Interfacial dynamics of two immiscible fluids in spatially periodic porous media: The role of substrate wettability

We delineate the contact line dynamics of two immiscible fluids in a medium having spatially periodic porous structures. The flow is driven by an external applied pressure gradient. We bring out the combined consequences of the solid fraction distribution and the substrate wettability on the resulting dynamics of the contact line, by employing phase-field formalism. We capture the sequence of spatiotemporal events leading to formation of liquid bridges by trapping a small amount of displaced phase fluid between two consecutive porous blocks, as dictated by the combinations of substrate wettability and solid fraction. We also demonstrate the existence of a regime of complete interfacial recovery, depending on the parametric space of the governing parameters under concern. Our results essentially demonstrate the intricate mechanisms by virtue of which the wettabilities of the substrates alter the dynamical evolutions of interfaces and the subsequent shapes and sizes of the adsorbed dispersed phases, bearing far-ranging consequences in several practical applications ranging from oil recovery to groundwater flow.