Effects of fracture apertures on droplet splitting through unsaturated fracture intersections

An in-depth understanding of liquid flows through fracture intersections is important for predicting the seepage characteristics of fracture networks. The flow behavior of liquid at unsaturated intersections is closely related to the flow mode and geometric characteristics of fractures. A modeling study is given on the physical process of droplet splitting through unsaturated fracture intersections, which usually occurs under low flow rate and low saturation conditions. The effects of fracture apertures on droplet splitting behaviors are systematically investigated by varying the main channel width w₁ and the branch width w₂ of the fracture intersection. It is found that there are two droplet splitting patterns related to the droplet length: the flows dominated by the main channel and those dominated by the branch, which can be distinguished by the critical droplet length. This critical length is controlled by capillary force and permeability of channels, both varying with the channel widths. When the two controlling factors have opposite effects on the droplet splitting, the critical droplet length changes non-monotonously with w₂. Conversely, the critical droplet length changes monotonously with w₁. In addition, there is an optimal range for the width ratio w₂/w₁ to maximize the critical droplet length. This study provides theoretical support for predicting the seepage structure of fractured rocks under the conditions of low flow and low saturation.