We study suspensions of hydrophobic charged colloidal spheres dispersed in a demixed oil-water mixture by means of a modified Poisson-Boltzmann theory, taking into account image charge effects and partitioning of the monovalent ions. We find that the ion's aversion for oil can destroy the double layers of the oil-dispersed colloids. This affects the salt-concentration dependence of the colloidal adsorption to the oil-water interface qualitatively. The theory also predicts a narrow range of the oil-dielectric constant in which micron-sized water-in-oil droplets acquire enough charge to crystallize at volume fractions as small as ∼10−3 in the absence of colloids. These findings explain recent observations [M.E. Leunissen {\em et al.}, Proc. Nat. Ac. Sci {\bf 104}, 2585 (2007)].
@article{arxiv.0705.2327,
title = {Destructed double-layer and ionic charge separation near the oil-water interface},
author = {Jos Zwanikken and René van Roij},
journal= {arXiv preprint arXiv:0705.2327},
year = {2016}
}