Manipulating Viscous Fingering of Complex Fluids

We demonstrate the feasibility of controlling the viscous fingering instability of complex (yield-stress) fluids when a less-viscous fluid pushes another immersible one in a narrow cell. We experimentally show that a radially tapered cell, implying a permeability gradient, can be used to inhibit the viscous fingering instability of a complex yield-stress fluid. We observe a stable flat or wavy finger-like interface using two different yield-stress fluids experimentally depending on the gap gradient, the injection flow rate, and local rheological parameters. Furthermore, we develop a theoretical linear-stability analysis generalized for common complex fluids possessing a power-law varying viscosity and yield stress. A critical criterion differentiating a stable and unstable viscous fingering interface is established and is consistent with the experimental results of fluid-fluid displacement with the complex fluids.