell, R. N. 1986. The Fourier Transform and Its Applications, 2nd ed. (revised). McGraw-Hill, New York.
Brady, J. F. 1993. The rheological behaviour of concentrated colloidal dispersions. J. Chem. Phys., 99, 567–581.
Brady, J. F. and Bossis, G. 1988. Stokesian Dynamics. Ann. Rev. Fluid Mech., 20, 111–157.
Brady, J. F. and Morris, J. F. 1997. Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J. Fluid Mech., 348, 103–139.
Brady, J. F. and Vicic, M. A. 1995. Normal stresses in colloidal dispersions. J. Rheol., 39, 545–566.
Bretherton, F. P. 1962. The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech., 14, 284–304.
Bruneau, D., Feuillebois, F., Anthore, R., and Hinch, E. J. 1996. Intrinsic convection in a settling suspension. Phys. Fluids, 8, 2236–2238.
Caflisch, R.E. and Luke, J. H. C. 1985. Variance in the sedimenting speed of a suspension. Phys. Fluids, 28, 759–760.
Chandler, D. 1987. Introduction to Modern Statistical Mechanics. Oxford University Press.
Cox, R. G. 1970. The motion of long slender bodies in a viscous fluid. Part 1 General theory. J. Fluid Mech., 44, 791–810.
da Cunha, F. R. and Hinch, E. J. 1996. Shear-induced dispersion in a dilute suspension of rough spheres. J. Fluid Mech., 309, 211–223.
Davis, R. H. and Acrivos, A. 1985. Sedimentation of noncolloidal particles at low Reynolds numbers. Ann. Rev. Fluid Mech., 17, 91–118.
Di Carlo, D. 2009. Inertial microfluidics. Lab on a Chip, 9, 3038–3046.
Doi, M. and Edwards, S. 1986. The Theory of Polymer Dynamics. Oxford Science Publications.
Drew, D. A. and R. T., Lahey. 1993. Analytical modeling of multiphase flow. In Particulate Two-Phase Flows, ed. M. C., Roco. Butterworth-Heinemann, Boston.
Eckstein, E. C., Bailey, D. G., and Shapiro, A. H. 1977. Self-diffusion of particles in shearflow of a suspension. J. Fluid Mech., 79, 191–208.
Einstein, A. 1905. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik (4), 17, 549–560; 1956. Reprinted in Investigations on the Theory of Brownian Movement, Dover Publications, New York.
Einstein, A. 1906. Eine neue Bestimmung der Moleküldimensionen. Annalen der Physik (4), 19, 289–306; 1956. reprinted in Investigations on the Theory of Brownian Movement, Dover Publications, New York.
Feng, J., Hu, H. H., and Joseph, D. D. 1994. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 1 Sedimentation. J. Fluid Mech., 261, 95–134.
Fortes, A. F., Joseph, D. D., and Lundgren, T. S. 1987. Nonlinear mechanics of fluidization of beds of spherical particles. J. Fluid Mech., 177, 467–483.
Foss, D. R. and Brady, J. F. 2000. Structure, diffusion and rheology of Brownian suspensions by Stokesian Dynamics simulation. J. Fluid. Mech., 407, 167–200.
Frank, M., Anderson, D., Weeks, E. R., and Morris, J. F. 2003. Particle migration in pressure-driven flow of a Brownian suspension. J. Fluid Mech., 493, 363–378.
Geigenmüller, U. and Mazur, P. 1988. Sedimentation of homogeneous suspensions in finite vessels. J. Statist. Phys., 53, 137–173.
Geigenmüller, U. and Mazur, P. 1991. Intrinsic convection near a meniscus. Physica A, 171, 475–485.
Guazzelli, É. and Hinch, E. J. 2011. Fluctuations and instability in sedimentation. Ann. Rev. Fluid Mech., 43, 87–116.
Guyon, E., Hulin, J.-P., and Petit, L. 1991. Hydrodynamique Physique, Inter Editions/Éditions du CNRS; 2001. Republished by EDP Sciences/Éditions du CNRS; 2001. First edition available in English as Physical Hydrodynamics with a fourth author, Mitescu C. D., Oxford University Press.
Hadamard, J. S. 1911. Mouvement permanent lent d'une sphère liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. (Paris), 152, 1735–1738.
Ham, J. M. and Homsy, G. M. 1988. Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspensions. Int. J. Multiphase Flow, 14, 533–546.
Hansen, J. P. and McDonald, I. R. 2006. Theory of Simple Liquids, 3rd ed. Academic Press, New York.
