Colloids in Confined Geometries: Hydrodynamics, Simulation and Rheology

Abstract

The hydrodynamics of colloids in confined geometries is studied hierarchically beginning with the exact solutions for a spherical particle translating, rotating and deforming in the presence of a plane wall at low Reynolds number. The many-bodied hydrodynamic interactions among a collection of spherical particles near a plane wall are computed and used to study the Brownian motion of confined suspensions. The method of reflections is used to describe the motion of a single spherical particle embedded in the fluid constrained by two, parallel plane walls. From this, tables which are independent of the channel width are generated describing the particle’s response to various force moments. This same approach is expanded to describe the hydrodynamic interactions among the particles comprising a colloidal dispersion confined in a channel. The simulations arising from this theory depict the short-time self-diffusivity, sedimentation rate and high frequency viscosity of suspensions of varying volume fractions in channels of varying widths. A theory for the scattering of evanescent waves by colloidal dispersions is developed and cast in the form of the diffusivity measured by classical light scattering. A series of simulations is conducted to predict the short- time self-diffusivity and the collective diffusivity measured by evanescent wave dynamic light scattering. The thesis concludes with a discussion of how the developed simulations and theories can be extended to make dynamic measurements as well as a brief consideration of some remaining, open questions.