Rayleigh–Bénard instability in n-component reactive fluids

Abstract

We study the hydrodynamic stability of n-component reactive fluids undergoing a single reversible reaction in the Bénard geometry and the Boussinesq approximation, and take the Soret, Dufour, and cross-diffusion effects to be negligible. The boundaries are assumed to be rigid and perfectly conducting; the dependence of the critical Rayleigh number on the assumed boundary conditions for concentrations is discussed in the limit of fast reactions. In this limit we show that, if the boundaries are impermeable to mass flow (the easiest to achieve experimentally), the critical Rayleigh number, R∞cr, is proportional to the one for nonreactive binary fluids. Apart from multiplicative factors, R∞cr depends only on a single dimensionless parameter δ which vanishes when all the diffusion coefficients are equal. For δ≳0 (<−1) stationary convection may set in only if R∞cr≳0(<0); for intermediate values of δ there exist both positive and negative solutions for R∞cr.