Happel, J. and Brenner, H. 1965. Low Reynolds Number Hydrodynamics. Prentice-Hall; 1986. Republished by Martinus Nijhoff, Leiden.
Haw, M. 2007. Middle World. The Restless Heart of Matter and Life. Macmillan.
Hinch, E. J. 1988. Sedimentation of small particles. In: Disorder and Mixing. E., Guyon, J-P., Nadal, and Y., Pomeau, Pages 153–161 Kluwer Academic, Dordrecht.
Hinch, E. J. 1991. Perturbation Methods. Cambridge University Press.
Hinch, E. J. and Leal, L. G. 1972. The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech., 52, 683–712.
Ho, B. P. and Leal, L. G. 1974. Inertial migration of rigid spheres in 2-dimensional unidirectional flows. J. Fluid Mech., 65, 365–400.
Hocking, L. M. 1964. The behaviour of clusters of spheres falling in a viscous fluid: Part 2. Slow motion theory. J. Fluid Mech., 20, 129–139.
Homsy, G. M., et al. 2000. Multimedia Fluid Mechanics – DVD-ROM; 2008. Multilingual Version, Cambridge University Press.
Jackson, J. D. 1999. Classical Electrodynamics, 3rd ed. John Wiley, New York.
Jackson, R. 2000. The Dynamics of Fluidized Particles. Cambridge University Press.
Jánosi, I. M., Tamás, T., Wolf, D. E., and Gallas, J. A. C. 1997. Chaotic particle dynamics in viscous flows: The three-particle Stokeslet problem. Phys. Rev. E, 56, 2858–2868.
Jayaweera, K. O. L. F., Mason, B. J., and Slack, G. W. 1964. The behaviour of clusters of spheres falling in a viscous fluid: Part 1. Experiment. J. Fluid Mech., 20, 121–128.
Jeffery, G. B., 1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proc. Royal Soc. London. Series A, 102, 161–179.
Kim, S. and Karrila, S. J. 1989. Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann; 2005. Reprinted by Dover Publications, New York.
Koch, D. L. and Hill, R. J. 2001. Inertial effects in suspension and porous media flows. Ann. Rev. Fluid Mech., 33, 619–647.
Koch, D. L. and Shaqfeh, E. S. G. 1989. The instability of a dispersion of sedimenting spheroids. J. Fluid Mech., 209, 521–542.
Koh, C. J., Hookham, P., and Leal, L. G. 1994. An experimental investigation of concentrated suspension flows in a rectangular channel. J. Fluid Mech., 266, 1–32.
Krieger, I. M. 1972. Rheology of monodisperse lattices. Adv. Colloid Interface Sci. 2, 111–136.
Kynch, G. J. 1952. A theory of sedimentation. Trans. Faraday Soc., 48, 166–176.
Kulkarni, P. M. and Morris, J. F. 2008. Pair-sphere trajectories in finite Reynolds number shear flow. J. Fluid Mech., 596, 413–435.
Kulkarni, S. D. and Morris, J. F. 2009. Ordering transition and structural evolution under shear in Brownian suspensionsJ. Rheol., 53, 417–439.
Lamb, H. 1932. Fluid Mechanics, 6th ed. Dover Publications, New York.
Landau, L. and Lifshitz, E. 1959. Fluid Mechanics; 1987. Second ed. Butterworth-Heinemann, London.
Langevin, P. 1908. Sur la théorie du mouvement brownien. C. R. Acad. Sci. Paris, 146, 530–533.
Leal, L. G. 2007. Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, Cambridge Series in Chemical Engineering, Cambridge University Press.
Leal, L. G. and Hinch, E. J. 1971. The effect of weak Brownian rotations on particles in shear flow. J. Fluid Mech., 46, 685–703.
Leighton, D. T. and Acrivos, A. 1987a. Measurement of shear-induced self-diffusion in concentrated suspensions of spheresJ. Fluid Mech., 177, 109–131.
Leighton, D. T. and Acrivos, A. 1987b. The shear-induced migration of particles in concentrated suspensionsJ. Fluid Mech., 181, 415–439.
Lhuillier, D. 2009. Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 21, 023302.
Lighthill, M. J. 1958. An Introduction to Fourier Analysis and Generalised Functions, Cambridge University Press.
Lin, C. J., Peery, J. H., and Schowalter, W. R. 1970. Simple shear flow round a rigid sphere: inertial effects and suspension rheology. J. Fluid Mech., 44, 1–17.
