  Manipulation of the charge of the dielectric interface between two bulk
liquids not only enables the adjustment of the interfacial tension but also
controls the storage capacity of ions in the ionic double layers adjacent to
each side of the interface. However, adjusting this interfacial charge by
static external electric fields is difficult since the external electric fields
are readily screened by ionic double layers that form in the vicinity of the
external electrodes. This leaves the liquid-liquid interface, which is at a
macroscopic distance from the electrodes, unaffected. In this study we show
theoretically, in agreement with recent experiments, that control over this
surface charge at the liquid-liquid interface is nonetheless possible for
macroscopically large but finite closed systems in equilibrium, even when the
distance between the electrode and interface is orders of magnitude larger than
the Debye screening lengths of the two liquids. We identify a crossover
system-size below which the interface and the electrodes are effectively
coupled. Our calculations of the interfacial tension for various electrode
potentials are in good agreement with recent experimental data.
