The electroviscous effect for suspensions of solid spherical particles

Abstract

In this paper a theoretical analysis is made of the electrokinetic phenomenon known as the 'electroviscous effect'. A general formula is given for the effective viscosity of a suspension of solid, spherical, charged non-conducting particles in an electrolyte. The increase of the effective viscosity due to the surface charge and the ionic double layer surrounding the particles is determined by a modification of Einstein's method for the calculation of the viscosity of solid suspensions. The effective viscosity may be expressed in the form $\eta $ = $\eta _{0}\left\{1+2\cdot 5(v/V)\left(1+\underset r=1\to{\overset \infty \to{\sum}}a_{r}Q^{r}\right)\right\}$, where $\eta _{0}$ is the viscosity of the electrolyte, v the volume of suspension in volume V of solution and Qe is the charge on each particle. It is shown that a$_{1}$ = 0 and a$_{2}$ is determined explicitly. It is found that the electroviscous contribution to $\eta $, for a given charge Q, tends to increase as the thickness of the double layer increases. When the thickness of the double layer is small compared with the radius of the particle the effect vanishes. A comparison with previous theoretical work is made, and it is shown that much improved agreement with experiment is obtained.