Density fingering of an exothermic autocatalytic reaction

Bánsági, Tamás; Horváth, Dezsö; Tóth, Ágota; Yang, Jian‐Bo; Kalliadasis, Serafim; Wit, A. De

doi:10.1103/physreve.68.055301

Cited by 50 publications

(69 citation statements)

References 22 publications

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“…Moreover, in some cases, the exothermicity of the reaction cannot be neglected and the nonlinear dynamics is influenced as well by the heat released in the front. 55 Finally, from a mathematical point of view, characterization of the self-similar asymptotic profiles using nonlinear analytical techniques would be of great elegance.…”

Section: Discussionmentioning

confidence: 99%

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

Wit

2004

Physics of Fluids

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Nonlinear interactions between chemical reactions and Rayleigh-Taylor type density fingering are studied in porous media or thin Hele-Shaw cells by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a chemically reacting solute controlling the density of miscible solutions. In absence of flow, the reaction-diffusion system features stable planar fronts traveling with a given constant speed v and width w. When the reactant and product solutions have different densities, such fronts are buoyantly unstable if the heavier solution lies on top of the lighter one in the gravity field. Density fingering is then observed. We study the nonlinear dynamics of such fingering for a given model chemical system, the iodate-arsenious acid reaction. Chemical reactions profoundly affect the density fingering leading to changes in the characteristic wavelength of the pattern at early time and more rapid coarsening in the nonlinear regime. The nonlinear dynamics of the system is studied as a function of the three relevant parameters of the model, i.e., the dimensionless width of the system expressed as a Rayleigh number Ra, the Damköhler number Da, and a chemical parameter d which is a function of kinetic constants and chemical concentration, these two last parameters controlling the speed v and width w of the stable planar front. For small Ra, the asymptotic nonlinear dynamics of the fingering in the presence of chemical reactions is one single finger of stationary shape traveling with constant nonlinear speed VϾv and mixing zone WϾw. This is drastically different from pure density fingering for which fingers elongate monotonically in time. The asymptotic finger has axial and transverse averaged profiles that are self-similar in unit lengths scaled by Ra. Moreover, we find that W/Ra scales as Da Ϫ0.5 . For larger Ra, tip splittings are observed.

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Section: Discussionmentioning

confidence: 99%

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

Wit

2004

Physics of Fluids

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“…Type I dispersion curves cross the line Re(σ ) = 0 at the three wavenumbers k = 0, k 1 and k 2 such that growth rates with positive real parts occur for 0 < k 1 < k < k 2 . Such dispersion curves lead to fingers maintaining a finite wavenumber in time (Bánsági et al 2003) and long-wave instabilities are absent. Type II dispersion curves cross the line Re(σ ) = 0 at the two wavenumbers k = 0 and k c such that growth rates with positive real parts occur for 0 < k < k c .…”

Section: Linearized Equationsmentioning

confidence: 99%

Viscous fingering of a miscible reactive A + B → C interface: a linear stability analysis

et al. 2010

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When one solution of reactant A is displacing another miscible solution of reactant B, a miscible product C can be generated in the contact zone if a simple A + B → C chemical reaction takes place. Depending on the relative effect of A, B and C on the viscosity, different viscous fingering (VF) instabilities can be observed. In this context, a linear stability analysis of this reaction-diffusion-convection problem under the quasi-steady-state approximation is performed to classify the various possible instability scenarios. To do so, we determine the criteria for an instability, obtain dispersion curves both at initial contact time using an analytical implicit solution and at later times via numerical stability analysis. Along with recovering known results for non-reactive systems where the displacement of a more viscous fluid by a less viscous one leads to a VF instability, it is found that in the presence of a chemical reaction, injecting a more viscous fluid into a less viscous fluid can also lead to instabilities. This occurs when the chemical reaction leads to the build up of non-monotonic viscosity profiles. Various instability scenarios are classified in a parameter plane spanned by R b and R c representing the log-mobility ratios of the viscosities of the B and C solution respectively with respect to that of the injected solution of A. A parametric study of the influence on stability of the Damköhler number and of the time elapsed after contact of the two reactive solutions is also conducted.

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“…In contrast to similar experiments performed in capillary tubes for which only one or two convection rolls can develop, [10][11][12] experimental results in extended Hele-Shaw cells allow us to have insight into dispersion relations featuring the growth rate of the perturbations as a function of their wave number k. Such dispersion relations have been measured experimentally for the iodate-arsenious acid ͑IAA͒ reaction 4,5 as well as for the chlorite-tetrathionate ͑CT͒ reaction. [6][7][8][9] They show that a band of unstable modes exists ranging typically from kϭ0 to a critical value k c . Recently, Horváth et al have analyzed experimentally the influence of a tilt of the Hele-Shaw cell with regard to the vertical on the dispersion relation for the CT reaction.…”

Section: Introductionmentioning

confidence: 99%

“…1 Recent experiments have analyzed such an instability in Hele-Shaw cells, [2][3][4][5][6][7][8][9] two planar glass plates of large lateral extent separated by a thin gap width. In such a geometry, the convective instability of the front induced by the unfavorable density stratification leads to a fingering of the front characterized by several wavelengths.…”

Section: Introductionmentioning

confidence: 99%

“…Further experiments demonstrate that, as the CT reaction is exothermic, an increase of the gap also leads to more pronounced heat effects. 7,8 On the basis of Darcy's law coupled to an evolution equation for both the concentration and the temperature, it has been shown theoretically that heat effects can qualitatively change the characteristics of the dispersion curves. 8,16 This enlightens the fact that, even in very thin Hele-Shaw cells for which Darcy's law is valid, the coupling between solutal and thermal effects can affect the nature of dispersion curves.…”

Section: Introductionmentioning

confidence: 99%

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Dispersion relations for the convective instability of an acidity front in Hele-Shaw cells

Vasquez

Wit

2004

The Journal of Chemical Physics

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Autocatalytic chemical fronts of the chlorite-tetrathionate ͑CT͒ reaction become buoyantly unstable when they travel downwards in the gravity field because they imply an unfavorable density stratification of heavier products on top of lighter reactants. When such a density fingering instability occurs in extended Hele-Shaw cells, several fingers appear at onset which can be characterized by dispersion relations giving the growth rate of the perturbations as a function of their wave number. We analyze here theoretically such dispersion curves comparing the results for various models obtained by coupling Darcy's law or Brinkman's equation to either a one-variable reaction-diffusion model for the CT reaction or an eikonal equation. Our theoretical results are compared to recent experimental data.

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Density fingering of an exothermic autocatalytic reaction

Cited by 50 publications

References 22 publications

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

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

Viscous fingering of a miscible reactive A + B → C interface: a linear stability analysis

Dispersion relations for the convective instability of an acidity front in Hele-Shaw cells

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