  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.
