Multifractal Viscous Fingering and Non-Newtonian Growth

Abstract

The first part of this paper is in collaboration with H.E.Stanley and G. Daccord. We have calculated for experimental viscous fingers the hierarchy of fractal exponents which describe the growth of the two fluid interface. Our analysis is based on a “coastline” method and is applied to the growth of Newtonian viscous fingers. In the second part we show how present statistical models for the viscous finger instability can be extended to enable the study of non-Newtonian viscous fingers. We present results on the change of finger thickness as a function of the shear-thinning index m.