A numerical study on reaction-induced radial fingering instability. (11th January 2019)

• Record Type: Journal Article
• Authors: Sharma, Vandita; Pramanik, Satyajit; Chen, Ching-Yao; Mishra, Manoranjan
• Is Part Of: Journal of fluid mechanics. Volume 862(2019)
• Page Start: 624
• Page End: 638
• Publication Date: 2019-01-11
• Subjects: fingering instability, -- laminar reacting flows, -- porous media; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.963
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : The dynamics of $A+B\rightarrow C$ 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 $R_{c}^{-}\leqslant R_{c}\leqslant R_{c}^{+}$ . The effect of geometry is observable on the onset of instability, where we obtain significant differences from existing results in the rectilinear geometry.