Similarity characteristics in the growth of radial fingering in a Hele-Shaw

We conduct nonlinear simulations based on a boundary integral method to describe the radial growth of viscous fingers in a Hele-Shaw. The system is governed by two dimensionless parameters, the viscosity contrast, A, and an effective surface tension, B. Most numerical investigations of the problem have analyzed the case in which the viscosity contrast is large, fixed at A=1. Experimentally, this corresponds to having air as the displacing fluid. By exploring a wide range of parametric values, we find that for smaller values of the viscosity contrast, which are typical of the displacement between two immiscible liquids, the effective surface tension behaves as a similarity parameter. As such, similar morphological patterns are obtained as B-values are increased, but these patterns are larger and take longer to develop than their lower-value counterparts. These numerical results are compared to experiments.