The electroviscous effect for suspensions of solid spherical particles

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 η = η ₀ {1+2.5 (v/V) (1+Ʃ ^∞ _{r -1} a _r Q ^r )}, where η 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 η, 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.