Viscous fingering stabilization in miscible fluids under oscillatory translational shear

Viscous fingering occurs when one fluid penetrates a second one of higher viscosity in the narrow gap between the two plates of a Hele-Shaw cell. Using miscible fluids in a radial geometry, we study the onset and growth rate of fingers while an oscillatory, translational shear is applied between the two plates. This shear changes the interfacial structure between the fluids in the thin dimension traversing the gap and thus decreases the viscosity contrast at the interface. In the direction parallel to the shear axis, the finger length is suppressed and the instability onset is delayed as the shear rate and amplitude are increased.  We extract the relevant length and time scales leading to stabilization by varying the gap size and fluid-injection rate over a wide range of fluid viscosity ratios. We present results from experimentally validated simulations to show the structure in the gap.

Liu, Z., Alqatari, S., Videbaek, T., & Nagel, S. (2021). The effect of oscillatory translational shear on viscous fingering in miscible fluids. Bulletin of the American Physical Society.