Liquid fragmentation and intermittent flow regimes in unsaturated fractured media

Flow processes in unsaturated fractures considerably differ from flow in rock matrix because of the dominance of gravitational forces, accentuated by variations in fracture geometry. This gives rise to liquid fragmentation, fingering, and intermittent flow regimes that are not amenable to standard continuum representation. We develop an alternative modeling framework to describe the onset of liquid fragmentation and subsequent flow behavior of discrete liquid clusters. The transition from a slowly growing anchored liquid element to a finger-forming mobile liquid element is estimated from the force balance between retarding capillary forces dominated by contact angle hysteresis and suspended liquid weight. A model for liquid fragmentation within the fracture plane (smooth and parallel walled fractures) for given a steady input flux and aperture size is developed and tested. Predictions of sizes and detachment intervals of liquid elements are in good agreement with experimental results. The results show that the mass of detached liquid element is only weakly related to flow rate but increases with fracture aperture size. Periodic discharge similar to that experimentally observed is a result of the interplay between capillary, viscous, and gravitational forces. We show that the presence of even a few irregularities in a fracture plane may induce complicated flux patterns downstream. Similar erratic fluxes are observed in studies involving gravity-driven unsaturated flow.