FINGERING PATTERNS AND THEIR FRACTAL DIMENSIONS

Using a radial Hele-Shaw cell we look into the dynamics of fingering as the Reynolds number is increased into the inertial range by increasing both the gap as well as the pressure. For water flowing into glycerol the fractal dimension of the interface reduces as one goes from the viscous to the inertial range (from values around 1.7 for Re approximate to 1 to 1.5 for Re approximate to 200 using the dilation method). Further, we examine some effects when the cell-fluid is shear thinning (water-in-clay) as well as shear thickening (water-in-starch), The above inertial instability becomes less significant for the former case. For the latter case we find a new fingering form with long radially oriented fingers whose fractal dimension is around unity. It seems that the gap width is a very important parameter in determining which forms are generated, both for Newtonian as well as for shear thinning fluids.