Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Thermodynamic principle of virtual dissipation and the dynamics of physical-chemical fluid mixtures including radiation pressure


Author: M. A. Biot
Journal: Quart. Appl. Math. 39 (1982), 517-540
MSC: Primary 80A32; Secondary 49H05, 80A15, 85A05
DOI: https://doi.org/10.1090/qam/644105
MathSciNet review: 644105
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Abstract: Equations of motion are obtained for a viscous fluid mixture including thermal and intermolecular diffusion as well as chemical reactions and radiation pressure. They are derived by applying the thermodynamic principle of virtual dissipation. The method also incorporates a new approach to the chemical thermodynamics of open systems which leads to new concepts and formulas for the heat of reaction and the affinity. They are simpler and more general than classical values. Instead of chemical potentials, new `` convective potentials `` are used which involve physical properties restricted to the system. They do not require extrapolations to absolute zero or the use of undetermined constants. No statistical theory is involved. A noncalorimetric evaluation of the heat of mixing is obtained from the concept of injection pressure of each substance in the mixture. Field equations are derived and a coupling between viscous stress gradients and diffusion is brought out. The convective potentials lead to a new evaluation of the thermodynamic functions of mixtures as well as a new generalized formulation of the Gibbs-Duhem theorem. Translational invariance of the dissipation is discussed and related to total momentum balance. Lagrangian equations of motion with generalized collective coordinates are derived directly from the variational principle and should provide a powerful approach to problems of stellar dynamics with radiation pressure.


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DOI: https://doi.org/10.1090/qam/644105
Article copyright: © Copyright 1982 American Mathematical Society


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