Abstract: As a key structural element of fracture networks, fracture intersections play an important role in water infiltration in unsaturated fractured rocks. With the decrease in flow rate, the flow mode within intersecting fracture changes from continuous and stable rivulet flow to intermittent and unstable droplet flow. Most studies have focused on the rivulet flow, while less attention has been paid to the droplet flow. In this paper, theoretical and experimental work on the characteristics of droplets flowing through unsaturated fracture intersections is performed. It is found that there are two regimes of droplet splitting: capillary dominated splitting regime and capillary-gravitational splitting regime. Based on force balance analysis, we propose a quasi-static model and a semi-analytical solution approach to predict the dynamic splitting behavior of droplets at fracture intersections. Additionally, by investigating the detailed processes of different splitting regimes, we clarify the microscopic mechanism about the combined influence of gravity, capillary force and viscous force on the dynamic splitting behavior. We elucidate the mechanisms based on the variation of interface velocities and droplet splitting volume ratio under different initial droplet lengths and inclination angles. This work provides a theoretical and experimental basis for prediction of seepage in unsaturated fractured rocks under low flow rate and low saturation conditions.

Key words: unsaturated flow, fracture intersection, droplets, splitting dynamics