  The charge distribution at the interface between two electrolytes is studied
for the case of non-vanishing ion fluxes. The analysis is an extension of the
established Verwey-Niessen theory to non-equilibrium situations. Applying
matched asymptotic expansions for the region of the electric double layer and
the bulk electrolytes, analytical expressions for the ion concentrations and
the electrostatic potential are derived. It is found that the electric double
layer is surprisingly stable. Even in cases where the applied electric field is
so strong that it completely cancels the field of the charge clouds at the
interface, two opposing space charge regions are formed. This phenomenon is
qualitatively explained using a simple model incorporating ion partitioning and
diffusive ion transport. Another notable phenomenon is that the interface
acquires a net charge in the presence of an applied electric field, being of
relevance for the hydrodynamic stability of interfacial flows.
