Surface permeability of porous media particles and capillary transport

  • Penpark Sirimark
  • Alex V. LukyanovEmail author
  • Tristan Pryer
Open Access
Regular Article


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.

Graphical abstract


Flowing Matter: Granular Matter 


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Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Penpark Sirimark
    • 1
  • Alex V. Lukyanov
    • 1
    Email author
  • Tristan Pryer
    • 1
  1. 1.School of Mathematical and Physical SciencesUniversity of ReadingReadingUK

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