Relaxation modes of an adhering bilayer membrane

Abstract

We determine the relaxational dynamics of the shape fluctuations of a fluid membrane in the vicinity of a substrate. Extending the "classical" description, we include the coupling between the local shape and the difference of the two monolayer densities as well as a lateral tension in the membrane. These extensions introduce additional length scales to the problem. The asymptotic behavior of the dispersion relation and the correlation functions can be understood from limiting cases in which either a free bilayer or a bound incompressible membrane is considered. In many cases, however, the relevant length scales do not separate very well, so that the full dispersion relation will be needed for the interpretation of experiments. It is shown that in addition to the damping due to bulk viscosity the dissipation due to friction between the monolayers is observable and indeed dominates the long-time behavior of the dynamical height correlation function for large wave vectors. As demonstrated with typical sets of parameters, the transition to this regime will be accessible by optical techniques only for weak adhesion and strong friction between the monolayers.