Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front

摘要

A buoyancy-driven hydrodynamic instability appearing when an aqueous acid solution of HCl overlies a densernalkaline aqueous solution of NaOH in a vertically oriented Hele-Shaw cell is studied both experimentally andntheoretically. The peculiarity of this reactive convection pattern is its asymmetry with regard to the initial contactnline between the two solutions as convective plumes develop in the acidic solution only. We investigate herenby a linear stability analysis (LSA) of a reaction-diffusion-convection model of a simple A + B → C reactionnthe relative role of solutal versus thermal effects in the origin and location of this instability. We show thatnheat effects are much weaker than concentration-related ones such that the heat of reaction only plays a minornrole on the dynamics. Computation of density profiles and of the stability analysis eigenfunctions confirm thatnthe convective motions result from a diffusive layer convection mechanism whereby a locally unstable densitynstratification develops in the upper acidic layer because of the difference in the diffusion coefficients of thenchemical species. The growth rate and wavelength of the pattern are determined experimentally as a function ofnthe Brinkman parameter of the problem and compare favorably with the theoretical predictions of both LSA andnnonlinear simulations.