Mass exchange, diffusion and large deformations of poroelastic materials
- Wilmański, Krzysztof
2010 Mathematics Subject Classification
- 80A15 76S05 73S10 73D40 76R50
- Flows in porous media, micromechanics of solids, interfaces in porous media
The paper contains a review of fundamental equations of the two component thermoporoelastic materials with the balance equation of porosity. By means of the exploitation of the second law of thermodynamics restricted to small deviations from thermodynamical equilibrium it is proven that there exists no thermodiffusional coupling of components through intrinsic parts of fluxes. Certainly such a coupling is still present due to convective contributions. Simultaneously we show that classical partial dynamical compatibility conditions on material interfaces cannot hold. For boundary conditions on permeable boundaries to hold true it must be required that global balance equations contain at least surface sources of momentum, entropy, and porosity. We show as well that the requirement of the local thermodynamical equilibrium on permeable interfaces yields the continuity of absolute temperature. It means that temperature becomes a measurable physical field in porous materials undergoing processes with small deviations from thermodynamical equilibria. This result allows to extend models of mass exchange in poroelastic materials from adsorption isothermal processes to chemical reactions, and phase transformations. Details of the latter problems are not discussed in this paper.
- Modeling and Mechanics of Granular and Porous Materials, G. Capriz, V. N. Ghionna, P. Giovine (eds.) pp. 211--242, Birkhaeuser, 2002