  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.
