Electrical Conductivity of a Concentrated Suspension of Spherical Colloidal Particles

Abstract

A general expression for the electrical conductivity of a concentrated suspension of spherical colloidal particles is obtained for the case where the particle zeta potential is low and the overlapping of the electrical double layers of adjacent particles is negligible by using Kuwabara's cell model. It is shown how the conductivity of a concentrated suspension depends on the particle volume fraction, the zeta potential ζ, and the reduced particle radius κa(κ = Debye–Hückel parameter anda= particle radius). It is also found that the obtained conductivity formula tends to Maxwell's formula for two different extreme cases: (i) when the particles are uncharged (ζ = 0) and (ii) when the electrical double layers around the particles are infinitesimally thin (κa→ ∞). That is, in the latter limiting case (κa→ ∞), the conductivity becomes independent of the zeta potential, just as in the case of dilute suspensions.