Experimental study on the role of polymer addition in Saffman–Taylor instability in miscible flow displacement

The role of nonlinear rheology of polymeric fluids in finger formation and the ensuing morphology of the patterns in miscible flow displacement is examined experimentally. The poly(ethylene oxide) (PEO) is introduced in either displaced or displacing fluid. The PEO solutions exhibit shear-thinning viscosity as well as normal stresses. As viscous fingering is primarily caused by the viscosity contrast between two miscible fluids, the zero-shear viscosities of the two fluids are controlled mainly by their composition. The contribution of rheological behavior in fingering is studied by varying the molecular weight of the polymer. The development of fingering patterns in PEO solutions is observed to be more complex showing more branches and tip-splitting vis-à-vis Newtonian fluid even for the same value of effective viscosity contrast regardless of polymer addition in either fluids. Particularly, flow displacement with displaced PEO solution exhibits significantly intensified patterns such that a fractal-like growth is observed when PEO solution of either high concentration or high molecular weight is being displaced. The additional nonlinear behavior, sidebranching, tip-splitting, and shielding is attributed to the inhomogeneity in fluid viscosity and normal stresses (or elasticity) due to local flow behavior. While shear-thinning behavior promotes the longitudinal growth of fingers leading to the shielding effect, the presence of normal stresses inhibits longitudinal growth of fingers promoting fingers in the transverse direction that imparts tip-splitting. Overall, the nonlinear rheology of the fluids gives rise to the effects, in addition to the viscosity modifications, and hence, is crucial for determining the morphology of the fingering instability.