Hostname: page-component-7dd5485656-7jgsp Total loading time: 0 Render date: 2025-10-31T01:51:41.445Z Has data issue: false hasContentIssue false
  • English
  • Français

Motion of a rigid particle in Stokes flow: a new second-kind boundary-integral equation formulation

Published online by Cambridge University Press:  26 April 2006

Nadav Liron  and
Efrath Barta
Nadav Liron
Affiliation:
Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
Efrath Barta
Affiliation:
Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

A new singular boundary-integral equation of the second kind is presented for the stresses on a rigid particle in motion in Stokes flow. The integral equation is particularly suitable for the mobility problem – when the forces and moments on the particle are given. A generalized Faxén law is also presented. The power of the method is demonstrated by easily reproducing known results as well as new ones, both analytically and numerically, in infinite medium as well as in confined regions.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 579 - 598
Copyright
© 1992 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.)

Article purchase

Temporarily unavailable

References

Barta, E. & Liron, N. 1988a Slender body interactions for low Reynolds numbers - Part I: Body-wall interactions. SIAM J. Appl. Maths 48, 992–1008.Google Scholar
Barta, E. & Liron, N. 1988b Slender body interactions for low Reynolds numbers - Part II: Body-body interactions. SIAM J. Appl. Maths 48, 1262–1280.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
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
Brenner, H. 1964 The Stokes resistance of an arbitrary particle - IV. Arbitrary fields of flow. Chem. Engng Sci. 19, 703–727.Google Scholar
Brenner, H. 1966 The Stokes resistance of an arbitrary particle - V. Symbolic operator representation of intrinsic resistance. Chem. Engng Sci. 21, 97–109.Google Scholar
Brenner, H. & Condiff, D. W. 1974 Transport mechanics in systems of orientable particles IV. Convective transport. J. Colloid Interface Sci. 47, 199–264.Google Scholar
Brenner, H. & Haber, S. 1983 Symbolic operator representation of generalized Faxén relations, Physicochem. Hydrodyn. 4, 271–278.Google Scholar
Caflisch, R. E. & Rubinstein, J. 1986 Lectures on the mathematical theory of multi-phase flow. NYU Courant Inst. of Math. Sci. Lecture Notes.Google Scholar
Chwang, A. T. 1975 Hydromechanics of low-Reynolds-number flow. Part 3. Motion of a spheroidal particle in quadratic flows. J. Fluid Mech. 72, 17–34.Google Scholar
Chwang, A. T. & Wu, T. Y. 1974 Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies. J. Fluid Mech. 63, 607–622.Google Scholar
Chwang, A. T. & Wu, T. Y. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flow. J. Fluid Mech. 67, 787–815.Google Scholar
Durlofsky, L. J. & Brady, J. F. 1989 Dynamic simulation of bounded suspensions of hydrodynamically interacting particles, J. Fluid Mech. 200, 39–67.Google Scholar
Edwardes, D. 1892 Steady motion of a viscous liquid in which an ellipsoid is constrained to rotate about a principal axis. Q. J. Maths 26, 70–78.Google Scholar
Ganatos, P., Weinbaum, S. & Pfeffer, R. 1980a A strong interaction theory for creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion. J. Fluid Mech. 99, 739–753.Google Scholar
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1980b A strong interaction theory for creeping motion of a sphere between plane boundaries. Part 2. Parallel motion. J. Fluid Mech. 99, 755–783.Google Scholar
Gavze, E. 1989 The accelerated motion of rigid bodies in non-steady Stokes flow. Int J. Multiphase Flow 16, 153–166.Google Scholar
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics, with Special Applications to Particulate Media. 2nd rev. edn. Leyden: Noordhoff.
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
Hsu, R. & Ganatos, P. 1989 The motion of a rigid body in viscous fluid bounded by a plane wall. J. Fluid Mech. 207, 29–72.Google Scholar
Jeffrey, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Johnson, R. E. & Wu, T. Y. 1979 Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus. J. Fluid Mech. 95, 263–277.Google Scholar
Karrila, S. J., Fuentes, Y. O. & Kim, S. 1989 Parallel computational strategies for hydrodynamic interactions between rigid particles of arbitrary shape in a viscous fluid. J. Rheol. 33, 913–947.Google Scholar
Karrila, S. J. & Kim, S. 1989 Integral equations of the second kind for Stokes flow: direct solution for physical variables and removal of inherent accuracy limitations. Chem. Engng Commun. 82, 123–161.Google Scholar
Kim, S. 1985 A note on Faxén laws for nonspherical particles. Intl J. Multi phase Flow 11, 713–719.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics, Principles and Selected Applications. Butterworth-Heinemann.
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow, rev. English edn. Gordon and Breach.
Lamb, H. 1945 Hydrodynamics, 6th edn. Cambridge University Press.
Liron, N. 1978 Fluid transport by cilia between parallel plates. J. Fluid Mech. 86, 705–726.Google Scholar
Liron, N. 1984 Stokeslet arrays in a pipe and their application to ciliary transport. J. Fluid Mech. 143, 173–195.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
Liron, N. & Shahar, R. 1978 Stokes flow due to a Stokeslet in a pipe. J. Fluid Mech. 86, 727–744.Google Scholar
Oseen, C. W. 1927 Hydrodynamik. Leipzig: Akad. Verlagsgesellschaft.
Power, H. & Miranda, G. 1987 Second kind integral equation formulation of Stokes flow past a particle of arbitrary shape. SIAM J. Appl. Maths. 47, 689–698.Google Scholar
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191–200.Google Scholar
Tran-Cong, T. & Phan-Thien, N. 1989 Stokes problems of multiparticle systems: a numerical method for arbitrary flows. Phys. Fluids. A 1, 453–461.Google Scholar
Weinbaum, S., Ganatos, P. & Yan, Z. Y. 1990 Numerical multipole and boundary integral equation techniques in Stokes flow. Ann. Rev. Fluid Mech. 22, 275–316.Google Scholar
Youngren, G. K. & Acrovos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377–403.Google Scholar