A micromechanical investigation of interfacial transport processes. II. Interfacial constitutive equations
Gretchen M. Mavrovouniotis, Howard Brenner, David Albert Edwards, Li Ting · Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences · 1993
Abstract Macroscale interfacial constitutive equations, as well as expressions for the phenomenological functions appearing therein, are derived via a rigorous matched asymptotic expansion scheme for transport processes occurring in immiscible fluid—fluid systems possessing moving and deforming interfaces. The usefulness of an asymptotic approach is demonstrated by examining a model in which the three-dim ensional microscale fluid continuum is assumed to obey an incompressible, transversely-isotropic, linear, newtonian-type constitutive equation possessing position-dependent phenomenological coefficients which depend strongly upon distance normal to the interface. In such circumstances, them acroscale interfacial stress tensor reduces to the familiar isotropic Boussinesq-Scriven form . Similarly, a two-dimensional, isotropic, macroscale interfacial Fick’s law relation is derived from a comparable, three-dimensional, transversely-isotropic, microscale fickian form for the case of a diffusion-controlled surfactant transport exchange between the bulk phases and the interface.