Hydrodynamics of membranes: the bilayer aspect and adhesion

We review recent work on the dynamics of membranes. First, we discuss the viscous modes of a free bilayer membrane, laking inlo account the couplina betwccn bending and the local density of the two monolayers. Ap:art from import:ant corrections to the conventional bending mode, we obtain a second slow mode which is essentially a fluctuation in the density difference of the two monoiayers. dalllDCd by intcnnonolayer friction. Estimates for a stack of membranes show reasonable agreement with a recent spin-echo study of membrane undulations. Second, we discuss the dispemon relation for both fluid and polymerized membranes bound to a substrate by an attractive potential. The interplay between the hydrodynami& dampio8 by the ~urroundin8 liquid and the restoring force in the binding polcnlialleads to a ql dependence of the dampina rate "'t at small waveve<:lor q. With increasing q. various crossovers can occur, including the possibility of nonmonotonic damping in which "'t decreases with q as l jq.