Studies in Interfacial Dynamics

Several aspects of the dynamics and stability of fluid-fluid interfaces are considered. The spectral density of the thermal fluctuations in the shape of fluid droplets is derived and discussed when the droplet surface contains a compressible Newtonian surface fluid. The analysis is extended to include surfaces with bending resistance, with emphasis on interfaces containing a layer of oriented molecules. The director is elastically coupled to the surface normal, and the static fluctuations in the director and the local normal are derived. An extended rheological model for the interface is also considered which includes the possibility of chemically induced curvature. The conditions for instability and the critical mode selection are investigated, and applications to biological cells are discussed.