Electrical conductivity of dispersions: from dry foams to dilute suspensions

TL;DR

This paper provides a unified empirical model for the electrical conductivity of dispersions, covering a wide liquid fraction range from dry foams to dilute suspensions, integrating previous data and classical limits.

Contribution

It introduces a comprehensive empirical formula that accurately describes electrical conductivity across diverse dispersion states, bridging dry foams and dilute suspensions.

Findings

Unified empirical model fits all data

Recovers Lemlich's result for dry foams

Recovers Maxwell's result for dilute suspensions

Abstract

We present new data for the electrical conductivity of foams in which the liquid fraction ranges from two to eighty percent. We compare with a comprehensive collection of prior data, and we model all results with simple empirical formul\ae. We achieve a unified description that applies equally to dry foams and emulsions, where the droplets are highly compressed, as well as to dilute suspensions of spherical particles, where the particle separation is large. In the former limit, Lemlich's result is recovered; in the latter limit, Maxwell's result is recovered.