Suppression and control of miscible viscous fingering using rotational shear

When one fluid displaces a more viscous one inside the small gap between two parallel flat plates, the interface between the fluids becomes unstable and grows protrusions. For pairs of immiscible fluids, the instability forms only when the ratio of the inner to outer viscosity, η_in/η_out < 1. Experiments using miscible fluids, for which the interfacial tension is negligible, show that the fingering instability is suppressed for η_in/η_out > 1/3. It is believed that this suppression is caused by structure in the interface in the thin direction between the two plates. We study the relevance of the gap structure for the formation of viscous fingers by applying oscillatory rotational shear between the two plates. This shear smears the finger profiles in the direction perpendicular to their radial propagation. Our experiments show that this shear widens the fingers and delays the instability onset; for sufficiently large shear amplitudes or small fluid injection rates, the shear suppresses the instability. We use numerical simulations to clarify the effect of shear on the interfacial gap structure and on the transition to stability.