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

A model for the electric field-driven deformation of a drop or vesicle in strong electrolyte solutions