Experimental Pressure Analysis Techniques in the Viscous Fingering Instability

When a lower viscosity fluid displaces a higher viscosity one in a confined geometry, the interface between the two fluids is unstable to the formation of fingers. The fluid flow is governed by Darcy’s law so that the local velocity is proportional to the pressure gradient. Using thin rings of dyed fluid we visualize the local flow field within a radial Hele-Shaw cell and are able to map pressure gradients throughout the pattern-formation process. In particular, we measure the pressure gradients as a function of distance from the unstable fluid interface. Using various image processing techniques, we examine the role of the fluids’ viscosity ratio as a parameter governing pattern formation.