Radial viscous fingers and diffusion-limited aggregation: Fractal dimension and growth sites

Abstract

We show that fractal viscous fingers can be formed in a Hele-Shaw cell with radial symmetry, thereby permitting their study---for the first time---without the complicating effects of boundary conditions such as those present in the conventional linear cell. We find---for a wide range of shear-thinning fluids, flow rates, and plate separations---that radial viscous fingers have a fractal dimension ${\mathrm{d}}_{\mathrm{f}}$=1.70\ifmmode\pm\else\textpm\fi{}0.05, the same as diffusion-limited aggregation. We also quantitatively measure the set of growth sites and compare with diffusion-limited aggregation.