Electrical conductivity of dispersions: from dry foams to 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 formulae. 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.

Structure and energy of liquid foams

“…the conductivity of the foam, divided by the conductivity of the bulk liquid. Non-linear corrections are required for increasing liquid fraction, and Feitosa et al [81] have established reliable semi-empirical relationships for both σ(φ) and φ (σ).…”

Electrical conductivity of quasi-two-dimensional foams

“…which has been confirmed by numerous experiments [21][22][23]. The equation does not take into account the effect of the swollen junctions of Plateau borders.…”

“…The measure of electrical conductivity is a powerful tool to determine the foam liquid fraction ε defined as the ratio between the volume of liquid and the total volume of the foam. For 3D foams the relative conductivity σ (being the ratio of the foam σ f and the liquid σ l conductivities) is found to be primarily a function of the liquid fraction ε and does not depend on the bubble size [21]. Theories describing the exact form of this function are well elaborated for three-dimensional foams [22] in two limiting cases of "dry" and "wet" foams.…”

Foamed emulsion drainage: flow and trapping of drops

“…A commercially available device Foamscan (Teclis, France) is used to measure the normalized conductivity of the foamed emulsion Λ = σ foam σ W , linked to ε W through a semi-empirical relation [23] :…”