Small amplitude shape oscillations of a spherical liquid drop with surface viscosity

The analysis of surface oscillations of liquid drops allows measurements of the surface tension and viscosity of the liquid. For small oscillations of spherical drops with a free surface, classical formulae by Rayleigh and Lamb relate these quantities to the frequency and damping of the oscillations. In many cases, however, the drop's surface is covered by a surface film, typically an oxide layer or a surfactant, exhibiting a rheological behaviour different from the bulk fluid. It is the purpose of this paper to investigate how such surface properties influence the oscillation spectrum of a spherical drop. For small bulk shear viscosity, the cases of small, finite and large surface viscosities are discussed, and the onset of aperiodic motion as a function of the surface parameters is also derived.