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, taking into account the coupling between bending and the local density of the two monolayers. Apart from important corrections to the conventional bending mode, we obtain a second slow mode which is essentially a fluctuation in the density difference of the two monolayers, damped by intermonolayer friction. Estimates for a stack of membranes show reasonable agreement with a recent spin-echo study of membrane undulations. Second, we discuss the dispersion relation for both fluid and polymerized membranes bound to a substrate by an attractive potential. The interplay between the hydrodynamic damping by the surrounding liquid and the restoring force in the binding potential leads to a q(2) dependence of the damping rate gamma at small wavevector q. With increasing q, various crossovers can occur, including the possibility of nonmonotonic damping in which gamma decreases with q as similar to 1/q.