Similarity characteristics in the morphology of radial viscous fingers

We conduct nonlinear simulations to investigate the radial growth of viscous fingers in a Hele-Shaw cell by performing a wide parametric study on the two dimensionless parameters that govern the dynamics. These are the viscosity contrast, A, and the effective surface tension, B, which compares the influence of surface tension with the injection rate that drives instability. It is well known that the surface tension between the fluids has a stabilizing influence on pattern formation leading to slower fingering growth and a reduced number of fingers. Moreover, the current results show that, for fixed A values, larger values of the effective surface tension lead to the formation of fingering patterns that are similar to each other. As such, the calculated interfacial shapes are larger and take longer to develop. Furthermore, the calculated shapes offer a visually striking portrait of instability evolution, and comparison to our experimental measurements highlights the close resemblance between the two with a few discrepancies pointed out. Finally, we observe how changes to the initial nearly circular interface affect both the morphology of viscous fingers and the timescale for pattern formation.

Automated summary

We performed nonlinear simulations to study the radial growth of viscous fingers in a Hele-Shaw cell, varying two dimensionless parameters: the viscosity contrast (A) and the effective surface tension (B). Higher surface tension led to slower and fewer fingering growth patterns. Higher surface tension also resulted in the formation of similar fingering patterns with larger sizes and longer development times. Comparison between the calculated interfacial shapes and experimental measurements showed a close resemblance with a few discrepancies. Changes to the initial nearly circular interface affected both the morphology of viscous fingers and the timescale for pattern formation.