Rate of deposition of Brownian particles under the action of London and double-layer forces

Abstract

The rate of collection of Brownian particles under the influence of interaction forces between the collector surface and the particles is calculated by (a) incorporating the interaction forces in the rate constant of a virtual, first order, chemical reaction taking place on the surface of the collector, and by (b) solving the convective diffusion equation subject to that chemical reaction as a boundary condition. Several geometries (sphere, cylinder, rotating disc) are considered for the collector.

An Arrhenius type equation is obtained for the apparent reaction rate constant. Equations for the apparent activation energy and for the frequency factor are established as functions of Hamaker's constant, ionic strength, surface potentials and particle radius.