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A stochastic approach to the filling dynamics of an open topology porousstructure permeated with a perfectly wetting fluid is presented. From thediscrete structure of the disordered voids network with only nearest neighborslinks, we derive the "microscopic" (at the pores scale) dynamical equationsgoverning the filling dynamics of the coupled pores and the fluid pressuredynamics. The model yields two fundamental consequences. The first consequenceregards the emergence of Darcy's law and the dependence of the predictedpermeability with the voids network topology. The second one is the predictionof a diffusive dynamics for the degrees of freedom of the pores filling. Theseequations exhibit a new type of symmetry manifested by their invariance underthe full/empty pores duality transformation jointly with the velocity reversal.Non-trivial steady non-equilibrium pores filling states are also obtained andfound to follow a Fermi-Dirac type law. The analogy with the single occupationof lattice sites by fermions is highlighted together with the correspondinghole-particle symmetry.

A stochastic approach to the filling dynamics of a porous medium: full/empty pores duality symmetry and the emergence of Darcy's law