Patterns in the variable Hele-Shaw cell for different viscosity ratios: Similarity to river network geometry

Abstract

This paper reports the generation of interesting viscous fingering patterns in a variable Hele-Shaw cell using a non-Newtonian paint as the displaced fluid. Patterns with infinite and finite ratios of viscosity between the displaced and displacing fluids are produced. We find a qualitative difference between the patterns generated in the two cases. However, displaced fluids of different viscosity generate similar patterns, as long as the viscosity ratio is kept infinite. The infinite ratio of the viscosity of the two fluids produces a paint pattern that exhibits fractal nature. The fractal pattern resembles very much the simulated river basin boundary geometry, which earlier workers have shown to emerge from a minimum energy dissipation principle.