A micromechanical investigation of interfacial transport processes. II. Interfacial constitutive equations
A micromechanical investigation of interfacial transport processes. II. Interfacial constitutive equations
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界面传输过程的微观机械研究。
DOI：
10.1098/rsta.1993.0128
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
L. Ting
中科院分区：
文献类型：
--
作者：
G. M. Mavrovouniotis;H. Brenner;D. Edwards;L. Ting
宏观界面本构方程，以及表达式中出现的唯象功能，推导出通过严格匹配的渐近展开方案的输运过程中发生的不混溶的流体-流体系统具有移动和变形界面。渐近方法的有用性证明通过检查一个模型，其中的三维微尺度流体连续假设服从不可压缩的，横向各向同性的，线性的，牛顿型本构方程具有位置依赖的唯象系数，强烈依赖于距离垂直的接口。在这种情况下，他们acrosale界面应力张量减少到熟悉的各向同性Boussinesq-Scriven形式。类似地，一个二维的，各向同性的，宏观界面的菲克定律关系是从一个可比的，三维的，横向各向同性的，微观尺度的菲克形式的情况下，扩散控制的表面活性剂之间的运输交换体相和界面。
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.