A numerical study on reaction-induced radial fingering instability

Abstract

The dynamics of A + B -> C fronts is analysed numerically in a radial geometry. We are interested to understand miscible fingering instabilities when the simple chemical reaction changes the viscosity of the fluid locally and a non-monotonic viscosity profile with a global maximum or minimum is formed. We consider viscosity-matched reactants A and B generating a product C having different viscosity than the reactants. Depending on the effect of C on the viscosity relative to the reactants, different viscous fingering (VF) patterns are captured which are in good qualitative agreement with the existing radial experiments. We have found that, for a given chemical reaction rate, an unfavourable viscosity contrast is not always sufficient to trigger the instability. For every fixed Peclet number (Pe), these effects of chemical reaction on VF are summarized in the Damkohler number (Da) - the log-mobility ratio (R-c) parameter space that exhibits a stable region separating two unstable regions corresponding to the cases of more and less viscous product. Fixing Pe, we determine Da-dependent critical log-mobility ratios R-c(+) and R-c(-) such that no VF is observable whenever R-c(-) <= R-c <= R-c(+). The effect of geometry is observable on the onset of instability, where we obtain significant differences from existing results in the rectilinear geometry.