Behind the Interface and Beyond

Fluid fingers form when a lower viscosity fluid penetrates a higher viscosity one within a confined geometry such as in the gap of a Hele-Shaw cell. Experiments using a novel flow-tracking technique make observable formerly hidden structures in the pattern growth of this iconic instability. By alternately injecting fluid with varying opacity from the center and through the gap between two parallel circular glass plates, we can measure the local velocities of propagating rings of dyed fluid. As inner fluid approaches the interface, and as the outer fluid is approached by the interface, we observe local variation in the fluid velocity along a finger protrusion and in an adjacent valley resulting in the deformation of dyed fluid rings. We relate this structure in the flow far from the interface to local pressure gradients which decay exponentially with distance from the interface. The associated decay length represents a new length scale for the flow which increases with time from finger onset. It is present in both the inner and outer fluids but differs in magnitude and growth rate.