Onset of convection for autocatalytic reaction fronts: Laterally unbounded system

The linear stability of exothermic autocatalytic reaction fronts that convert unreacted fluid into a lighter reacted fluid is considered using the viscous thermohydrodynamic equations. For upward front propagation and a thin front, the discontinuous jump in density at the front is reminiscent of the Rayleigh-Taylor problem of an interface between two immiscible fluids, whereas the vertical thermal gradient near the front is reminiscent of the Rayleigh-Bénard problem of a fluid layer heated from below. The problem is also similar to flame propagation, except that here the front propagation speed is limited by catalyst diffusion rather than by activation kinetics. For a thin ascending front and small density changes in a laterally unbounded system, the curvature dependence of the front speed stabilizes perturbations with short wavelengths λ${\lambda }_{\mathit{c}}$, whereas long wavelengths are unstable to convection, indicating that the density discontinuity dominates over thermal gradients. Simple analytical results for the critical wavelength ${\lambda }_{\mathit{c}}$ for onset of convection, the growth rate near onset of convection, and the maximum growth rate are found. Agreement with experiments on iodate–arsenous acid solutions in vertical tubes motivates linear and nonlinear calculations in cylindrical geometries.