Dynamics of shear instability in A+B→C reactive flow yielding high-viscosity products

Abstract

This numerical study investigates shear instabilities in a two-layered reactive system within a 2D channel, governed by the Navier–Stokes equations. Examining laminar Poiseuille flow, we explore the shearing of reactant fluids $A$ and $B$, undergoing the $A+B\to C$ reaction. The favorable shear due to increased viscosity of the product fluid $C$ amplifies periodic perturbations, forming roll-ups resembling interfacial waves. Increased Reynolds number leads to ligament formation. Vorticity field strength correlates with product fluid viscosity, enhancing instability growth. In the stable flow regime, the streamlines initially remain horizontally straight, but they start oscillating synchronously for a favorable viscosity ratio, which amplifies the growth of roll-ups in the unstable regime. A nonlinear energy budget analysis reveals that the growth of the shear instability primarily arises from the energy contributions of axial and vertical convection, rather than from the reaction source or diffusion terms. Shear instability induces opposite transverse motion of the reaction rate and product center of mass. Measurement of transverse spreading reveals an intermediate convection-dominated time regime in unstable flow, interspersed with diffusion-dominated early and later regimes. Proximity of the reactive zone to the bottom wall induces streamlines to shift out of phase, forming humps, and changing the wavelength of perturbations with a delayed intermediate convection-dominated regime.