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Thermodynamics of Binary Solid–Fluid Cosserat Mixtures

  • Kolumban HutterEmail author
  • Yongqi Wang
Chapter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)

Abstract

It is demonstrated in this chapter, how complex it is to deduce a saturated binary solid–fluid Cosserat mixture model that is in conformity with the second law of thermodynamics and sufficiently detailed to be ready for application in fluid dynamics. The second law is formulated for open systems using the ClausiusDuhem inequality without mass and energy production under phase change for class II mixtures of elastic solids and viscoelastic fluids. It turns out that even with all these restrictions the detailed exploitation of the entropy inequality is a rather involved endeavor. Inferences pertain to extensive functional restrictions of the fluid- and solid- free energies and allow determination of the constitutive quantities in terms of the latter in thermodynamic equilibrium and small deviations from it. The theory is presented for four models of compressible–incompressible fluid–solid constituents. Finally, explicit representations are given for the free energies and for the constitutive quantities that are obtained from them via differentiation processes

Keywords

Open systems thermodynamics ClausiusDuhem exploitation of the entropy principle Elastic solids \(+\) viscoelastic fluids Volume fraction parameterization Alternative viscoelastic compressible/incompressible models 

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Authors and Affiliations

  1. 1.c/o Laboratory of Hydraulics, Hydrology, GlaciologyETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany

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