Adsorption of interacting Brownian particles onto surfaces: II. Results for hydrodynamic interactions

Abstract

In this study we have derived a generalized diffusion equation for interacting Brownian particles in a space that includes a fixed external surface of arbitrary shape. Both fluid convection and external forces are also included in a general fashion. The Brownian particles can interact with each other and with the fixed surface. These interactions include direct strong force interactions, such as various types of electrostatic interactions, and indirect, hydrodynamic interactions due to the presence of the intervening fluid. The hydrodynamic interactions are treated through a superposition approximation of the particle-fixed surface and particle-particle hydrodynamic problems. The generalized diffusion equation obtained is shown to recover Felderhof's equation (6) in the absence of a fixed surface and the more commonly studied single-particle convective diffusion equation in the absence of interparticle interactions. The conditions of applicability of the generalized diffusion equation are established by asymptotic analysis (Appendix 1). As a specific example, the problem of convective transport and adsorption of hydrodynamically interacting particles onto a fixed external surface was solved under the conditions of low fluid Reynolds numbers and large Peelet numbers, thereby extending the analysis of Part I (4) for nonhydrodynamically interacting particles. Also, a critical examination of the superposition approximation of the hydrodynamic problem is given on the basis of recently published solutions involving many interacting spheres and a plane wall.