Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers . We: explore various polymer architectures, molecular weights, and solutio n concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the "finger mobility," which relates the velocity t o the pressure gradient. The flow discontinuities, characterized by jumps i n the finger tip velocity, which are observed in experiments with some of t he polymer solutions, can be modeled by using a nonmonotonic dependence bet ween a characteristic shear stress and the shear rate at the tip of the fin ger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is sh own to agree with the experimental data. [S1063-651X(99)08910-2].