The interpretation of electrokinetic measurements using a dynamic model of the stern layer: I. The dynamic model

Abstract

Results from recent electrophoresis, electrical conductivity, and electro-osmosis experiments on polystyrene latices have been ambiguous. ζ potentials derived from complementary measurements of mobility and electrical conductivity, for example, fail to agree with each other. One mechanism which can account for the discrepancy is the lateral movement of ions within the Stern layer in response to concentration gradients and the tangential electric field. A mathematical model of electrokinetics is presented here in which a dynamic model of the Stern layer is coupled to the standard Gouy-Chapman model of the diffuse layer. Transport within the Stern layer is modeled with a two-dimensional analog of the Nernst-Planck equation used to describe electromigration and diffusion in the bulk solution. Adsorption-desorption processes are employed to depict the equilibrium charge using a model which relates concentrations in the Stern layer to those in the adjacent part of the diffuse layer. The model equations are solved numerically and the solutions used to show how various parameters affect the electrophoretic mobility of individual particles and the conductivity of a suspension of particles. It is shown that the presence of mobile counterions in the Stern layer lowers the ζ potentials inferred from mobility measurements and raises those from conductivity measurements, compared to the ζ potentials that correspond to the intrinsic particle charge. In Part II (C. F. Zukoski IV and D. A. Saville, J. Colloid Interface Sci. 114, 45–53 (1986)) the model will be used in the interpretation of experimental measurements.