Buoyant Plumes and Vortex Rings in an Autocatalytic Chemical Reaction

Rogers, Michael C.; Morris, Stephen W.

doi:10.1103/physrevlett.95.024505

Cited by 32 publications

(43 citation statements)

References 28 publications

(46 reference statements)

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“…Indeed, several experimental and theoretical works have focused on characterizing Rayleigh-Taylor induced deformation of ascending IAA fronts in capillary tubes, 6,8,[32][33][34][35][36] in Hele-Shaw cells, 22,23,30,[36][37][38][39][40][41][42]45 and in threedimensional tanks. 31 A similar situation occurs for combustion fronts for which cold liquid fuel reactants are converted into hot gas products. 19,20 Intuitively, it is thus expected that all families of reactions for which solutal and thermal effects have the same sign and are thus reinforcing each other ͑a class that we will qualify here as "cooperative"͒, the only instability to be expected is of a Rayleigh-Taylor type appearing when the solute-heavier and cooler side of the front lies on top of the solute-lighter and hotter one in the gravity field.…”

Section: Classification Of Autocatalytic Reactionsmentioning

confidence: 99%

“…An autocatalytic reaction that has been the focus of several experimental studies on convection-driven deformation of fronts is the iodate-arsenous acid ͑IAA͒ system that features reactants that are heavier than the products such that ⌬ c Ͻ 0. 6,8,22,23,30,31 This reaction is exothermic as well ͑⌬ T Ͻ 0͒; hence, the solutal and thermal effects are cooperative for the IAA reaction. According to the model of Pojman and Epstein, 5 only simple convection is expected in that case; i.e., only IAA fronts ascending the gravity field should be unstable.…”

Section: Classification Of Autocatalytic Reactionsmentioning

confidence: 99%

“…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.…”

Section: Classification Of Autocatalytic Reactionsmentioning

confidence: 99%

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

D’Hernoncourt

Zebib

Wit

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Exothermic autocatalytic fronts traveling in the gravity field can be deformed by buoyancy-driven convection due to solutal and thermal contributions to changes in the density of the product versus the reactant solutions. We classify the possible instability mechanisms, such as Rayleigh-Bénard, Rayleigh-Taylor, and double-diffusive mechanisms known to operate in such conditions in a parameter space spanned by the corresponding solutal and thermal Rayleigh numbers. We also discuss a counterintuitive instability leading to buoyancy-driven deformation of statically stable fronts across which a solute-light and hot solution lies on top of a solute-heavy and colder one. The mechanism of this chemically driven instability lies in the coupling of a localized reaction zone and of differential diffusion of heat and mass. Dispersion curves of the various cases are analyzed. A discussion of the possible candidates of autocatalytic reactions and experimental conditions necessary to observe the various instability scenarios is presented. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2405129͔It is common knowledge that light fluids rise while heavy fluids sink in the gravity field. Buoyant convection due to a hydrodynamic Rayleigh-Taylor instability can therefore be triggered if a heavy solution lies on top of a lighter one. Rayleigh-Bénard convection appears when a fluid is heated from below. Convection can also result from double-diffusive instabilities of a statically stable density stratification if solutal and thermal effects are in competition. However, it is expected that a stratification of a solute-light and hot fluid over a solute-heavy and cold one should always be stable. Here we show that chemical reactions can change this intuitive picture and trigger convection even in cases where concentration and heat both contribute to a stable density stratification. We find that the balance between intrinsic thermal and solutal density gradients initiated by a spatially localized reaction zone and double-diffusive mechanisms are at the origin of a new convective instability of stable density stratifications the mechanism of which is explained by a displaced particle argument. We also classify the stability properties and dispersion curves to be observed for various classes of exothermic chemical fronts depending whether they ascend or descend in the gravity field and whether their solutal and thermal contributions to the density jump across the front are cooperative or antagonistic.

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Section: Classification Of Autocatalytic Reactionsmentioning

confidence: 99%

Section: Classification Of Autocatalytic Reactionsmentioning

confidence: 99%

Section: Classification Of Autocatalytic Reactionsmentioning

confidence: 99%

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

D’Hernoncourt

Zebib

Wit

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…26 Acidic chloritetetrathionate reaction fronts have a quartic reaction rate and Final catalyst concentration ͑long after passage of the chemical front͒ C 3 Small negative ratio of rate constants…”

Section: ͑6͒mentioning

confidence: 99%

Propagation velocities of chemical reaction fronts advected by Poiseuille flow

Edwards

2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Poiseuille flow between parallel plates advects chemical reaction fronts, distorting them and altering their propagation velocities. Analytical solutions of the cubic reaction-diffusion-advection equation resolve the chemical concentration for narrow gaps, wide gaps, and small-amplitude flow. Numerical solutions supply a general description for fluid flow in the direction of propagation of the chemical reaction front, and for flow in the opposite direction. Empirical relations for the velocity agree with numerical solutions to within a few percent, and agree exactly with the analytical limits. Chemical waves generally alter the mass densities of the aqueous solutions through which they propagate. These density changes can lead to buoyancy-driven convection. When bounded by parallel no-slip plates, such convection has a local velocity profile which peaks at the gap center and is zero at the walls. Such nonuniform "Poiseuille" flow distorts chemical reaction fronts and alters their velocities of propagation. The purpose of the study is to investigate these effects using the Navier-Stokes equations and the cubic reaction-diffusion-advection equation pertinent to the iodate-arsenous acid reaction. In contrast with previous assumptions, the propagation velocity is found to exceed the sum of the velocity of a planar front in a static fluid and the average flow velocity. Velocity results preclude the need for the reaction-diffusionadvection equation in future studies of nonlinear fingering.

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“…4,5 In particular, the iodate-arsenous acid reaction has exhibited deformations under Poiseuille flow, 6,7 symmetric and axisymmetric fronts in vertical tubes, 8 and upward plumes 9 driven by density differences between reacted and unreacted fluids. Recent literature on buoyancy-driven instabilities of fronts has studied autocatalytic fronts in extended Hele-Shaw cells.…”

Section: Introductionmentioning

confidence: 99%

Stability of convective patterns in reaction fronts: A comparison of three models

Vasquez

Coroian

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three different models for front propagation. We use a model based on a reaction-diffusion-advection equation coupled to the Navier-Stokes equations to account for fluid flow. A second model replaces the reaction-diffusion equation with a thin front approximation where the front speed depends on the front curvature. We also introduce a new low-dimensional model based on a finite mode truncation. This model allows a complete analysis of all stable and unstable fronts. © 2010 American Institute of Physics. ͓doi:10.1063/1.3467858͔Chemical fronts propagating in vertical cylinders exhibit flat, nonaxisymmetric, and axisymmetric fronts. The different types of fronts are determined by convection. In the case of flat fronts, there is no convection. For nonaxisymmetric fronts, fluid rises on one side and falls on the opposite side of the tube. For axisymmetric fronts, fluid rises in the middle of the tube and falls on the sides. In this work we model the transition between different fronts using a two-dimensional domain. We compared three different models of front propagation, one based on a reaction-diffusion-advection equation, the other on a front propagation equation, and finally a low-dimensional model. We study the stability of different solutions.

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Buoyant Plumes and Vortex Rings in an Autocatalytic Chemical Reaction

Cited by 32 publications

References 28 publications

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

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

Propagation velocities of chemical reaction fronts advected by Poiseuille flow

Stability of convective patterns in reaction fronts: A comparison of three models

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