Fractal nature of non-Newtonian viscous fingering

A renormalization-group theory is developed to study the fractal and the multifractal structures in the viscous fingering of a non-Newtonian displaced fluid at an infinite viscosity ratio. The effect of the non-Newtonian fluid on the multifractal scaling of the growth-probability distribution is investigated by using a finite lattice renormalization. The dependences of the α-f spectra of the growth-probability distribution are shown on the parameter k describing the different non-Newtonian fluids. It is found that the non-Newtonian fluid has important effects on the multifractal structure of the growth-probability distribution.