Dynamics of viscoelastic membranes

We determine both the in-plane and out-of-plane dynamics of viscoelastic membranes separating two viscous fluids in order to understand microrheological studies of such membranes. We demonstrate the general viscoelastic signatures in the dynamics of shear, bending, and compression modes. We show that these modes remain independent in the presence of hydrodynamic interactions. The full response functions for motion both in-plane and out-of-plane are derived for the general case of viscoelastic films in contact with arbitrary viscous fluids. Specifically, we derive closed-form expressions for the in-plane longitudinal and transverse response functions for viscous membranes embedded in fluid media. We also find a screening of the otherwise two-dimensional character of the response to point forces due to the presence of the solvent.