Machu, G., Meile, W., Nitsche, L. C., and Schaflinger, U. 2001. Coalescence, torus formation and breakup of sedimenting drops: Experiments and computer simulations. J. Fluid Mech., 447, 299–336.
Matas, J.-P., Morris, J. F., and Guazzelli, É. 2004. Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech., 515, 171–195.
Matas, J.-P., Glezer, V., Guazzelli, É., and Morris, J. F. 2004. Trains of particles in finite-Reynolds-number pipe flow. Phys. Fluids, 16, 4192–4195.
Matas, J.-P., Morris, J. F., and Guazzelli, É. 2009. Lateral force on a rigid sphere in large-inertia laminar pipe flow. J. Fluid Mech., 621, 59–67.
McQuarrie, D. A. 2000. Statistical Mechanics, University Science Books, London.
Metzger, B., Nicolas, M., and Guazzelli, É. 2007. Falling clouds of particles in viscous fluids. J. Fluid Mech., 580, 283–301.
Mikulencak, D. R. and Morris, J. F. 2004. Stationary shear flow around fixed and free bodies at finite Reynolds number. J. Fluid Mech., 520, 215–242.
Morris, J. F. 2009. A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta., 48, 909–923.
Morris, J. F. and Boulay, F. 1999. Curvilinear flows of noncolloidal suspensions: The role of normal stresses. J. Rheol., 43, 1213–1237.
Morris, J. F. and Katyal, B. 2002. Microstructure from simulated Brownian suspension flows at large shear rate. Phys. Fluids, 14, 1920–1937.
Nicolai, H., Herzhaft, B., Hinch, E. J., Oger, L., and Guazzelli, É. 1995. Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres. Phys. Fluids, 7, 12–23.
Nitsche, J. M. and Batchelor, G. K. 1997. Break-up of a falling drop containing dispersed particles. J. Fluid Mech., 340, 161–175.
Nott, P. R. and Brady, J. F. 1994. Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech., 275, 157–199.
Nott, P. R., Guazzelli, É., and Pouliquen, O. 2011. The suspension balance model revisited. Phys. Fluids, 23, 043304.
Ockendon, H. and Ockendon, J. R. 1995. Viscous Flow. Cambridge University Press.
Okagawa, A. and Mason, S. G. 1973. Suspensions: Fluids with fading memories. Science, 181, 159–161.
O'Malley, R. E. 2010. Singular perturbation theory: A viscous flow out of Göttingen. Ann. Rev. Fluid Mech., 42, 1–17.
Oseen, C. W. 1910. Über die Stokessche Formel und über eine Verwandte Aufgabe in der Hydrodynamik. Ark. Mat. Astron. Fys., 6, No. 29.
Oseen, C. W. 1913. Über den Goltigkeitsbereich der Stokesschen Widerstandsformel. Ark. Mat. Astron. Fys., 9, No. 16.
Parsi, F. and Gadala-Maria, F. 1987. Fore-and-aft asymmetry in a concentrated suspension of solid spheres. J. Rheol. 31, 725–732.
Patankar, N. A. and Hu, H. H. 2002. Finite Reynolds number effect on the rheology of a dilute suspension of neutrally buoyant circular particles in a Newtonian fluid. Intl. J. Multiphase Flow, 28, 409–425.
Petrie, C. J. S. 1999. The rheology of fibre suspensions. J. Non-Newtonian Fluid Mech., 87, 369–402.
Peysson, Y. and Guazzelli, É. 1998. An experimental investigation of the intrinsic convection in a sedimenting suspension. Phys. Fluids, 10, 44–54.
Perrin, J. 1914. Les Atomes, Alcan Paris; 1991.; 1916. Atoms. translated by D. A. Hammick. Van Nostrand, New York.
Phillips, R. J., Armstrong, R. C., Brown, R. A., Graham, A., and Abbott, J. R. 1992. A constitutive model for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A 4, 30–40.
Phung, T. N., Brady, J. F., and Bossis, G. 1996. Stokesian Dynamics simulation of Brownian suspensions. J. Fluid Mech., 313, 181–207.
Pignatel, F., Nicolas, M., and Guazzelli, É. 2011. A falling cloud of particles at a small but finite Reynolds number. J. Fluid Mech. 671, 34–51.
Pine, D. J., Gollub, J. P., Brady, J. F., and Leshansky, A. M. 2005. Chaos and threshold for irreversibility in sheared suspensions. Nature, 438, 997–1000.
Pozrikidis, C. 1992. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Pres.
Proudman, I. and Pearson, J. R. A. 1957. Expansion at small Reynolds number for the flow past a sphere and a circular cylinder. J. Fluid Mech., 2, 237–262.
