Diffusivity ratio effect on the onset of the buoyancy-driven instability of an A + B → C chemical reaction system in a Hele-Shaw cell: Asymptotic and linear stability analyses

Abstract

The effects of an A + B → C chemical reaction and different diffusivity on the onset of the buoyancy-driven instability in a Hele-Shaw cell are analyzed theoretically. For an instantaneous chemical reaction system, new concentration and density fields are derived, and based on the density profiles, asymptotic stability characteristics are analyzed. Also, using the linear stability theory, we derive new stability equations and obtain the onset time of instabilities by solving the linear stability equations theoretically and numerically. As expected, the onset instabilities are dependent on the various parameters, such as the diffusivity ratio, reactant concentration ratio, and densification coefficient ratio. Through the asymptotic analysis, we propose that the system can be gravitationally unstable without an adverse density gradient due to the double diffusive effects. In addition, a newly proposed stability condition is tested through systematic linear stability analysis. The linear stability analysis shows that the effects of different diffusivities accelerate and retard the onset of instabilities and induce them without an adverse density gradient. The present asymptotic and linear stability analyses are in good agreement.