Effects of low and high viscous product on Kelvin-Helmholtz instability triggered by A + B → C type reaction

Abstract

The dynamics of the Kelvin–Helmholtz (K–H) instability triggered by a non-linear second order 𝐴+𝐵→𝐶 type reaction is analyzed through direct numerical simulations. This paper aims to understand the chemo-hydrodynamic K–H instability when the chemical reaction decreases or increases the viscosity gradient at the reactive interface. Thus, we consider the viscosity of the obtained product C is to be different from both the iso-viscous reactants A and B. It is observed that for both the cases of less and more-viscous product C, K–H roll-ups occur at the reactive interface and hence various flow features are compared for both of these scenarios. Moreover, depending on the product's viscosity, the flow-directed K–H roll-ups occur either at A–C interface or C–B interface. Strikingly the number of K–H roll-ups at the reactive interface is more when the product is less viscous and full vortex completion of K–H roll-ups is noticed. It is demonstrated that even for a significantly large Damköhler number (high rate of reaction), the K–H roll-ups may not occur at the reactive front. Thus, a favorable log-mobility ratio (Mc) having a greater magnitude than the critical log-mobility ratio (𝑀𝑐𝑟𝑖𝑡𝑐) is required to trigger the K–H instability within a desirable time for both the cases of Mc < 0 and Mc > 0. Moreover, asymmetric onset dynamics are encountered with respect to Mc = 0 axis.