A new matrix for multiphase couplings in a membrane porous medium

Summary The empirical Darcy's law of water transport in porous media, Fick's law of chemical diffusion, and Fourier's law of thermal transport have been widely used in geophysics/geochemistry for over 150 years. However, the strong couplings between water, temperature, and chemicals i...

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Bibliographic Details
Published in:International journal for numerical and analytical methods in geomechanics 2018-07, Vol.42 (10), p.1144-1153
Main Authors: Chen, Xiaohui, Wang, Manhui, Hicks, Michael A., Thomas, Hywel R.
Format: Article
Language:English
Subjects:
Chemical diffusion
Computational fluid dynamics
Connectors
coupling
Couplings
Darcys law
Dye dispersion
Fluid flow
Fourier law
Frameworks
Geochemistry
Geophysics
Mathematical analysis
Mathematical models
Matrix methods
membrane porous media
mixture coupling theory
multiphase
Multiphase flow
Nonequilibrium thermodynamics
Organic chemistry
Osmosis
Porous materials
Porous media
Robustness (mathematics)
Transport
Water temperature
Water transport
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Summary:Summary The empirical Darcy's law of water transport in porous media, Fick's law of chemical diffusion, and Fourier's law of thermal transport have been widely used in geophysics/geochemistry for over 150 years. However, the strong couplings between water, temperature, and chemicals in a membrane porous medium have made these laws inapplicable and present a significant hurdle to the understanding of multiphase flow in such a material. Extensive experiments over the past century have observed chemical osmosis and thermal osmosis, but a model for understanding their underlying physicochemical basis has remained unavailable, because of the highly cross‐disciplinary and multiscale‐multiphase nature of the coupling. Based on the fundamental principles of nonequilibrium thermodynamics and mixture coupling theory, a rigorously theoretical and mathematical framework is proposed and a general model accounting for all of the coupled influences is developed. This leads to a simple and robust mathematical matrix for studying multiphase couplings in a membrane porous medium when all chemical components are electrically neutral.
ISSN:0363-9061
1096-9853
DOI:10.1002/nag.2783