Development of Viscous Fingering Patterns

The development of viscous fingering patterns has been observed from very early times to deep in the nonlinear regime for the flow of immiscible liquids in a Hele-Shaw cell. If the dimensionless viscosity contrast, $A$, is large, the number of fingers decreases rapidly with time after the initial pattern is established. If $A\simeq 0$, all fingers grow through the entire time range of this experiment. For all values of $A$ there is a power-law relation between the length of the longest finger and the time.