Unstable miscible displacements in Hele-Shaw cell with chemical reactions producing viscoelastic solution

Viscous fingering accompanied by chemical reactions is encountered in many processes, such as petroleum recovery, chromatographic separation, and polymerization. Therefore, the understanding of the coupling between hydrodynamics and chemical reaction in viscous fingering is quite appealing. Herein, we study the flow displacement involving a chemical reaction at the interface between displacing and displaced fluids. The two reacting fluids are considered to be miscible and Newtonian, which produces a gel-like product exhibiting viscoelastic behavior. The effect of chemical reactions on instability is examined by performing full flow simulations. The viscoelastic product is rheologically described using the White-Metzner model. It was observed that the shear-thinning behavior of the product always strengthens the instability whereas the elastic behavior of the product attenuates the finger growth as compared to the Newtonian product. Both the cases, where the product is more or less viscous than the reactants are analyzed.