Viscosity scaling of fingering instability in finite slices with Korteweg stress

Abstract

We perform linear stability analyses and direct numerical simulations to investigate the influence of the dynamic viscosity on viscous fingering instability in miscible slices. Selecting the characteristic scales appropriately, the importance of the magnitude of the dynamic viscosity of individual fluids on viscous fingering in miscible slice has been shown in the context of the transient interfacial tension. Further, we have confirmed this result for immiscible fluids and shown the similarities between viscous fingering in immiscible and miscible slices with transient interfacial tension. In a more general setting, the findings of this letter will be very useful for different viscous flows, such as displacement of a buoyant miscible layers in a vertical Hele-Shaw cell, viscous fingering instability with viscosity-dependent dispersion, etc.