Understanding fluid flow in fractured rock is essential for accurately predicting subsurface transport behavior. This study examines how fracture contact area, fractal dimension, and flow velocity influence the development of preferential flow. A series of controlled simulations was conducted, varying contact area (0%–50%), fractal dimension (2.1–2.5), and flow velocity (0.01–2.5 m/s), to quantify the impact of each parameter. The results show that contact area exerts the strongest influence: as it increases, preferential flow volume declines, especially sharply between 20% and 40% contact area. Flow velocity exhibits distinct threshold behavior linked to the transition from Darcy to non-Darcy flow regimes. Below the critical velocity (non-Darcy effect factor E = 0.1), preferential flow volume increases linearly with velocity. Above this threshold, preferential flow stabilizes as inertial effects emerge and geometric constraints dominate. Notably, this critical velocity decreases with decreasing contact area—at 0% contact, flow immediately enters the non-Darcy regime (E > 0.1), causing preferential flow to stabilize from the onset. Fractal dimension (FD) shows non-monotonic effects, with intermediate roughness (FD = 2.3) consistently producing minimum preferential flow, suggesting optimal geometric complexity for flow resistance. These factors interact through a hierarchical control system: contact area establishes the primary flow framework and determines the transition between flow regimes, fractal dimension modulates internal channel complexity, and flow velocity governs fluid distribution within structurally-determined constraints. These insights deepen our theoretical understanding of fractured media flow and inform more accurate predictive models for environmental and engineering applications.

Groundwater contamination in heterogeneous aquifer systems containing high-permeability zones (analogous to fractures) and adjacent low-permeability zones (analogous to rock matrices) persists long after source removal due to back-diffusion, whereby contaminants stored in low-permeability zones gradually migrate back into high-permeability pathways. While this process critically controls contamination longevity and remediation effectiveness, the coupled influence of groundwater flow velocity and matrix hydraulic conductivity on back-diffusion remains poorly quantified. We conducted systematic laboratory experiments using sandbox models to simulate heterogeneous dual-permeability systems across four hydraulic conductivity levels and four flow velocities. Real-time electrical resistivity monitoring tracked sodium chloride tracer movement, enabling continuous, minimally-invasive characterization of back-diffusion dynamics. Results demonstrate strong inverse relationships between flow velocity and back-diffusion intensity: a 30% flow increase reduced contaminant release by 78% in high-conductivity systems. Matrix hydraulic conductivity exerted equally significant control, with high-conductivity materials accelerating contaminant exchange (reducing delay times by 65% and back-diffusion duration by 40%), while low-conductivity materials sustained release for over 4000 s. Dimensionless analysis using Péclet and Damköhler numbers demonstrated that all 16 experimental datasets collapse onto a single relationship, confirming the generalizability of the findings.These findings establish quantitative relationships between hydraulic properties and back-diffusion behavior, providing a predictive framework for assessing long-term contamination persistence and optimizing remediation strategies in heterogeneous aquifer systems.

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.