Shape oscillations of drops in the presence of surfactants

Abstract

The shape oscillations of drops in another fluid with or without surfactants has been analysed by normal mode expansions. The effects of surfactants are accommodated by considering the Gibbs elasticity, associated with the redistribution of surfactants, and a Boussinesq surface fluid with two surface viscosities. A general transcendental equation for the complex frequency of the free oscillations is derived. Explicit dispersion relations are given for fluids of small bulk viscosities and an interface of small, moderate, and large interfacial properties by a perturbation method. We have found that the oscillation always damps out faster for an interface exhibiting interfacial properties other than the interfacial tension, and the Gibbs elasticity is the most important parameter that alters the free-oscillation frequency and the damping constant. Moreover, the energy dissipation for an extensible interface can be much higher than that of an inextensible interface owing to the strong vorticity generated in the boundary layers.