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The Quarterly Journal of Mechanics and Applied Mathematics 1971 24(4):473-485; doi:10.1093/qjmam/24.4.473
© 1971 by Oxford University Press
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ENTROPY INEQUALITIES FOR MIXTURES

A. E. GREEN1 and P. M. NAGHDI2

( 1Mathematical Institute, University of Oxford
2Division of Applied Mechanics, University of California Berkeley )

This is an exploratory paper and is concerned with the use of suitable entropy production inequalities for each constituent in mixture theory, in addition to an entropy production inequality for the mixture as a whole. Consequences of the restrictions imposed by the separate inequalities on constitutive equations are examined for a mixture of any number of ideal fluids, each of which may have a different temperature. Results are also given for a mixture of any number of materials with elastic and viscous properties. Although the idea of entropy production inequalities for each constituent is not generally accepted, it is found that the ones used here place only mild additional restrictions on the constitutive equations, the main effect being further restrictions on the forms of the partial free energy functions for each constituent.


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