Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. I....

Area of Science:

• Chemical kinetics
• Fluid dynamics
• Instability phenomena

Background:

• Reaction fronts can exhibit complex behaviors due to coupled instabilities.
• Autocatalytic reactions provide a model system for studying these phenomena.
• Understanding these interactions is crucial for predicting reaction propagation.

Purpose of the Study:

• To investigate the interplay between buoyancy-driven and diffusion-driven instabilities in an autocatalytic reaction system.
• To analyze twelve distinct cases based on gravitational orientation, density differences, and diffusion rates.
• To elucidate the conditions under which reaction fronts become unstable or stable.

Main Methods:

• Linear stability analysis (LSA) was employed to derive dispersion curves.
• Asymptotic analysis was performed for small wave numbers.
• System parameters included front propagation direction, reactant-product density ratio, and relative diffusion rates.

Main Results:

• Upward-propagating fronts with denser reactants remain unstable, with diffusion enhancing instability.
• Downward-propagating fronts, stable due to buoyancy, can become unstable when diffusion is also destabilizing.
• Diffusionally unstable upward fronts are stabilized by minor buoyancy effects when reactants are lighter than products.
• A strong interaction between diffusion and buoyancy instabilities occurs in downward-propagating fronts with lighter reactants.

Conclusions:

• The interplay between buoyancy and diffusion significantly dictates reaction front stability.
• Density and diffusion differences create complex instability dynamics, leading to diverse propagation behaviors.
• Predicting reaction front stability requires considering both gravitational and diffusive transport effects.