  A model is constructed to describe the arbitrary deformation of a drop or
vesicle that contains and is embedded in an electrolyte solution, where the
deformation is caused by an applied electric field. The applied field produces
an electrokinetic flow or induced charge electro-osmosis. The model is based on
the coupled Poisson-Nernst-Planck and Stokes equations. These are reduced or
simplified by forming the limit of strong electrolytes, for which ion densities
are relatively large, together with the limit of thin Debye layers. Debye
layers of opposite polarity form on either side of the drop interface or
vesicle membrane, together forming an electrical double layer.
  Two formulations of the model are given. One utilizes an integral equation
for the velocity field on the interface or membrane surface together with a
pair of integral equations for the electrostatic potential on the outer faces
of the double layer. The other utilizes a form of the stress-balance boundary
condition that incorporates the double layer structure into relations between
the dependent variables on the layer's outer faces. This constitutes an
interfacial boundary condition that drives an otherwise unforced Stokes flow
outside the double layer. For both formulations relations derived from the
transport of ions in each Debye layer give additional boundary conditions for
the potential and ion concentrations outside the double layer.
