Role of interfacial geometry in miscible viscous fingering

The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid, of viscosity η_in, displaces a more viscous one, of viscosity η_out, in a narrow gap between parallel plates—a model system for studying pattern formation and interfacial dynamics. For immiscible fluids, unstable growth occurs when η_in/η_out < 1, whereas for miscible fluids, where interfacial tension is negligible, the growth is stable when 1/3 < η_in/η_out < 1. This regime of enhanced stability has been linked to the miscible interfacial structure inside the gap. We investigate the role of gap structure by applying oscillatory rotational shear to one plate relative to the other. This effectively smears the fingering profile perpendicular to the fingers' radial propagation while keeping η_in/η_out unchanged. Increasing shear induces a transition between two distinct instability regimes with different fingering morphology, onset, and growth dynamics. For sufficiently large shear, fingering is entirely suppressed. Our experiments and simulations highlight the role of interfacial geometry and provide insight into the physics of confined viscous flow and instability control.