A Numerical Study of Pore Scale Partially Wet Interfacial Displacements

Here, we study the pore-scale interfacial dynamics of immiscible two-phase flow in a partially wet regime using direct numerical simulation. We consider the displacement of a wetting fluid by a nonwetting one in a drainage scenario and a nonwetting fluid by a wetting one in an imbibition scenario. In a capillary tube we validate the previous experimental observations of pinch-off dynamics for a drainage scenario given a more viscous fluid being displaced by a less viscous one and extend such observations through a systematic study to an imbibition regime. We find that beyond a wettability dependent critical capillary number, a stable displacement by a less viscous fluid can transition into a growing finger that eventually leads to a series of pinch-off events in both wetting and non-wetting contact angles. For the phase separation in the form of pinch-off for drainage and imbibition, this work provides a quantitative study of the emerging length and time scales and their dependence on the wettability conditions, capillary effects, and viscous forces.