Dynamics of a fluid interface Equation of motion for Newtonian surface fluids

Abstract

The importance of interface rheology to foam stability and to the calming of water waves by oil has long been recognized in a general way. Recent research reveals its vital importance in many free-boundary flows, for example in distillation and liquid extraction. In order to understand quantitatively these flows, mathematical descriptions of the dynamics of an interface are needed. Herein is derived a completely general formulation of the dynamics of a Newtonian fluid interface, that is, one whose rheological behaviour is characterized by its equilibrium interfacial tension and Boussinesq's [18] two coefficients of surface viscosity. With consideration of the intimate coupling between surface and substrate, the analysis finally yields interfacial boundary conditions on two-phase flows. © 1960.