Surface permeability, capillary transport and the Laplace-Beltrami problem

Penpark Sirimark, Alex V. Lukyanov, Tristan Pryer

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)


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.
Original languageEnglish
Article number106
JournalThe European Physical Journal E
Early online date14 Sept 2018
Publication statusPublished - 2018


  • physics.flu-dyn
  • cond-mat.soft


Dive into the research topics of 'Surface permeability, capillary transport and the Laplace-Beltrami problem'. Together they form a unique fingerprint.

Cite this