Dynamics of a bound membrane

The dispersion relation for the overdamped bending modes of a membrane bound to a substrate by an attractive potential is determined. The damping rate {γ} as a function of the wave vector q behaves, for small q, like {γ}{~}q² arising from the interplay between the hydrodynamic damping by the surrounding liquid and the restoring force in the binding potential. With increasing wave vector q, various crossovers can occur, leading to the possibility of nonmonotonic damping where {γ} decreases with q as {~}1/q.