Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction

We compare extensive experimental results for the gravity-driven steady drainage of oil-in-water emulsions with two theoretical predictions, both based on the assumption of Poiseuille flow. The first is from standard foam drainage theory, applicable at low aqueous volume fractions, for which a correction is derived to account for the effect of the confinement of the foam. The second arises from considering the permeability of a model porous medium consisting of solid sphere packings, applicable at higher aqueous volume fractions. We find excellent quantitative agreement between experiment and the two theories in each of these limits, providing a master curve for the permeability of foams and emulsions. Using our experimental data, we also demonstrate the analogy between the problem of electrical flow and liquid flow through foams and emulsions.