Governing equations in non-isothermal diffusion |
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Institution: | 1. IFP Énergies Nouvelles, Rond-point de l''échangeur de Solaize, BP 3, 69360 Solaize, France;2. LMFA, École Centrale de Lyon, 36, avenue Guy de Collongue, 69134 Écully, France |
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Abstract: | Generalizations of Fick's law for the diffusion flux are often considered in the literature by analogy with those for the heat flux. The paper reviews the balance equations for a fluid mixture and provides the equations for the diffusion fluxes. As a consequence, the mass densities are shown to satisfy a system of hyperbolic equations. Moreover, for a binary mixture of ideal gases in stationary conditions, Fick's law is recovered. Next, diffusion fluxes are regarded as constitutive functions and a whole set of thermodynamic restrictions are determined which account for diffusion, heat conduction, viscosity and inhomogeneities. Hyperbolic models for diffusion and heat fluxes are established which involve the co-rotational derivative. The driving term of diffusion turns out to be the gradient of chemical potential rescaled by the temperature. |
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Keywords: | Diffusion Fick's law Hyperbolic models Evolution equations Co-rotational derivative |
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