Poiseuille Advection of Chemical Reaction Fronts

Edwards, Boyd F.

doi:10.1103/physrevlett.89.104501

Cited by 61 publications

(94 citation statements)

References 7 publications

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“…20,30,31 The question raised now is whether such a conclusion can be extended to the nonlinear regime as well. 54 In other words, would nonlinear dynamics such as the switch from one asymptotic self-similar single finger towards tip splittings when the dimensionless width of the domain is increased or the more effective coarsening induced by increasing the speed of the front or sharpening its width be robust with regard to three-dimensional effects? Could any new dynamics come into play?…”

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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“…3 of Ref. 8, Fig. 1 shows enough detail in the concentration profiles to reveal this front thickening, which results from the high positive curvature and correspondingly high catalyst concentrations near x = ± 1, advancing the c = 0.1 profile relative to the other profiles and thereby thickening the front.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…͑1͒. 2,3,8 These approximations, which are not made herein, imply a local front velocity U = U 0 + W that equals the sum of the velocity U 0 of a planar front propagating through a static fluid and the component W = p · V of the average fluid velocity in the direction p of propagation of the front in the y−z plane.…”

Section: Introductionmentioning

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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Poiseuille Advection of Chemical Reaction Fronts

Cited by 61 publications

References 7 publications

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

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

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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