Understanding stable/unstable miscible $A + B → C$ reaction front and mixing in porous medium

The transport phenomena of A + B → C type reactive miscible front undergoing radial displacement in a porous medium are numerically investigated. For a stable displacement when the viscosity of fluids A, B, and C is same, the dependence of various reaction characteristics on the Damköhler number (Da) is analyzed. The total reaction rate is found to be a non-monotonic function of time depending upon Da, while the total amount of product follows the temporal scaling ∝ t f ( D a ). The viscosity contrast in the system renders unstable flow and results in a hydrodynamic instability called viscous fingering. The effect of hydrodynamics on the reaction product formation is discussed. An insight into the reaction characteristics due to interaction of chemical reaction and instability is obtained for various log-mobility ratios R b   and   R c. It is observed that the onset of instability, as well as the mixing of the fluids, depends on whether the reaction generates a high or less viscous product or equivalently, the sign of | R b − R c |, keeping Rb fixed. Furthermore, the relation between the first moment of averaged reaction rate for stable and unstable displacement is influenced by the sign of | R b − R c | and Da. The coupling of convection and diffusion on the chemo-hydrodynamic instability is presented, and the existence of the frozen fingers in this reactive fluid system is reported. Our numerical results allow us to understand how instability and chemical reaction interplay to affect the reaction characteristics and the mixing of fluids.