GAS BUBBLE SNAP-OFF UNDER PRESSURE-DRIVEN FLOW IN CONSTRICTED NONCIRCULAR CAPILLARIES

A model for snap-off of a gas thread ina 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 g radients significantly increase the frequency of liquid accumulation f or snap-off, as compared to liquid rearrangement driven only by differ ences in pore-wall curvature. For moderate and large pressure gradient s, the frequency of accumulation increases linearly with pressure grad ient, 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 excelle nt ability to snap off gas threads even when the initial capillary pre ssure is high or equivalently when the liquid saturation is low. A mac roscopic momentum balance across the lens, resulting from snap-off, re veals that lens displacement rates are not linear with the imposed pre ssure drop. Instead, the frequency of lens displacement scales with po wers between 0.5 and 0.6 for pores with dimensionless constriction rad ii between 0.15 and 0.40. Statistical percolation arguments are employ ed to form a generation rate expression and connect pore-level foam ge neration 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 relat ionship with respect to the imposed gas-phase pressure gradient.