Pushing a non-Newtonian fluid in a Hele-Shaw cell:: From fingers to needles

We make a theoretical study of the finger behavior of a simple fluid displacing a non-Newtonian fluid confined in a Hele-Shaw cell. We study the Saffman-Taylor instability when the viscosity of the displaced fluid changes with shear. Our results predict a decrease of the finger width that goes to zero for large values of the velocity. An analytical treatment allows the predictions of the dynamics in radial growth. (C) 1999 American Institute of Physics. [S1070-6631(99)00907-1].