Rayleigh–Taylor instability of reaction-diffusion acidity fronts

Abstract

We consider the buoyancy driven Rayleigh–Taylor instability of reaction-diffusion acidity fronts in a vertical Hele–Shaw cell using the chlorite–tetrathionate (CT) reaction as a model system. The acid autocatalysis of the CT reaction coupled to molecular diffusion yields isothermal planar reaction-diffusion fronts separating the two miscible reactants and products solutions. The reaction is triggered at the top of the Hele–Shaw cell and the resulting front propagates downwards, invading the fresh reactants, leaving the product of the reaction behind it. The density of the product solution is higher than that of the reactant solution, and hence a hydrodynamic instability develops due to unfavorable density stratification. We examine the linear stability of the isothermal traveling wavefront with respect to disturbances in the spanwise direction and demonstrate the existence of a preferred wavelength for the developed fingering instability. Our linear stability analysis is in excellent agreement with two-dimensional numerical simulations of the fully nonlinear system.