Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-10T17:25:46.351Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic simulation of bounded suspensions of hydrodynamically interacting particles

Published online by Cambridge University Press:  26 April 2006

Louis J. Durlofsky  and
John F. Brady
Louis J. Durlofsky
Affiliation:
Chevron Oil Field Research Company, PO Box 446, La Habra, CA 90633–0446, USA
John F. Brady
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A general method for computing the hydrodynamic interactions among an infinite suspension of particles immersed between two infinite plane boundaries, under the condition of vanishing particle Reynolds number, is presented. The method accounts for both near-field particle-particle and particle-boundary lubrication effects as well as dominant many-body effects, which include reflections with both particles and boundaries. Through relative motion of the boundaries, a bulk shear flow can be generated, and the resulting particle motions, as well as the forces exerted by the boundaries on the fluid, computed. Knowledge of the boundary forces allows for the calculation of the suspension viscosity. The simulation method is applied to several example problems; in one, the resuspension of a sediment layer of particles is illustrated. The general method can also be extended to dynamically simulate suspensions immersed in a pressure driven flow between two walls or through a tube.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 39 - 67
Copyright
© 1989 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
Blake, J. R.: 1971 A note on the image system for a stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303–310.Google Scholar
Blanc, R., Belzons, M., Camoin, C. & Bouillot, J. L., 1983 Cluster statistics in a bidimensional suspension: comparison with percolation. Rheol. Acta 22, 505–511.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. 87, 5437–5448.Google Scholar
Bouillot, J. L., Camoin, C., Belzons, M., Blanc, R. & Guyon, E., 1982 Experiments on 2-D suspensions. Adv. Colloid Interface Sci. 17, 299–305.Google Scholar
Brady, J. F. & Bossis, G., 1985 The rheology of concentrated suspensions of spheres in simple shear flow. J. Fluid Mech. 155, 105–129.Google Scholar
Brady, J. F., Phillips, R. J., Lester, J. C. & Bossis, G., 1988 Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 195, 257–280.Google Scholar
Brenner, H.: 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng. Sci. 16, 242–251.Google Scholar
Cox, R. G. & Brenner, H., 1967 The slow motion of a sphere through a viscous fluid towards a plane surface. II. Small gap widths, including inertial effects. Chem. Engng Sci. 22, 1753–1777.Google Scholar
Dean, W. R. & O'Neill, M. E. 1963 A slow motion of viscous liquid caused by the rotation of a solid sphere. Mathematika 10, 13–24.Google Scholar
Durlofsky, L.: 1986 Topics in fluid mechanics: I. Flow between finite rotating disks. II. Simulation of hydrodynamically interacting particles in Stokes flow. PhD thesis, Massachusetts Institute of Technology.
Durlofsky, L. & Brady, J. F., 1987 Analysis of the Brinkman equation as a model for flow in porous media. Phys. Fluids 30, 3329–3341.Google Scholar
Durlofsky, L., Brady, J. F. & Bossis, G., 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49.Google Scholar
Gadala-Maria, F. A.: 1979 The rheology of concentrated suspensions. PhD thesis, Stanford University.
Ganatos, P., Pfeffer, R. & Weinbaum, S., 1980a A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 2. Parallel motion. J. Fluid Mech. 99, 755–783.Google Scholar
Ganatos, P., Weinbaum, S. & Pfeffer, R., 1980b A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion. J. Fluid Mech. 99, 739–753.Google Scholar
Ganatos, P., Weinbaum, S. & Pfeffer, R., 1982 Gravitational and zero-drag motion of a sphere of arbitrary size in an inclined channel at low Reynolds number. J. Fluid Mech. 124, 27–43.Google Scholar
Goldman, A. J., Cox, R. G. & Brenner, H., 1967a Slow viscous motion of a sphere parallel to a plane wall. I. Motion through a quiescent fluid. Chem. Engng Sci. 22, 637–651.Google Scholar
Goldman, A. J., Cox, R. G. & Brenner, H., 1967b Slow viscous motion of a sphere parallel to a plane wall. II. Couette Flow. Chem. Engng Sci. 22, 653–660.Google Scholar
Happel, J. & Brenner, H., 1973 Low Reynolds Number Hydrodynamics, 2nd edn. Noorhoof.
Ho, B. P. & Leal, L. G., 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365–400.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. & 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
Ladyzhenskaya, O. A.: 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach.
Leighton, D. & Acrivos, A., 1986 Viscous resuspension. Chem. Engng Sci. 41, 1377–1384.Google Scholar
Leighton, D. & Acrivos, A., 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.Google Scholar
Liron, N. & Mochon, S., 1976 Stokes flow for a Stokeslet between two parallel flat plates. J. Engng Maths 10, 287–303.Google Scholar
Maude, A. D.: 1961 End effects in a falling-sphere viscometer. Brit. J. Appl. Phys 12, 293–295.Google Scholar
O'Brien, R. W.: 1979 A method for the calculation of the effective transport properties of suspensions of interacting particles. J. Fluid Mech. 91, 17–39.Google Scholar
O'Neill, M. E.: 1964 A slow motion of viscous liquid caused by a slowly moving solid sphere. Mathematika 11, 67–74.Google Scholar
O'Neill, M. E.: 1968 A sphere in contact with a plane wall in a slow linear shear flow. Chem. Engng Sci. 23, 1293–1298.Google Scholar
O'Neill, M. E. & Stewartson, K. 1967 On the slow motion of a sphere parallel to a nearby plane wall. J. Fluid Mech. 27, 705–724.Google Scholar