Diffuse Double-Layer Interactions in One-, Two-, and Three-Dimensional Particle Swarms

Abstract

The theory of diffuse double‐layer interactions in homogeneous isotropic swarms of particles is developed by means of a cell model. Energies of interaction are conveniently treated in terms of the partial volumetric Gibbs free energy. Calculations use (in part) a simple “matched Debye–Hückel approximation” to exact solutions of the nonlinear Poisson–Boltzmann equation. Geometrical effects exert a dominant influence on the variation of partial Gibbs free energy with particle area per unit volume of solution. Evaluation of the relative importance of double‐layer interactions and particle Brownian motion provides a check on the cell model. Results for the three‐dimensional swarm are found to be consistent with available estimates of the repulsive force between two spherical particles. Application of the approach to heterogeneous swarms is discussed.