Onset and growth of miscible viscous finger instabilities for shear-thinning viscoelastic fluids

The viscous fingering instability, which occurs when a fluid displaces another fluid of higher viscosity in a narrow gap, is not well understood when a shear-thinning fluid is displaced by another miscible fluid. We study this problem by experimentally quantifying the displacement of a shear-thinning polyacrylamide solution by dyed water and comparing it to a Newtonian glycerol solution of similar viscosity in a radial Hele-shaw cell. Using novel image processing techniques, velocities of the moving Newtonian and non-Newtonian interfaces are tracked, from which local pressure gradients can be found. We also measure dye concentration to monitor the evolution of finger profiles across the gap throughout each experiment. A comparison of finger profiles and local pressures for the Newtonian and non-Newtonian cases gives us new insights into the mechanisms driving instability formation and growth. Our measurements show a significant number of tip-splitting events in the displacement of the Newtonian solution, while the non-Newtonian polymer solution exhibits no tip-splitting for a wide range of flow rates. We attribute this behavior to a competition between miscibility and viscous forces. We also observe the number of viscous fingers increases for the polyacrylamide solution which we attribute to viscoelastic effects.