Abstrakt
The dusty gas model (DGM) is a theoretical tool for description of multi-component gas diffusion in porous materials based on the Maxwell- Stefan diffusion model. Krishna and Wesselingh have, in their article [2], shown a derivation of the DGM in the terms of Classical irreversible thermodynamics (CIT).
Such derivation is inherently non-systematic because Maxwell-Stefan diffusion model is based on the assumption of me- chanical equilibrium, which means that the viscous interaction is neglected. On contrary, the interaction with porous media occurs mainly due to the viscosity.
Hence the dusty gas limit introduces once forgotten viscous interaction again. A generalized, richer, version of dusty gas model was developed by Mason and Malinauskas in their book [3] from the Zdhanov's result for the thirteen-moment approximation for the Boltzmann equation solution.
Although, the generalized DGM has been greatly successful in capturing multicomponent diffusion through porous media in practice, the methods of the derivation used in [3] are far from physically rigorous methods used in irreversible thermodynamics, e.g. the entropy production of the generalized DGM is not treated at all. Moreover, Kerkhof reported inconsistencies of the Manson's generalized DGM in [5], e.g. the single component diffusion.
The Extended irreversible thermodynamics (EIT) presented in article [1] assumes partial momenta as the state variables unlike the CIT, e.g. de Groot [4], where only partial densities and momentum are considered. This feature provides a sufficiently robust framework in which a thermody- namically rigorous derivation of the generalized DGM can be done.
The major benefit of the generalized DGM inclusion into the framework of the EIT is in the field of applications. The entropy production has been identified and therefore a serious thermodynamic optimization can be under- taken in cases where diffusion is modelled with making use of the generalized DGM.
Moreover, some empirical terms appearing in the Mason's generalized DGM are newly related to measurable quantities. REFERENCES [1] Pavelka, M., Mark F; Klika V.
Consistent theory of mixtures on different levels of description. International Journal of Engineering Science 78 (2014): 192-217. [2] Krishna, R.; Wesselingh, J.
A. The Maxwell-Stefan approach to mass transfer.
Chemical Engineering Science, 1997, 52.6: 861-911. [3] Mason, E. A.; Malinauskas A.
P. Gas transport in porous media: the dusty-gas model.
Vol. 17. Elsevier Science Ltd, 1983. [4] de Groot, S.R.; Mazur, P.
Non-equilibrium thermodynamics. Courier Corporation, 2013. [5] Kerkhof, Piet JAM.
A modified Maxwell-Stefan model for transport through inert membranes: the binary friction model. The Chemical Engi- neering Journal and the Biochemical Engineering Journal, 1996, 64.3: 319-343.