Directional-dependent invasion dynamics in anisotropic porous media with customised disorder*

We show possibility of achieving a directional-dependent two-phase flow behaviour during the process of invasion of a viscous fluid into anisotropic porous media with customised pore-scale morphology and heterogeneity. Via pore-scale numerical simulations, we observe a substantially different invasion dynamics according to the medium orientation relative to the direction of fluid injection, i.e. with flow-aligned or flow-opposing oriented pillars. The porous medium anisotropy induces a lower effective resistance when the pillars are flow-opposing oriented, suppressing front roughening and capillary fingering, while promoting transverse invasion with respect to the direction of fluid injection. We argue that fluid infiltration occurs as long as the pressure drop is larger then the macroscopic capillary pressure determined by the front roughness. We present a simple approximated model, based on Darcy's assumptions, that links the macroscopic effective permeability with the directional-dependent front roughening. The model correctly predicts an intermediate flow regime, defined by a specific range of values of the ratio between the macroscopic pressure drop and the medium characteristic pore-scale capillary threshold, within which the injected viscous fluid reaches the outlet only whith flow-opposing oriented pillars. The prediction of the observed directional-dependent fluid conductance is important for e.g. the fabrication of porous materials that act as capillary valves to control the flow along certain specific directions.