Stability of additive-free water-in-oil emulsions

Abstract

We calculate ion distributions near a planar oil–water interface within nonlinearPoisson–Boltzmann theory, taking into account the Born self-energy of the ions in the twomedia. For unequal self-energies of cations and anions a spontaneous charge separation isfound, such that the water and oil phases become oppositely charged in slabs with a typicalthickness of the Debye screening length in the two media. From the analyticalsolutions, the corresponding interfacial charge density and the contribution to theinterfacial tension is derived, together with an estimate for the Yukawa potentialbetween two spherical water droplets in oil. The parameter regime is explored wherethe plasma coupling parameter exceeds the crystallization threshold, i.e. wherethe droplets are expected to form crystalline structures due to a strong Yukawarepulsion, as recently observed experimentally. Extensions of the theory that wediscuss briefly, include numerical calculations on spherical water droplets in oil, andanalytical calculations of the linear PB-equation for a finite oil–water interfacialwidth.