Thermochemistry of Reacting Materials

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Abstract
This paper is concerned with the formulation of a thermomechanical theory of a mixture of chemically reacting materials without diffusion. The independent variables that influence the response of the mixture are assumed to be the temperature, the temperature gradient, the deformation gradient, the time rate of change of the deformation gradient, and the extent of reaction. The Clausius–Duhem inequality is used to derive a set of necessary and sufficient conditions that the constitutive functions must obey. Among these conditions are ones that determine the role of De Donder's chemical affinity in determining whether or not chemical reactions are present. In particular, a criterion is deduced that determines whether or not false equilibrium is possible. It is also shown under what circumstances vanishing of the chemical affinity is equivalent to vanishing of the reaction rate. The additional restrictions on the response of the mixture by the axiom of material frame—indifference and special types of material symmetry are also presented. It is also shown that if the free energy of the mixture satisfies a certain inequality, then any equilibrium state that has both a zero chemical affinity and a zero reaction rate is necessarily stable for chemical reactions taking place at constant temperature and deformation.

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