A MICROMECHANICAL INVESTIGATION OF INTERFACIAL TRANSPORT PROCESSES .2. INTERFACIAL CONSTITUTIVE-EQUATIONS

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-dimensional 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, the macroscale 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.