Influence of inertia on liquid splitting at fracture intersections

Abstract

Liquid splitting behavior at fracture intersections is an important process affecting unsaturated flow in fractured rocks. The role of inertia in liquid splitting at a fracture intersection, however, remains poorly understood. In this study, a theoretical model considering inertia is proposed to explore the inertial effect on liquid splitting at idealized facture intersections consisting of a main fracture and a branch fracture. The liquid droplet splitting behaviors predicted by the proposed model are in good agreement with the carefully controlled visualization experiments. By comparing the model predictions with and without inertia and comparing with experimental data, we show that neglecting the inertial effect leads to underestimation of liquid partitioning into the branch fracture with a smaller aperture than the main fracture. Furthermore, a threshold droplet length is defined to quantify the droplet length at which the inertial effect starts to exert an impact on the splitting dynamics. The influence of key parameters, such as the inclination angle, the fracture apertures, and the dynamic contact angles, on the droplet splitting behaviors is investigated through a systematic parameter sensitivity analysis. We show that the inclination angle affects the threshold droplet length mainly by controlling the initial droplet velocity. It is also demonstrated that the fracture apertures and the advancing and receding contact angles have significant impact on the volume percentage partitioned into the branch fracture. The improved understanding in this work may provide new insights into unsaturated flow and contaminant transport behaviors in fractured networks with implications for hydrological and environmental applications.