Beginning with the free energy potential for long-range interactions between parallel flat sheets and the mechanical energy of bending those sheets, we have derived an upper bound for repulsion enhanced by thermal undulations of sheets in a multilamellar array. Through a self-consistent (mean-field) potential, we cover the full range of layer separations from close-in to far-apart, where the enhanced repulsion approaches the weak steric interaction derived previously by Helfrich [Helfrich, W. (1978) Z. Naturforsch. 33a, 305-315]. We have examined the effect of the fluctuation-enhanced repulsion in experimental studies of osmotic (and mechanical) compression of multilamellar lipid arrays, mechanical compression of bilayers immobilized on mica substrates, and controlled adhesion of giant bilayer membrane vesicles.
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