Diffusion-driven transition between two regimes of viscous fingering

Abstract: Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable. For miscible fluids the situation is more complicated due to the formation of interfacial structure in the thin dimension spanning the gap. Here we study the effect of the inherent diffusion between the two miscible fluids on this structure and on the viscous fingering patterns that emerge. We discover an unexpected transition separating two distinct regimes where the pattern morphologies and mode of onset are different. This transition is marked by a regime of transient stability as the structure of the fingers evolves from having three-dimensional structure to being quasi-two dimensional. The presence of diffusion allows an instability to form where it was otherwise forbidden.