Stability of additive-free water-in-oil emulsions

TL;DR

This paper investigates the stability of additive-free water-in-oil emulsions by analyzing ion distributions and interfacial charges using non-linear Poisson-Boltzmann theory, revealing spontaneous charge separation and conditions for droplet crystallization.

Contribution

It introduces a theoretical framework for ion distributions and interfacial charge in water-in-oil emulsions considering ion self-energies, predicting spontaneous charge separation and droplet crystallization.

Findings

Spontaneous charge separation occurs at the oil-water interface.

Interfacial charge density and tension contributions are analytically derived.

Conditions for droplet crystallization due to Yukawa repulsion are identified.

Abstract

We calculate ion distributions near a planar oil-water interface within non-linear Poisson-Boltzmann theory, taking into account the Born self-energy of the ions in the two media. For unequal self-energies of cations and anions, a spontaneous charge separation is found such that the water and oil phase become oppositely charged, in slabs with a typical thickness of the Debye screening length in the two media. From the analytical solutions, the corresponding interfacial charge density and the contribution to the interfacial tension is derived, together with an estimate for the Yukawa-potential between two spherical water droplets in oil. The parameter regime is explored where the plasma coupling parameter exceeds the crystallization threshold, i.e. where the droplets are expected to form crystalline structures due to a strong Yukawa repulsion, as recently observed experimentally. Extensions of the theory that we discuss briefly include numerical calculations on spherical water droplets in oil, and analytical calculations of the linear PB-equation for a finite oil-water interfacial width.