Abstract
The Kelvin–Helmholtz (K–H) interfacial instability induced by an infinitely fast bimolecular chemical reaction (A + B → C) is studied numerically by considering that the depth of the boundary layer and the reaction front develop simultaneously in the channel flow. In a flow of one reactant fluid (A) to another reactant fluid (B), the generation of a more viscous or less viscous product (C) induces a viscosity gradient at the reaction front, resulting in instability motions of different types. According to the redefinition of the log viscosity ratio, RChem and RPhys, which is used to describe the viscosity ratio between the product and non-iso-viscous reactants, the growth of K–H instability is identified chemically and hydrodynamically. Instability with roll-ups occurs along the reaction front near the wall for a less viscous product compared to that with two reactants; i.e., RChem>0, and the number of roll-ups increases with an increase in RChem. For a system with RChem<0, the growth of instabilities is greatly delayed and incomplete roll-ups (billows) arise along the reaction front. This instability motion is determined by the complex contribution of the diffusive flow effect, which delocalizes the vorticity source/sink, and the vorticity effect, which is localized according to the viscosity gradient. Interestingly, for a small Re, the system instead becomes destabilized by a strong wall effect within the boundary layer, showing the active growth of roll-ups at the reaction front near the wall. The wall critically impedes the unstable motion in the entrance region, resulting in the instability becoming localized within the boundary layer, δ∼xRe−1/2, especially for a positive RChem system. This study suggests that the boundary layer thickness plays an important role in the development of instability motion. This wall effect is not profound for a negative RChem system showing billow-type instability motion.
Funder
National Research Foundation of Korea