Abstract
A real-space renormalisation group method is applied to viscous fingering to analyse the fractal nature at a finite viscosity ratio. The renormalisation group transformation is obtained for the permeability of the surface layer which plays the role of coupling constant in the renormalisation group of the phase transition. A stable fixed point is found as a function of the viscosity ratio. The growth probabilities on the perimeter bonds of the injected fluid are evaluated at the fixed point. The multifractal scaling properties are found to be described by the generalised dimensions and the alpha -f spectra. It is shown that at a finite viscosity ratio the displaced area is compact with a surface fractal dimension between 1 and the DLA result with increasing viscosity ratio. This result is consistent with that of King's numerical simulation (1987).
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