Flow-field development during finger splitting at an exothermic chemical reaction front

Abstract

Fingertip splitting may be observed at chemical reaction fronts subject to buoyancy-induced Rayleigh-Taylor fingering, as investigated in ascending fronts of the iodate-arsenous acid reaction in vertical Hele-Shaw cells. We study the properties of the flow-field evolution during a tip-splitting event both experimentally and theoretically. Experimental particle-image velocimetry techniques show that the flow field associated to a finger displays a quadrupole of vortices. The evolution of the flow field and the reorganization of the vortices after a tip-splitting event are followed experimentally in detail. Numerical integration of a model reaction-diffusionconvection system for an exothermic reaction taking into account possible heat losses through the walls of the reactor shows that the nonlinear properties of the flow field are different whether the walls are insulating or conducting. In insulating systems, the flow field inside one finger features only one pair of vortices. A quadrupole of flow vortices arranged around a saddle-node structure similar to the one observed experimentally is obtained in the presence of heat losses suggesting that heat effects, even if of very small amplitude, are important in understanding the nonlinear properties of fingering of exothermic chemical fronts.

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

“…[19][20][21][22][23][24] Various scenarios of buoyancy-driven instabilities have been shown to arise from the combination of solutal and thermal contributions to the density difference across the front. 9,[25][26][27][28][29] In horizontal geometries, the situation can become even more complicated if the solution is open to air. Indeed, besides possible density gradients, there is an additional source of fluid motions, the Marangoni effects triggered by surface tension gradients at the air-liquid interface.…”

“…54) but, as mentioned earlier, convection can affect the dynamics and propagation speeds of these fronts in aqueous solutions. 9,19,20,27,33,41,47,52 As discussed above, the complexity of such experimental systems arises from the fact that it is not always trivial to discriminate between surface tension-driven and buoyancy-driven convection.…”

Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. II. Nonlinear simulations

“…Such a coarsening tendency has long been noted in viscous and density fingering in nonreactive fluids. 11 It has also been observed experimentally in the RT fingering of autocatalytic fronts both in the IAA reaction 12,13 and in the CT system [14][15][16] where it is seen that some slightly more advanced fingers can shield their neighbors leading to an overall decrease in the wavelength with time. In some regimes tip splitting, through which large fingers split into two smaller ones, are observed as well.…”

“…The isothermal RT fingering of fronts is known to feature tip splitting for large systems and/or large Rayleigh numbers. [12][13][14]17,20 Heat losses through the walls of the reactor have also been shown to favor tip splittings. 13,29 However, for the width L y , the small values of the Rayleigh numbers and the isothermal conditions chosen here, no tip splitting is observed.…”

“…In some regimes tip splitting, through which large fingers split into two smaller ones, are observed as well. [12][13][14][15][16] From a numerical point of view, nonlinear simulations on both a cubic scheme modeling the IAA reaction 17,18 and a kinetic scheme of order four modeling the CT reaction 19,20 show coarsening toward one single asymptotic finger featuring self-similar properties. 17,20 For large Rayleigh numbers, this coarsening trend is counterbalanced by tip splitting events.…”