Surface permeability of porous media particles and capillary transport
- 65 Downloads
We have established previously, in a lead-in study, that the spreading of liquids in particulate porous media at low saturation levels, characteristically less than 10% of the void space, has very distinctive features in comparison to that at higher saturation levels. In particular, we have found that the dispersion process can be accurately described by a special class of partial differential equations, the super-fast non-linear diffusion equation. The results of mathematical modelling have demonstrated very good agreement with experimental observations. However, any enhancement of the accuracy and predictive power of the model, keeping in mind practical applications, requires the knowledge of the effective surface permeability of the constituent particles, which defines the global, macroscopic permeability of the particulate media. In the paper, we demonstrate how this quantity can be determined through the solution of the Laplace-Beltrami Dirichlet problem, we study this using the well-developed surface finite-element method.
KeywordsFlowing Matter: Granular Matter
- 2.J.L. Vazquez, The Porous Medium Equation: Mathematical Theory (Oxford University Press, 2006)Google Scholar
- 8.M. Scheel, R. Seemann, M. Brinkmann, M.D.I. Michiel, A. Sheppard, S. Herminghaus, J. Phys.: Condens. Matter 20, 494236 (2008)Google Scholar
- 9.J. Bear, Dynamics of Fluids in Porous Media (Dover, 1972)Google Scholar
- 16.O. Koorevaar, G. Menelik, C. Dirksen, Elements of Soil Physics (Elsevier, Amsterdam, 1983)Google Scholar
- 17.G. Dziuk, Finite elements for the Beltrami operator on arbitrary surfaces, in Partial Differential Equations and Calculus of Variations, Lect. Notes Math., Vol. 1357 (Springer, 1988) pp. 142--155Google Scholar
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.