Pore-scale effects during the transition from capillary- to viscosity-dominated flow dynamics within microfluidic porous-like domains.

We perform a numerical and experimental study of immiscible two-phase flows within predominantly 2D transparent PDMS microfluidic domains with disordered pillar-like obstacles, that effectively serve as artificial porous structures. Using a high sensitivity pressure sensor at the flow inlet, we capture experimentally the pressure dynamics under fixed flow rate conditions as the fluid-fluid interface advances within the porous domain, while also monitoring the corresponding phase distribution patterns using optical microscopy. Our experimental study covers 4 orders of magnitude with respect to the injection flow rate and highlights the characteristics of immiscible displacement processes during the transition from the capillarity-controlled interface displacement regime at lower flow rates, where the pores are invaded sequentially in the form of Haines jumps, to the viscosity-dominated regime, where multiple pores are invaded simultaneously. In the capillary regime, we recover a clear correlation between the recorded inlet pressure and the pore-throat diameter invaded by the interface that follows the Young-Laplace equation, while during the transition to the viscous regime such a correlation is no longer evident due to multiple pore-throats being invaded simultaneously (but also due to significant viscous pressure drop along the inlet and outlet channels, that effectively mask capillary effects). The performed experimental study serves for the validation of a robust Level-Set model capable of explicitly tracking interfacial dynamics at sub-pore scale resolutions under identical flow conditions. The numerical model is validated against both well-established theoretical flow models, that account for the effects of viscous and capillary forces on interfacial dynamics, and the experimental results obtained using the developed microfluidic setup over a wide range of capillary numbers. Our results show that the proposed numerical model recovers very well the experimentally observed flow dynamics in terms of phase distribution patterns and inlet pressures, but also the effects of viscous flow on the apparent (i.e. dynamic) contact angles in the vicinity of the pore walls. For the first time in the literature, this work clearly shows that the proposed numerical approach has an undoubtable strong potential to simulate multiphase flow in porous domains over a wide range of Capillary numbers.