Onset of convection for autocatalytic reaction fronts: Laterally unbounded system

Abstract

The linear stability of exothermic autocatalytic reaction fronts that convert unreacted fluid into a lighter reacted fluid is considered using the viscous thermodynamic 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-Benard 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 stabihzes perturbations with short wavelengths A, (A,"whereas long wavelengths are unstable to convection, indicating that the density discontinuity dominates over thermal gradients.Simple analytical results for the critical wavelength A, , for onset of convection, the growth rate near onset of convection, and the maximum growth rate are found. Agreement with experiments on iodatearsenous acid solutions in vertical tubes motivates linear and nonlinear calculations in cylin00 drical geometries.

Convective chemical-wave propagation in the Belousov-Zhabotinsky reaction

“…This relation, an asymptotic form of the reaction-diffusion equations for wave propagations, has been successfully applied to spiral waves in the BZ reaction [10] as well as to convective chemical waves in the iodate-arsenous acid systems [8,14]. In our case (Fig.…”

“…In fact, since the typical thermal diffusivities (=10 cm /s) are about 100 times greater than typical molecular diffusivities (=10 cm /s), any thermal gradient can be rapidly smoothed out by thermal diffusion, leaving the density gradient practically the same as the purely compositional density gradient at the higher temperature of the reacted Quid. Previous calculations on the iodate-arsenous acid reaction have justified this argument [8]. Therefore, in this paper, we consider only the density gradient induced by changes in chemical composition.…”

“…(8), the reacting fiuid will be heavier than the remaining Auid and the tail will be unstable instead of the front for ascending waves. In fact, the system behavior of Eqs.…”

Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

“…Theoretical work for such narrow geometry provides the critical radius of the tube above which the hydrodynamic instability can develop, and a discussion on whether axi-or nonaxisymmetric modes should be observed at onset. [22][23][24][25][26][27] More recently, experiments in Hele-Shaw cells have shown that several fingers can develop in this geometry where the front is laterally extended. 16 -18,20 Dispersion curves providing the growth rate of the fingers as a function of their wave number have been measured experimentally.…”

“…9 In miscible systems, chemical reactions are more prone to provide density differences that can drive buoyantly unstable situations as soon as a heavier fluid lies on top of a lighter one. Experimental evidence [10][11][12][13][14][15][16][17][18][19][20] and theoretical studies [20][21][22][23][24][25][26][27][28][29][30][31][32] on density driven instabilities have shown that the coupling between buoyancy driven flows and chemical reactions can strongly affect the properties of the fingering instability. The coupling with chemical reactions has been addressed mainly concerning the stability of planar fronts with regard to Rayleigh-Taylor fingering.…”