We derived free energy functional of a bilayer lipid membrane from the firstprinciples of elasticity theory. The model explicitly includesposition-dependent mutual slide of monolayers and bending deformation. Our freeenergy functional of liquid-crystalline membrane allows for incompressibilityof the membrane and vanishing of the in-plane shear modulus and obeysreflectional and rotational symmetries of the flat bilayer. Interlayer slide atthe mid-plane of the membrane results in local difference of surface densitiesof the monolayers. The slide amplitude directly enters free energy via thestrain tensor. For small bending deformations the ratio between bending modulusand area compression coefficient, Kb/KA, is proportional to the square ofmonolayer thickness, h. Using the functional we performed self-consistentcalculation of steric potential acting on bilayer between parallel confiningwalls separated by distance 2d. We found that temperature-dependent curvatureat the minimum of confining potential is enhanced four times for a bilayer withslide as compared with a unit bilayer. We also calculate viscous modes ofbilayer membrane between confining walls. Pure bending of the membrane isinvestigated, which is decoupled from area dilation at small amplitudes. Threesources of viscous dissipation are considered: water and membrane viscositiesand interlayer drag. Dispersion has two branches. Confinement between the wallsmodifies the bending mode with respect to membrane in bulk solution.Simultaneously, inter-layer slipping mode, damped by viscous drag, remainsunchanged by confinement.
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