Effect of rotational shear on the viscous fingering instability in miscible fluids

When a fluid is injected into a more viscous one in the thin gap between the two plates of a Hele-Shaw cell, the interface between the fluids can become unstable to the growth of long protrusions. We use miscible fluids in a radial Hele-Shaw geometry to study the instability in the presence of an oscillatory rotational shear between the plates. The rotational shear delays the onset of the instability and creates broader fingers. We study how these effects depend on the amplitude and frequency of the shear, and on the injection rate and viscosity ratio of the two fluids. We use simulations to investigate how the shear alters the interface in the direction of the thin gap between the plates.