Primary electroviscous effect in suspensions of charged spherical particles

Abstract

The effective viscosity η of a suspension of charged spherical colloidal particles in a general electrolyte of viscosity η₀ is calculated to first order in the volume fraction ϕ to be η=η₀{1 + 5/2ϕ[1 +p(ζ, κa)]}. The primary electroviscous coefficient p(ζ, κa) as a function of the zeta potential ζ is derived in terms of the asymptotic behaviour of the hydrodynamic flow field far from a typical colloidal particle. The computation of p(ζ, κa)(for a general mixed electrolyte with ζ unrestricted in magnitude) is reduced to the solution of a set of linear coupled ordinary differential equations and an accurate and robust numerical scheme for solving them is demonstrated. An analytic approximate expression for p(ζ) correct to (ζ²) is derived and shown to agree with an early result of Booth. Exact numerical results are compared with the approximate expression of Booth. A maximum is predicted in the primary electroviscous coefficient p(ζ) for all κa values. The measurement of the magnitude of this maximum may be used to test the validity of the underlying equations.