Stable-unstable crossover in non-Newtonian radial Hele-Shaw flow

The miscible displacement of a non-Newtonian, shear thinning aqueous polymeric solution, by a Newtonian fluid in a radial Hele-Shaw cell is studied. Experiments where the Newtonian fluid viscosity is tuned to lie between high and low shear rate asymptotic apparent viscosities of the polymeric solution were carried out. A crossover from a stable displacement to an unstable situation displaying viscous fingering patterns, is observed, as the mean front velocity becomes lower than a critical value. The dependence of this critical velocity on Newtonian fluid viscosity and injection rate is investigated. The experimental critical velocity is compared to the velocity where the viscosity of both fluids is the same.