Nonlinear unstable viscous fingers in Hele–Shaw flows. I. Experiments

Post-instability viscous fingering in rectilinear flow in a Hele–Shaw cell has been studied experimentally. Of particular interest was the characterization of the range of length scales associated with tip splitting, over a reasonably wide range of parameters. A digital imaging system was used to record the patterns as a function of time, which allowed properties such as the tip velocity, finger width, perimeter, and area to be studied as functions of time and capillary number. The tip velocity was observed to be approximately constant regardless of the occurrence of splitting events, and the average finger width decreased as the degree of supercriticality increased. Quantitative measures of the fact that there is a limit to the complexity of viscous fingers are provided, and that over the range of parameters studied, no evidence for fractal fingering exists. A discussion of the dynamics of tip splitting explains why this is so.