  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.
