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The influence of an external electric field on a poorly conductive membrane such as a lipid bilayer is studied theoretically. The unbalanced electric stress created by an ionic current across a non-perfectly flat membrane gives rise to a destabilizing surface energy enhancing undulations. The deformation of a membrane attached to a frame is derived and the electrohydrodynamic instability of a free floating membrane is studied. We find a most unstable mode of undulation, of wavelength in the microm range, connected to the crossover between membrane and solvent dominated dissipations.
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Sens et al. (2002) studied this question.
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