CONTINUUM THEORIES OF MIXTURES: BASIC THEORY AND HISTORICAL DEVELOPMENT

doi:10.1093/qjmam/29.2.209

The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(2):209-244; doi:10.1093/qjmam/29.2.209
© 1976 by Oxford University Press

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CONTINUUM THEORIES OF MIXTURES: BASIC THEORY AND HISTORICAL DEVELOPMENT

R. J. ATKIN and R. E. CRAINE

( Department of Applied Mathematics & Computing Science, University of Sheffield
Department of Mathematics, University of Southampton )

In this paper we derive the basic equations of a continuum theoryof mixtures and outline the historical development of the subjectsince 1957. As a particular example, a constitutive theory fora chemically inert mixture of two ideal gases is consideredand the classical Fick's law is deduced from this theory. Theresults for a binary mixture of gases are also compared withthose derived from the kinetic theory. Applications of the basictheory to different types of mixtures are discussed in (1).

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