Pattern formation in foam displacement in a liquid-filled Hele-Shaw cell

Abstract

Foam injection in porous media is desirable for displacing less viscous fluids because of its ability to form a stable front and ensure uniform fluid distribution. In our experimental study, we investigated foam invasion in a radial Hele-Shaw cell initially saturated with either water or a surfactant solution at the same concentration as that of the foam. We report on an unexpected phenomenon whereby the typically stable process of foam displacing surfactant solution becomes unstable when the foam displaces water, a less viscous fluid, despite the higher viscosity of foam. Nevertheless, this instability can be moderated by either reducing the gas fraction in the foam or adding a small amount of surfactant solution to the water. Through single-bubble analysis, we observe that surfactant dilution, resulting from the mixture with water during foam injection, can trigger the rupture of thin films between large bubbles and the surfaces of the Hele-Shaw cell. This leads to the immobilization of larger bubbles, around which smaller bubbles accumulate densely. Such disturbances create side branching and a distinct fingering pattern within the foam flow. From the observations, the foam-water contact line growth follows a $L_c\sim t^{2/3}$ relation, deviating from the $L_c\sim t^{1/2}$ growth expected in stable displacement scenarios.