A planar lipid bilayer in an electric field: membrane instability, flow   field and electrical impedance
  For many biotechnological applications it would be useful to better understand the effects produced by electric fields on lipid membranes. This review discusses several aspects of the electrostatic properties of a planar lipid membrane with its surrounding electrolyte in a normal DC or AC electric field. In the planar geometry, the analysis of electrokinetic equations can be carried out quite far, allowing to characterize analytically the steady state and the dynamics of the charge accumulation in the Debye layers, which results from the application of the electric field. For a conductive membrane in an applied DC electric field, we characterize the corrections to the elastic moduli, the appearance of a membrane undulation instability and the associated flows which are built up near the membrane. For a membrane in an applied AC electric field, we analytically derive the impedance from the underlying electrokinetic equations. We discuss different relevant effects due to the membrane conductivity or due to the bulk diffusion coefficients of the ions. Of particular interest is the case where the membrane has selective conductivity for only one type of ion. These results, and future extensions thereof, should be useful for the interpretation of impedance spectroscopy data used to characterize e.g. ion channels embedded in planar bilayers. 
Falko Ziebert, David Lacoste
cond-mat.soft physics.bio-ph