Scaling behavior and connectivity-driven transport regimes of preferential flow in three-dimensional rough fractures

Preferential flow channelization in three-dimensional (3D) rough fractures is a fundamental fluid mechanics phenomenon governed by complex void geometries that produce non-uniform velocity distributions and severe tortuosity. Classical models relying on averaged aperture approximations or lubrication theory frequently break down in such highly constrained fractures. This study elucidates the core fluid physics of preferential flow. We establish a framework linking macroscopic transport capacity to microscopic geometric scaling and connectivity. We generated synthetic 3D fractures with systematically varied aperture, contact area, and fractal dimensions and performed coupled high-resolution 3D Navier–Stokes and electrical current simulations. We exploit the fundamental scaling disparity between the cubic dependence of hydrodynamic flow and the linear Ohmic scaling of electrical transport to derive a robust, nonlinear kinematic scaling relationship for preferential flow volume. The central physical insight is the identification of two distinct transport regimes separated by a critical percolation threshold (contact area ≈ 30%–35%). Above this threshold, an aperture-dominated regime prevails, where flow maintains multiple parallel pathways and broadly adheres to classical Stokes-flow scaling. Below this threshold, a contact area-dominated regime dictates transport; the lubrication approximation entirely breaks down, and fluid flow becomes severely localized, highly tortuous, and constrained by the spatial distribution of contact patches. Fractal dimension exerts only a secondary influence compared to spatial connectivity. These findings significantly advance our fundamental understanding of fracture flow physics, extending prior work on lubrication scaling and providing a rigorous mechanistic basis for predicting connectivity-driven channelization in heterogeneous geologic environments.