Summary
Some new partial differntial equations are developed to describe the diffusion of a dilute solute in a linear elastic solid supporting a static deformation. The analysis is based exclusively on the use of the conservation laws of mass and momentum, as well as, on the introduction of an internal diffusive force to evaluate the diffusion effects.
The interesting result is that steady states are insensitive to possible viscous behavior of the diffusing species. In addition, previous theories dealing with such problems are recovered and generalized. Finally, the important experimental observation that implies a linear dependence of the diffusion coefficient on the hydrostatic pressure is theoretically established.
Zusammenfassung
Einige neue partielle Differentialgleichungen werden, für die Beschreibung der Diffusion einer verdünnten Lösung in einen linear elastischen Festkörper, unter einer statischen Deformation, entwickelt. Die Analysis basiert ausschließlich auf der Anwendung der Erhaltungssätze für Masse und Impuls, sowie auf der Einführung einer inneren Diffusionskraft zur Bewertung der Diffusionseffekte.
Das interessante Ergebnis ist, daß stationäre Zustände unempfindlich gegen mögliches viskoses Verhalten der Diffusionsarten sind. Zusätzlich werden frühere Theorien wieder erhalten und verallgemeinert. Schließlich wird noch die wichtige experimentelle Beobachtung, die zu einer linearen Abhängigkeit des Diffusionskoeffizienten vom hydrostatischen Druck führt, theoretisch nachgewiesen.
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Aifantis, E.C., Gerberich, W.W. Diffusion of a gas in a linear elastic solid. Acta Mechanica 29, 169–184 (1978). https://doi.org/10.1007/BF01176635
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DOI: https://doi.org/10.1007/BF01176635