Viscous fingering of a miscible reactive A+B→C interface for an infinitely fast chemical reaction: Nonlinear simulations

Abstract

Nonlinear dynamics of miscible viscous fingering is analyzed numerically for a reactive system when a solution containing a reactant A is displacing another miscible solution containing another reactant B. A simple A+B→C reaction takes place upon contact of the solutions. The viscosity of the fluid depends on the concentration of the various chemicals. The nonlinear fingering dynamics is studied numerically for an infinite Damköhler number Da, i.e., for an infinitely fast reaction as a function of the log-mobility ratios Rb and Rc quantifying the viscosity ratios of the solutions of B and C, respectively, versus that of the solution of A. If Rb>0, i.e., if the system is genuinely viscously unstable because the displacing solution of A is less viscous than the displaced solution of B, we analyze the changes to classical nonreactive viscous fingering induced by the reaction. If on the contrary Rb<0, which corresponds to a hydrodynamically stable case in absence of reactions, we study chemically driven viscous fingering occurring when the chemical reaction triggers a nonmonotonic viscosity profile. Comparison between the present simulation results and corresponding linear stability analysis and experiments is also conducted.