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Dynamic simulation of hydrodynamically interacting particles

Published online by Cambridge University Press:  21 April 2006

L. Durlofsky ,
J. F. Brady  and
G. Bossis
L. Durlofsky
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
J. F. Brady
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
G. Bossis
Affiliation:
Laboratorie de Physique de la Matière Condensée, Université de Nice. Parc Valrose, 06034 Nice Cedex, France
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Abstract

A general method for computing the hydrodynamic interactions among N suspended particles, under the condition of vanishingly small particle Reynolds number, is presented. The method accounts for both near-field lubrication effects and the dominant many-body interactions. The many-body hydrodynamic interactions reproduce the screening characteristic of porous media and the ‘effective viscosity’ of free suspensions. The method is accurate and computationally efficient, permitting the dynamic simulation of arbitrarily configured many-particle systems. The hydrodynamic interactions calculated are shown to agree well with available exact calculations for small numbers of particles and to reproduce slender-body theory for linear chains of particles. The method can be used to determine static (i.e. configuration specific) and dynamic properties of suspended particles that interact through both hydrodynamic and non-hydrodynamic forces, where the latter may be any type of Brownian. colloidal, interparticle or external force. The method is also readily extended to dynamically simulate both unbounded and bounded suspensions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 21 - 49
Copyright
© 1987 Cambridge University Press

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References

Arp, P. A. & Mason, S. G. 1977 The kinetics of flowing dispersions. VIII. Doublets of rigid spheres (theoretical). J. Colloid Interface Sci. 61, 21–43.Google Scholar
Batchelor, G. K. 1970a The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Batchelor, G. K. 1970b Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419–440.Google Scholar
Batchelor, G. K. 1976 Brownian diffusion of particles with hydrodynamic interaction. J. Fluid Mech. 74, 1–29.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56, 375–400.Google Scholar
Beenakker, C. W. J. 1984 The effective viscosity of a concentrated suspension of spheres (and its relation to diffusion). Physica 128A, 48–81.Google Scholar
Beenakker, C. W. J. & Mazur, P. 1983 Self-diffusion of spheres in a concentrated suspension. Physica 120A, 388–410.Google Scholar
Bossis, G. & Brady, J. F. 1984 Dynamic simulation of sheared suspensions. I. General Method. J. Chem. Phys. 80, 5141–5154.Google Scholar
Bossis, G. & Brady, J. F. 1987 Self diffusion of Brownian particles in concentrated suspensions under shear. J. Chem. Phys. (submitted).Google Scholar
Brady, J. F. & Bossis, G. 1985 The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105–129.Google Scholar
Bretherton, F. P. 1964 Inertial effects on clusters of spheres falling in a viscous fluid. J. Fluid Mech. 20, 401–410.Google Scholar
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27–34.Google Scholar
Chwang, A. T. & Wu, Y.-T. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 67, 787–815.Google Scholar
Cox, R. G. 1974 The motion of suspended particles almost in contact. Intl J. Multiphase Flow 1, 343–371.Google Scholar
Durlofsky, L. 1986 Topics in fluid mechanics: I. Flow between finite rotating disks. II. Simulation of hydrodynamically interacting particles in Stokes flow. Ph.D. Thesis, Massachusetts Institute of Technology.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1978 A numerical-solution technique for three-dimensional Stokes flows, with application to the motion of strongly interacting spheres in a plane. J. Fluid Mech. 84, 79–111.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
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.Google Scholar
Howells, I. D. 1974 Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects. J. Fluid Mech. 64, 449–475.Google Scholar
Jayaweera, K. O. L. F., Mason, B. J. & Slack, G. W. 1964 The behaviour of clusters of spheres falling in a viscous fluid. Part 1. Experiment. J. Fluid Mech. 20, 121–128.Google Scholar
Jeffrey, D. J. & Onishi, Y. 1984 Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech. 139, 261–290.Google Scholar
Kim, S. 1986 Singularity solutions for ellipsoids in low-Reynolds-number flows: with applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids. Intl J. Multiphase Flow 12, 469–491.Google Scholar
Kim, S. & Mifflin, R. T. 1985 The resistance and mobility functions of two equal spheres in low-Reynolds-number flow. Phys. Fluids 28, 2033–2045.Google Scholar
Kynch, G. J. 1959 The slow motion of two or more spheres through a viscous fluid. J. Fluid Mech. 5, 193–208.Google Scholar
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach.
Mazur, P. & Saarloos, W. van 1982 Many-sphere hydrodynamic interactions and mobilities in a suspension. Physica 115A, 21–57.Google Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377–403.Google Scholar