  Spatially uniform electric fields have been used to induce instabilities in
liquids and polymers, and to orient and deform ordered phases of
block-copolymers. Here we discuss the demixing phase transition occurring in
liquid mixtures when they are subject to spatially nonuniform fields. Above the
critical value of potential, a phase-separation transition occurs, and two
coexisting phases appear separated by a sharp interface. Analytical and
numerical composition profiles are given, and the interface location as a
function of charge or voltage is found. The possible influence of demixing on
the stability of suspensions and on inter-colloid interaction is discussed.
