Miscible viscous fingering induced by a simple A plus B -> C chemical reaction

Viscous fingering (VF) is a hydrodynamical instability that occurs in porous media when a less viscous fluid displaces a more viscous one. We investigate here numerically how such an instability can be triggered by a simple A+B -> C reaction when a solution of one reactant is displacing linearly a miscible solution of another reactant of same viscosity producing a more viscous product C at the interface. The properties of the fingering pattern observed in the zone where the less viscous reactant pushes more viscous products are studied as a function of the relevant parameters of the problem. These are the Damkohler number, the viscosity contrast between reactants and product, the ratio of initial concentrations of A and B, and the diffusion coefficients of each species. Our study shows that the fingering pattern can in some cases be different whether A displaces B or vice versa, enlightening recent experimental observations of such asymmetries in micellar systems. In particular, we show that in this asymmetric case, VF is more intense when the invading chemical solution is either the less concentrated one for equal diffusivities or when it contains the slower diffusing reactant for fixed equimolar initial concentrations.