Non-Newtonian effects on immiscible viscous fingering in a radial Hele-Shaw cell

The displacement of a high-viscosity non-Newtonian fluid by a low-viscosity Newtonian fluid in a Hele-Shaw cell is capable of producing ramified viscous-fingering patterns exhibiting fractal characteristics. Recently, it was established that interfacial tension has little influence on the formation of these fractal patterns. However, the precise mechanism behind their formation is not as yet fully understood. In this paper, we consider the immiscible displacement of a non-Newtonian fluid in a radial Hele-Shaw cell, and present a detailed analysis of the flow, thus exposing features which until now have not been reported. In particular, we find an effective length compression for the formation of viscous-fingering patterns and accelerated growth rates, which upon consideration of recent experimental results, are consistent with the formation of fractal viscous-fingering patterns.