Controlling 3D viscous fingering and fluid mixing by fractures: a numerical study

Fingering instabilities and rock fractures strongly influence fluid displacement in subsurface reservoirs, such as during groundwater remediation and enhanced oil recovery. Yet, their coupled behaviour—especially in three-dimensional (3D) flows—remains poorly understood. Prior studies show that the channelling of the less viscous fluid limits fluid mixing. Here, we demonstrate that tilted, high-permeability fractures can overcome this limitation. By examining the topology of viscous fingers in longitudinal and transverse sections, we show how fracture orientation and viscosity contrast jointly govern tip-splitting, channelling and overall mixing. Our 3D simulations reveal that when a fracture is aligned with the flow direction, fingers converge more effectively into it. Enhanced mixing within the conductive fracture delays interfacial stretching, suppressing channel formation and generating a well-mixed plume downstream. We introduce a new method for characterizing channelling based on the probability density function (PDF) of the fluid–fluid interface length. Non-stationarity of this PDF emerges as a clear statistical marker of channelling. We extend the PDF framework to quantify how fracture orientation alters the concentration PDF shape and modifies channelling. These results provide insights into fracture–fingering interactions, with broad implications for improving fluid mixing in microfluidic systems and managing flow in fractured rocks.