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

  • Morton E. Gurtin

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.

Keywords

Vector Field Capillary Force Interfacial Structure Tensor Field Outward Unit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1999

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  • Morton E. Gurtin

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