  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 $\sim 10^{-3}$ in the absence of colloids. These
findings explain recent observations [M.E. Leunissen {\em et al.}, Proc. Nat.
Ac. Sci {\bf 104}, 2585 (2007)].
