Image system for Stokes-flow singularity between two parallel planar walls

Using a recently developed image representation for Stokes flow in a half-space bounded by a planar wall [Cichocki and Jones, Physica A 258, 273 (1998)], the image system is constructed for the flow field produced by a force multipole in the space bounded by two parallel walls. The image singularities are expressed in terms of products of double-reflection matrices, and the expansion is simplified using symmetries of the double-reflection operation. Our analysis yields recurrence relations for the strengths of the image multipoles. The relations are solved explicitly, and a complete image system is obtained for an arbitrary source-force multipole. Applications of our image representation for evaluating the hydrodynamic friction and mobility matrices of particles interacting with two parallel planar walls are indicated.

[1]  L. G. Leal,et al.  Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz , 1979, Journal of Fluid Mechanics.

[2]  Effect of hydrodynamic interactions on the irreversible deposition of colloidal particles: Deposition algorithm and simulations , 2000 .

[3]  M. D. Carbajal-Tinoco,et al.  Collective Dynamics in Quasibidimensional Colloidal Suspensions , 1998 .

[4]  Stokes flow in the presence of a planar interface covered with incompressible surfactant , 1999 .

[5]  J. Santana-Solano,et al.  Short-time dynamics of colloidal particles confined between two walls. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  E R Dufresne,et al.  Hydrodynamic coupling of two brownian spheres to a planar surface. , 2000, Physical review letters.

[7]  A. Nikolov,et al.  Universality in film stratification due to colloid crystal formation , 1992 .

[8]  C. Pozrikidis.  Boundary Integral and Singularity Methods for Linearized Viscous Flow: Index , 1992 .

[9]  J. Sherwood,et al.  Stokesian dynamics simulations of particle trajectories near a plane , 1991 .

[10]  J. Blake,et al.  A note on the image system for a stokeslet in a no-slip boundary , 1971, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  A. R. Edmonds.  Angular Momentum in Quantum Mechanics , 1957 .

[12]  R. B. Jones,et al.  Friction and mobility for colloidal spheres in Stokes flow near a boundary: The multipole method and applications , 2000 .

[13]  M. Kollmann,et al.  Brownian dynamics study of dynamic scaling and related freezing criteria in quasi-two-dimensional dispersions , 2001 .

[14]  Konrad Hinsen,et al.  Friction and mobility of many spheres in Stokes flow , 1994 .

[15]  Sangtae Kim,et al.  Microhydrodynamics: Principles and Selected Applications , 1991 .

[16]  J. Crocker,et al.  ENTROPIC ATTRACTION AND REPULSION IN BINARY COLLOIDS PROBED WITH A LINE OPTICAL TWEEZER , 1999 .

[17]  B. U. Felderhof.  FORCE DENSITY INDUCED ON A SPHERE IN LINEAR HYDRODYNAMICS II. MOVING SPHERE, MIXED BOUNDARY CONDITIONS , 1976 .

[18]  S. Rice,et al.  Experimental observations of non-Gaussian behavior and stringlike cooperative dynamics in concentrated quasi-two-dimensional colloidal liquids. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  David G. Grier,et al.  Brownian dynamics of a sphere between parallel walls , 2001 .

[20]  S. Mochón,et al.  Stokes flow for a stokeslet between two parallel flat plates , 1976 .

[21]  R. Jones,et al.  Image representation of a spherical particle near a hard wall , 1998 .

[22]  A. Nikolov,et al.  Dispersion stability due to structural contributions to the particle interaction as probed by thin liquid film dynamics , 1992 .