Viscous fingering of a miscible reactive A+B$\to $C interface with an infinite Damk\"ohler number: Nonlinear simulations

Nonlinear simulations of miscible viscous fingering are performed for a reactive system where a simple infinitely fast A+B$\to $C chemical reaction takes place when a solution containing the reactant A is displacing another miscible solution containing the reactant B. The viscosity of the fluid depends on the concentration of the chemicals B and C. The various nonlinear fingering dynamics are analyzed numerically for an infinite Damk\"ohler number $D_{a}$ as a function of the log-mobility ratios $R_{b}$ and $R_{c}$ quantifying the viscosity ratios of the solutions of B and C versus that of the solution of A respectively. If $R_{b}>$0, i.e. if the system is genuinely viscously unstable because the displaced solution of B is more viscous than the displacing solution of A, we analyze the changes to classical non-reactive viscous fingering induced by the reaction.