Numerical simulations of miscible viscous fingering involving viscosity changes of the displacing fluid by A + B → C chemical reactions

Nagatsu and De Wit [“Viscous fingering of a miscible reactive A + B → C interface for an infinitely fast chemical reaction: Nonlinear simulations,” Phys. Fluids 23, 043103 (2011)] simulated the nonlinear evolution of reactive miscible viscous fingering (VF) where the viscosity of the more viscous displaced fluid was changed by an instantaneous A + B → C chemical reaction. They analyzed the dynamics from the viewpoint of an underlying viscosity profile reconstructed from the concentrations of chemical species obtained by a one-dimensional diffusion–reaction equation. The present study develops a mathematical model for reactive miscible VF where the viscosity of the less viscous displacing fluid is changed by an instantaneous A + B → C chemical reaction. We obtain the same underlying viscosity profile as Nagatsu and De Wit by employing appropriate parameters. We perform numerical simulations of the nonlinear evolution of VF under these appropriate parameters. The results show that the present numerical solutions are exactly the same as those obtained by Nagatsu and De Wit, i.e., the same VF pattern is obtained. This numerically proves that the effects of a viscosity change by the chemical reaction on VF are independent of whether the viscosity of the displaced or displacing fluid changes. We obtain a mathematical formula to describe the switch from the parameters used by Nagatsu and De Wit to those used in this study to obtain the same shape of the underlying viscosity profile. This finding will lead to easier and more flexible VF chemical control methods in geoscience processes, where it is difficult to manipulate the properties of more viscous fluids, by manipulating the properties of less viscous fluids.