Summary
A phenomenological theory is proposed for the diffusion of a dilute solution of a gas in a thermoelastic solid. It is assumed that the thermomechanical behavior of the solid is unaffected by the presence of the gas. On the other hand the presence of the solid is recognized by the gas by letting certain thermomechanical variables of the solid to enter into the constitutive equations of the gas. The constitutive functionals of the gas are restricted by the principles of continuum physics. These principles are currently referred to as equipresence, material objectivity, entropy production inequality, as well as the balance equations of mass, linear and angular momentum and internal energy. By this approach, axiomatic statements on the existence of equations of state are avoided and the classical results of linear irreversible thermodynamics are obtained by further specialization of the proposed theory.
Zusammenfassung
Für die Diffusion einer verdünnten Lösung eines Gases in einen thermoelastischen Festkörper wird eine phänomenologische Theorie vorgeschlagen. Dabei wird vorausgesetzt, daß das thermomechanische Verhalten des Festkörpers durch das Gas nicht beeinflußt wird. Der Festkörper wird dadurch berücksichtigt, daß bestimmte thermomechanische Variable des Festkörpers in den Materialgleichungen für das Gas auftreten. Die das Gas beschreibenden Funktionale werden durch die Prinzipien der Kontinuumsphysik, wie das Prinzip der Äquipräsenz, das Prinzip der Bezugsindifferenz, den Zweiten Hauptsatz, sowie die Massenbilanzgleichung, den Impuls, den Drall und die innere Energie festgelegt. Durch diese Behandlung werden axiomatische Aussagen über die Existenz der Zustandsgleichungen vermieden und die klassischen Resultate der linearen irreversiblen Thermodynamik durch Spezialisierung der vorgeschlagenen Theorie erhalten.
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Aifantis, E.C., Gerberich, W.W. Gaseous diffusion in a stressed-thermoelastic solid. Part I: The thermomechanical formulation. Acta Mechanica 28, 1–24 (1977). https://doi.org/10.1007/BF01208785
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DOI: https://doi.org/10.1007/BF01208785