A model for the electromechanics of lipid bilayers, accounting for flexoelectricity, is obtained as the thin-film limit of the continuum electrodynamics of nematic liquid crystals.A priori restrictions on the polarization field consistent with minimum energy considerations effectively decouple the leading-order membrane problem from the computation of the self field, yielding a substantial simplification vis a vis the three-dimensional theory.Examples illustrate the strong interplay between the electric field and membrane geometry.
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