Experiment and simulation of quasistatic capillary rise in an ink-bottle setup resultingin pressure-saturation (p-s) hysteresis

During imbibition, fluid-fluid interface at the inlet of a constriction experiences an increase in capillary force that results in rapid fluid invasion known as Haines jump. During drainage, the interface gets pinned at the end of the constriction, which causes pressure-saturation (p-s) trajectories to follow different paths during imbibition and drainage resulting in p-s hysteresis. In this work, we performed quasistatic two-phase flow experiments and simulations of cyclic imbibition and drainage in a capillary tube with a constriction (ink-bottle) to have a quantitative understanding of p-s hysteresis. In the setup, drainage and imbibition were driven by quasitatically changing the pressure gradient between the inlet and the outlet of the tube. The experimental results were compared with the results from a numerical model in OpenFOAM, which solves the Navier-Stokes equations employing Volume of Fluid method to calculate the position of the interface. We observed that multiphase flow through a single constriction revealed distinct p-s hysteresis, a common trait in porous media. The steeper the constriction, the more pronounced the p-s hysteresis and vice versa. We derived an analytical solution to obtain the p-s curve and compared the results obtained from experiments and simulations. This comparative study will allow us to quantitatively link the pore-scale capillary physics to large-scale p-s hysteresis.