Application of electric fields tangent to the plane of a confined patch of fluid bilayer membrane can create lateral concentration gradients of the lipids. A thermody- namic model of this steady-state behavior is developed for binary systems and tested with experiments in supported lipid bilayers. The model uses Flory's approximation for the en- tropy of mixing and allows for effects arising when the components have different molecular areas. In the special case of equal area molecules the concentration gradient reduces to a Fermi-Dirac distribution. The theory is extended to include effects from charged molecules in the membrane.
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