We calculate the hydrodynamic interaction $\Lambda \left(k\right)$ (Oseen interaction kernel) and relaxation frequency $\omega \left(k\right)$ for the fluctuations of a membrane that is harmonically bounded to a permeable or impermeable wall. We show that due to the confining wall there is an increase in the effective viscosity of the fluid surrounding the membrane. This has been observed in experiments on confined membranes, such as lamellar phases and the red-blood cell membrane. Our results allow a quantitative analysis of these experiments, in terms of the strength of the membrane confining potential and dislocations.

• Received 23 October 2003

DOI:https://doi.org/10.1103/PhysRevE.70.011104