Gas bubble snap-off under pressure-driven flow in constricted noncircular capillaries

Abstract

A model for snap-off of a gas thread in a constricted, cornered pore is developed. The time for wetting liquid to accumulate at a pore throat into an unstable collar is examined, as is the time for the resulting pore-spanning lens to be displaced from the pore so that snap-off may repeat. A corner-flow hydrodynamic analysis for the accumulation rate of wetting liquid due to both gradients in interfacial curvature and in applied liquid-phase pressure reveals that wetting-phase pressure gradients significantly increase the frequency of liquid accumulation for snap-off, as compared to liquid rearrangement driven only by differences in pore-wall curvature. For moderate and large pressure gradients, the frequency of accumulation increases linearly with pressure gradient, because of the increased rate of wetting liquid flow along pore corners. Pore topology is important to the theory, because pores with relatively small throats connected to large bodies demonstrate excellent ability to snap off gas threads even when the initial capillary pressure is high or equivalently when the liquid saturation is low. A macroscopic momentum balance across the lens, resulting from snap-off, reveals that lens displacement rates are not linear with the imposed pressure drop. Instead, the frequency of lens displacement scales with powers between 0.5 and 0.6 for pores with dimensionless constriction radii between 0.15 and 0.40. Statistical percolation arguments are employed to form a generation rate expression and connect pore-level foam generation events to macroscopic pressure gradients in porous media. The rate of foam generation by capillary snap-off increases linearly with the liquid-phase pressure gradient and according to a power-law relationship with respect to the imposed gas-phase pressure gradient.