Stability of a layered reactive channel flow

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 & RARR;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, Damkohler 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 sigma M decrease with increasing Reynolds number.

Automated summary

This study analyzes the linear stability of a reactive plane Poiseuille flow in a two-dimensional channel where two miscible reactants A and B produce a viscous product C. The effects of various parameters such as mobility ratio, Damkohler number, Schmidt number, Reynolds number, and reactive zone characteristics on stability are examined. It is found that even a small viscosity stratification due to reaction can destabilize the flow at moderate and low Reynolds numbers, and the instability occurs due to the overlap of the critical layer with the viscosity-stratified layer. Surprisingly, in some cases, the reaction leads to a decrease in σM with increasing Reynolds number.