Reaction-induced Kelvin-Helmholtz roll-ups

A simple (A+B→C)-type reaction can induce Kelvin-Helmholtz (KH) roll-up patterns at the reactive zone by a local viscosity modification [1, 2]. However, the instability mechanism is not understood so far, and a flat initial interface is required for better analysis. To do so, we consider laminar Poiseuille flow where a reactant fluid A shears on the top of another iso-viscous reactant B in a layered fashion within a two-dimensional channel. Following an (A+B→C)-type reaction kinematics, two reactants produce another differently viscous fluid C, creating an inflectional base flow. The inflection points of velocity within the reactive zone are generated; as such, they exacerbate a periodic perturbation to grow viscous wavy patterns at one reaction front while the other just stably diffuses. Streamlines oscillate and behave as in a phase lock system, amplifying the disturbance wave's amplitude. Through direct numerical simulations (DNS), we calculate the onset time (t_on) of the instability for controlling parameters such as the log-mobility ratio (R_c), Damköhler number (Da), Péclet number (Pe), and Reynolds number (Re). The plots of t_on demonstrate the existence of a critical log-mobility ratio (Da, Pe, and Re-dependent), below which the instability never onsets [3]. Further, an Orr-Sommerfeld equation-based linear stability analysis (LSA) is used to obtain the onset time of instability for all unstable wave numbers in the linear regime. The onset dynamics from LSA agree with those obtained from DNS, except for the Reynolds number effect. At the end of this talk, we shall discuss the possible reasons and more suitable advanced LSA techniques that may provide the DNS-matching onset dynamics.