Stabilization of viscous fingering instability in miscible fluids under translational oscillatory shear

The viscous fingering instability happens when a less viscous fluid displaces a more viscous one within a confined geometry. While injecting miscible fluids radially in a Hele-Shaw cell, we apply uniaxial translational oscillatory shear between the two plates. This changes the viscosity profile spanning the thin gap. As we increase the shear amplitude and shear speed, the onset radius, where the fingering starts to occur, is delayed. In addition, the early-stage growth rate of the fingers is reduced. The onset radius and growth rate are different for fingers oriented in the directions parallel and perpendicular to the shear axis. As the fluid injection rate increases, the stabilization due to shear decreases. To study the relation between the gap viscosity profile and the finger growth, we measure the concentration profile for different fluid viscosity ratios.