Nonaxisymmetric and Axisymmetric Convection in Propagating Reaction-Diffusion Fronts

Abstract

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.

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

“…The first experiments were performed in capillary tubes and have addressed the influence of the radius of the tube or of the angle of orientation with respect to gravity on the onset of convection ͑characterized by one or two convection rolls͒ and on the speed of the front. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] More recently, experiments in Hele-Shaw cells [21][22][23][24][25][26][27][28][29][30] and in a three-dimensional tank 31 have allowed investigation of the dynamics of more extended systems and of the stability of a wider spectrum of instability modes.…”

The effect of the order of autocatalysis for reaction fronts in vertical slabs

“…A series of detailed experiments by Masere et al showed that convection increases the front speed and changes the curvature of the front. 5 In tubes of small diameter, the front is flat indicating no convection, where in tubes of larger diameter the front is nonaxisymmetric, and for even larger diameters the front is axisymmetric.…”

Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

“…[3][4][5] Although chemical fronts usually propagate at a constant speed, fronts of known autocatalytic reactions such as the iodate-arsenous acid (IAA) reaction or traveling waves have, however, been noted to propagate with larger velocities and be deformed in liquid solutions. 4,[6][7][8][9][10][11][12][13][14][15][16][17][18] This is now understood to be due to natural convection initiated by the spatio-temporal distribution of heat and mass across the front through a change in the physical properties of the solution (density, viscosity, or surface tension). The evolution of the system is then determined by an intricate interplay between chemical and transport processes, namely, diffusion and convective motions of the fluid.…”