In this work, we study gravity‐driven flow of water in the presence of air on a synthetic surface intersected by a horizontal fracture and investigate the importance of droplet and rivulet flow modes on the partitioning behavior at the fracture intersection. We present laboratory experiments, three‐dimensional smoothed particle hydrodynamics (SPH) simulations using a heavily parallelized code, and a theoretical analysis. The flow‐rate‐dependent mode switching from droplets to rivulets is observed in experiments and reproduced by the SPH model, and the transition ranges agree in SPH simulations and laboratory experiments. We show that flow modes heavily influence the “bypass” behavior of water flowing along a fracture junction. Flows favoring the formation of droplets exhibit a much stronger bypass capacity compared to rivulet flows, where nearly the whole fluid mass is initially stored within the horizontal fracture. The effect of fluid buffering within the horizontal fracture is presented in terms of dimensionless fracture inflow so that characteristic scaling regimes can be recovered. For both cases (rivulets and droplets), the flow within the horizontal fracture transitions into a Washburn regime until a critical threshold is reached and the bypass efficiency increases. For rivulet flows, the initial filling of the horizontal fracture is described by classical plug flow. Meanwhile, for droplet flows, a size‐dependent partitioning behavior is observed, and the filling of the fracture takes longer. For the case of rivulet flow, we provide an analytical solution that demonstrates the existence of classical Washburn flow within the horizontal fracture.

Core Ideas Mass redistribution at unsaturated fracture intersections depends on free‐surface flow modes. A Washburn‐type flow regime is recovered via an analytical solution for capillary fracture inflow. A Gaussian transfer function predicts mass partitioning for arbitrary‐sized fracture cascades. Infiltration and recharge dynamics in fractured aquifer systems often strongly deviate from diffuse Darcy–Buckingham type flows due to the existence of a complex gravity‐driven flow component along fractures, fracture networks, and fault zones. The formation of preferential flow paths in the unsaturated or vadose zone can trigger rapid mass fluxes, which are difficult to recover by volume‐effective modeling approaches (e.g., the Richards equation) due to the nonlinear nature of free‐surface flows and mass partitioning processes at unsaturated fracture intersections. In this study, well‐controlled laboratory experiments enabled the isolation of single aspects of the mass redistribution process that ultimately affect travel time distributions across scales. We used custom‐made acrylic cubes (20 by 20 by 20 cm) in analog percolation experiments to create simple wide‐aperture fracture networks intersected by one or multiple horizontal fractures. A high‐precision multichannel dispenser produced gravity‐driven free‐surface flow (droplets or rivulets) at flow rates ranging from 1 to 5 mL min−1. Total inflow rates were kept constant while the fluid was injected via 15 (droplet flow) or three inlets (rivulet flow) to reduce the impact of erratic flow dynamics. Normalized fracture inflow rates were calculated and compared for aperture widths of 1 and 2.5 mm. A higher efficiency in filling an unsaturated fracture by rivulet flow observed in former studies was confirmed. The onset of a capillary‐driven Washburn‐type flow was determined and recovered by an analytical solution. To upscale the dynamics and enable the prediction of mass partitioning for arbitrary‐sized fracture cascades, a Gaussian transfer function was derived that reproduces the repetitive filling of fractures, where rivulet flow is the prevailing regime. Results show good agreement with experimental data for all tested aperture widths.

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