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 (Mccrit) 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.

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We analyse the linear stability of a reactive plane Poiseuille flow, where a reactant fluid A overlies another reactant B in a layered fashion within a two-dimensional channel. Both reactants are miscible and have the same viscosity, while upon reaction, they produce either a less or more-viscous product fluid C . The reaction kinetics is of simple A + B → C type, and the production of C occurs across the initial contact line of reactants A and B in a mixed zone of small and finite width. All three fluids have the same density. We demonstrate the effects of various controlling parameters such as the log-mobility ratio, Damköhler number, Schmidt number, Reynolds number, position and thicknesses of the reactive zone on the stability characteristics. We show that a tiny viscosity stratification by the reaction destabilizes the flow at a moderate (10–1000) and even at low Reynolds numbers (0.01–1). The maximum growth occurs for shorter waves than for the Tollmien–Schlichting eigenmode, and the ranges of unstable wavenumbers are wider than that known for non-reactive channel flow systems. In most cases, the instability occurs due to the overlap of the critical layer with the viscosity-stratified layer. Surprisingly for some parameters, it is observed that the reaction can make σ M decrease with increasing Reynolds number.

No abstract