Analysis of Concentrated Colloidal Dispersions

Abstract

A long-standing area of research in colloid science concerns the determination of electrostatic, magnetic, and elastostatic fields in dispersions comprising densely packed particles whose material properties differ markedly from that of the background. As new materials with complex microstructures are being developed, there is a corresponding need for analytic and numerical methods to predict and understand their properties. Dense systems with large numbers of close-to-touching particles require very fine discretization which causes the linear system of equations that arise to be highly ill-conditioned. A framework for solving the many-body interface problems is provided by a mathematical transformation of the boundary value integral equation. The transformation avoids the use of asymptotics and involves no uncontrolled approximations which distinguishes this work from previous methods. Pointwise analysis of local charge densities in the bulk and at interfaces is now possible.