Interfacial instability induced by an (A+B→C)-type reaction in channel

When a miscible solution of reactant fluid A displaces another viscosity-matched reactant B in a channel, it is found that Kelvin-Helmholtz (K-H) type billows occur at the fluid-fluid interface.  A local viscosity contrast created by the high viscous product fluid C of (A+B→C)-type reaction induces these unstable K-H roll-ups at the reactive interface. The dynamics of instability are controlled by various governing parameters such as the log-mobility ratio (R), Damköhler number (Da), Péclet number (Pe), Reynolds number (Re).  Hence flow features such as enstrophy and mixing dynamics are analyzed by varying these parameters. Moreover, through the directional field of vorticity, it is shown that a Horse-shoe type instability develops at the wall near to inlet with an increasing log-mobility ratio. Strikingly it is found that, even at a higher reaction rate of reaction, if the log mobility ratio is lower than a critical value (R^crit), then the unstable K-H roll-ups do not show up. The dependency of the R^crit on other governing parameters (Da, Pe, and Re) is depicted through the onset time (t_on) and the log-mobility ratio (R) space. A manifested proportionate onset dynamic with respect to Pe and reversed dependency of onset on higher Re will be discussed in more detail.