Multiphase Thermomechanics with Interfacial Structure 1. Heat Conduction and the Capillary Balance Law

Abstract

In [1986g, 1988g] I began the development of a nonequilibrium thermomechanics of two-phase continua, a development based on dynamical statements of the thermomechanical laws in conjunction with GIBBS’S notion of a sharp phase-interface endowed with energy and entropy. I have since come to realize that there is an additional balance law appropriate to the interface. This law, which represents balance of capillary forces, has the form1 $$\int\limits_{{\partial c}} {{\text{C}}\upsilon {\text{ + }}\int\limits_{{\text{c}}} \pi } = 0,$$ (7.1) with an arbitrary subsurface of and ν the outward unit normal to the boundary curve ∂ of. Here C (x,t), the capillary stress, is a linear transformation of tangent vectors into (not necessarily tangent) vectors, while π(x,t), the interaction, is a vector field; C (x,t) represents microforces exerted across ∂c in response to the creation of new surface;π(X,t), characterizes the interaction between the interface and the bulk material. I view (1.1) as a balance law which is supplementary to the usual laws for forces and moments.