Ramachandran, A. and Leighton, D. T. 2008. The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 603, 207–243.
Reif, F. 1965. Fundamentals of Statistical Mechanics. McGraw-Hill, New York.
Reynolds, O. 1886. On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil. Phil. Trans. R. Soc. Lond., 177, 157–234.
Richardson, J. F. and Zaki, W. N. 1954. Sedimentation and fluidization: Part ITrans. Inst. Chem. Engrs., 32, 35–53.
Rybczyński, W. 1911. Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium. Bull. Acad. Sci. Cracovie, A, 40–46.
Rubinow, S. I. and Keller, J. B. 1961. The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech., 11, 447–459.
Russel, W. B., Saville, D. A., and Schowalter, W. R. 1989. Colloidal Dispersion. Cambridge University Press.
Saffman, P. G. 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech., 22, 385–400.
Saffman, P. G. 1973. On the settling speeds of free and fixed suspensions. Stud. Appl. Math., 52, 115–127.
Schonberg, J. A. and Hinch, E. J. 1989. Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech, 203. 517–524.
Segré, G. and Silberberg, A. 1962. Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech., 14, 136–157.
Shao, X., Yu, Z., and Sun, B. 2008. Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Phys. Fluids, 20, 103307.
Sierou, A. and Brady, J. F. 2002. Rheology and microstructure in concentrated noncolloidal suspensionsJ. Rheol., 46, 1031–1056.
Smoluchowski, M. 1906. Zur kinetischen Theorie der Brownschen Molekular-bewegung und der Suspensionen. Annalen der Physik, 21, 756–780.
Smoluchowski, M. 1911. Über die Wechselwirkung von Kugeln, die sich in einer zähen Flüssigkeit bewegen. Bull. Acad. Sci. Cracow, 1A, 28.
Stickel, J. J. and Powell, R. L. 2005. Fluid mechanics and rheology of dense suspensions. Ann. Rev. Fluid Mech., 37, 129–149.
Stokes, G. G. 1851. On the effect of the internal friction of fluids on the motion of pendulums. Trans. Cambridge Phil. Soc., IX, 8. Reprinted in Mathematical and Physical Papers, Sir George Gabriel Stokes and Sir J. Larmor, 3, 1880–1905.
Subramanian, G. and Brady, J. F. 2006. Trajectory analysis for non-Brownian inertial suspensions in simple shear flow. J. Fluid Mech., 559, 151–203.
Subramanian, G. and Koch, D. L. 2006. Centrifugal forces alter streamline topology and greatly enhance the rate of heat and mass transfer from neutrally buoyant particles to a shear flow. Phys. Rev. Lett., 96, 134503.
Subramanian, G. and Koch, D.L. 2008. Evolution of clusters of sedimenting low-Reynolds-number particles with Oseen interactions. J. Fluid Mech., 603, 63–100.
Sutherland, W. 1905. A dynamical theory of diffusion for non-electrolytes and the molecular mass of Albumin. Phil. Mag., 9, 781–785.
Taylor, G. I. 1966. Low Reynolds Number Flows, The U.S. National Committee for Fluid Mechanics Films.
Van Dyke, M. 1964. Perturbation Methods in Fluid Dynamics, Academic Press, New York. 1975. Annotated edition, Parabolic Press, Stanford.
Vasseur, P. and Cox, R. G. 1976. The lateral migration of a spherical particle in two-dimensional shear flows. J. Fluid Mech., 78, 385–413.
Wagner, N. J. and Brady, J. F. 2009. Shear thickening in colloidal dispersions. Phys. Today, 62, 27–32.
Whitehead, A. N. 1889. Second approximations to viscous fluid motion. Quart. J. Math., 23, 143–150.
Whitham, G. B. 1974. Linear and Nonlinear Waves. Wiley-Interscience, New York.
Wilson, H. J. 2005. An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow. J. Fluid Mech., 534, 97–114.
Yin, X. and Koch, D. L. 2007. Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers. Phys. Fluids, 19, 093302.
Yurkovetsky, Y. and Morris, J. F. 2008. Particle pressure in a sheared Brownian suspension. J. Rheol., 52, 141–165.
Zarraga, I. E., Hill, D. A., and Leighton, D. T. 2000. The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol., 44, 185–220.
Zirnsak, M. A., Hur, D. U., and Boger, D. V. 1994. Normal stresses in fiber suspensions. J. Non-Newtonian Fluid Mech., 54, 153–193.


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