PATTERNS IN THE VARIABLE HELE-SHAW CELL FOR DIFFERENT VISCOSITY RATIOS - SIMILARITY TO RIVER NETWORK GEOMETRY

This paper reports the generation of interesting viscous fingering pat terns 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 q ualitative difference between the patterns generated in the two cases. However, displaced fluids of different viscosity generate similar pat terns, as long as the viscosity ratio is kept infinite. The infinite r atio of the viscosity of the two fluids produces a paint pattern that exhibits fractal nature. The fractal pattern resembles very much the s imulated river basin boundary geometry, which earlier workers have sho wn to emerge from a minimum energy dissipation principle.