Delayed viscous fingering instability under translational oscillatory shear

When one fluid displaces a more viscous one inside a confined geometry, the interface between the fluids is unstable to the protrusion of fingers. In our experiment in a radial Hele-Shaw cell with miscible fluids, we apply a uniaxial translational oscillatory shear between the two plates during the injection of the lower-viscosity fluid. The onset of the fingering patters is increasingly delayed as shear rate or shear amplitude increases. The shear breaks the symmetry between the parallel and perpendicular directions to the shear axis; both the onset radius and the finger width becomes larger in the direction perpendicular to the shear. We observe that the gradient of gap-averaged viscosity profile at the tip of the interface decreases with increasing shear, an effect which may be important for explaining the effects of shear on the patterns.