On the vibration spectra of vesicle-like droplets: The effects of membranedensity fluctuations

The dynamics of vesicle-like droplets is studied within the Helfrich's conc ept of interfacial elasticity. The droplet shape fluctuations are accompani ed with the membrane density changes. As distinct from the previous theorie s, the (linearized) hydrodynamic and boundary equations contain inertial te rms and are solved exactly. Using the continuity equation for the interface , the secular equation for the vibration frequencies is obtained. Its analy sis results in the prediction of a couple of relaxation modes that exist fo r any finite compressibility of the membrane, and a higher frequency mode d etermined mainly by the membrane density and compressibility.