Dynamical fluctuations of droplet microemulsions and vesicles

The hydrodynamic fluctuations of nearly spherical vesicles and microemulsion droplets are considered. The incompressibility of the enclosed fluid and surfactant or lipid layer imposes a constraint of constant droplet volume and area on the fluctuations. These overdamped modes, driven by bending energy and damped by viscosity of the surrounding fluids, change the shape of the surface and may scatter neutrons or light. A dynamical structure factor S(q,t) is computed and a first frequency moment at fixed wave number ${\omega }_{\mathrm{char}(\mathrm{q}}$) obtained. In the limit of a stiff droplet at fixed ‘‘excess area,’’ a new mode is obtained —an overdamped oscillation among ellipsoidal shapes about the minimum-energy (usually prolate) shape. Prospects for observing this fluctuation are discussed.