A numerical study on reaction-induced radial fingering instability. (14th January 2019) - Sharma, Vandita; Pramanik, Satyajit; Chen, Ching-Yao; Mishra, Manoranjan
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 Péclet number ( Pe ), these effects of chemical reaction on VF are summarized in the Damköhler 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_cR_c^+ . The effect of geometry is observable on the onset of instability, where we obtain significant differences from existing results in the rectilinear geometry.