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We have established previously, in a lead-in study, that the spreading ofliquids in particulate porous media at low saturation levels,characteristically less than 10% of the void space, has very distinctivefeatures in comparison to that at higher saturation levels. In particular, wehave found that the dispersion process can be accurately described by a specialclass of partial differential equations, the super-fast non-linear diffusionequation. The results of mathematical modelling have demonstrated very goodagreement with experimental observations. However, any enhancement of theaccuracy and predictive power of the model, keeping in mind practicalapplications, requires the knowledge of the effective surface permeability ofthe constituent particles, which defines the global, macroscopic permeabilityof the particulate media. In the paper, we demonstrate how this quantity can bedetermined through the solution of the Laplace-Beltrami Dirichlet problem, westudy this using the well-developed surface finite element method.

Surface permeability, capillary transport and the Laplace-Beltrami problem