Poiseuille flow between parallel plates alters the shapes and velocities of chemical reaction fronts. In the narrow-gap limit, the cubic reaction-diffusion-advection equation predicts a front-velocity correction equal to the gap-averaged fluid velocity epsilon. In the singular wide-gap limit, the correction equals the midgap fluid velocity 3epsilon/2 when the flow is in the direction of propagation of the reaction front, and equals zero for adverse flow of any amplitude for which the front has a midgap cusp. Stationary fronts are possible only for adverse flow and finite gaps. Experiments are suggested.
Observations of steady nonaxisymmetric chemical wave fronts are reported for upward propagation in iodatearsenous acid solutions within vertical capillary tubes. These observations confirm a recent prediction of hydrodynamic stability theory that the onset of convection in such fronts should be nonaxisymmetric. The nonaxisymmetric waveform reflects the presence of a single convective roll in the vicinity of the moving front. IntroductionUnderstanding convective effects in chemical waves represents an interesting and important challenge. Chemical waves create temperature and concentration gradients which can lead to mass density gradients. In the presence of gravity, these density gradients can destabilize planar reaction-diffusion waves, leading to fluid convection and the development of curved fronts. This convection is the source of differences between ascending and descending front propagation speeds in the iron(I1)-nitric acid reaction,1.2 the chloritethiosulfate reaction: and the iodatearsenous acid r e a c t i~n~.~ in vertical capillary tubes. Measurements of front speed provide simple tests of proposed reaction-diffusion mechanisms;s+6 hence, it is important to know when convection contributes to the speed of propagation. Furthermore, it is of interest to understand and predict the effects of convection on the waveform of the propagating front.Previous experiments on iodatearsenous acid mixture3g4 revealed steady, curved fronts and an increase in propagation speed with increasing tube diameter for ascending waves. The iodate-arsenous acid reaction produces a reacted solution which is less dense than the unreacted solution, so that only upward propagation (with the lighter fluid below) is potentially unstable under the action of gravity. Indeed, descending fronts initiated at the top of the tube remain flat and propagate at a speed independent of the tube diameter. For a tube of diameter 0.94 mm, ascending fronts were also flat and had the same speed as descending fronts, indicating the absence of convection. For diameters of 1.8 mm and above, axisymmetric curved fronts were observed with an approximately parabolic profile and the highest point in the center of the cylindrical tube. The curvature of the ascending fronts increased with increasing tube diameter as did the speed. This curvature was attributed to convection driven by the buoyancy of the reacted fluid, with fluid moving up near the center of the cylinder and down near the cylinder walls.
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.
A linear rate equation describes fragmentation with continuous and discrete mass loss typified by consumption of porous reactive solids and two-phase heterogeneous solids. For a massdependent fragmentation rate x and a continuous-mass-loss rate ex ", o ya -1 & 0 yields a
We present a theory for the vertical propagation of chemical waves near the onset of convection.Fluid motion, coupled to a standard reaction-diffusion mechanism for chemical wave propagation, determines the speed and shape of the reaction front in a two-dimensional slab. Our model is compared with experiments in capillary tubes. For tilted and horizontal tubes, fluid motion is always present with a corresponding increase in front speed. PACS number(s): 47.20. Bp, 47.70.Fw, 82.20.Mj
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