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A numerical study on reaction-induced radial fingering instability

Published online by Cambridge University Press:  11 January 2019

Vandita Sharma Open the ORCID record for Vandita Sharma [Opens in a new window] ,
Satyajit Pramanik Open the ORCID record for Satyajit Pramanik [Opens in a new window] ,
Ching-Yao Chen  and
Manoranjan Mishra Open the ORCID record for Manoranjan Mishra [Opens in a new window]
Vandita Sharma
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001 Rupnagar, India
Satyajit Pramanik
Affiliation:
NORDITA, Royal Institute of Technology & Stockholm University, 106 91 Stockholm, Sweden
Ching-Yao Chen
Affiliation:
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, 30010Republic of China
Manoranjan Mishra*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001 Rupnagar, India Department of Chemical Engineering, Indian Institute of Technology Ropar, 140001 Rupnagar, India
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Interfacial Flows (free surface): Fingering instability Reacting Flows: Laminar reacting flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 624 - 638
Copyright
© 2019 Cambridge University Press 

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