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Dil’man VV, Musabekova LM, Brener AM, Kalbayeva AT, Kurakbayeva SD. Dynamics of Mobile Concentration Fronts in Gas–Liquid Reaction Systems: Analysis and Numerical Experiment. THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING 2020. [DOI: 10.1134/s0040579520020025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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2
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Mukherjee S, Paul MR. Propagating fronts in fluids with solutal feedback. Phys Rev E 2020; 101:032214. [PMID: 32290010 DOI: 10.1103/physreve.101.032214] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Accepted: 02/28/2020] [Indexed: 11/07/2022]
Abstract
We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counterrotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit square-root scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counterrotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Last, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.
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Affiliation(s)
- S Mukherjee
- Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - M R Paul
- Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
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Bába P, Rongy L, De Wit A, Hauser MJB, Tóth Á, Horváth D. Interaction of Pure Marangoni Convection with a Propagating Reactive Interface under Microgravity. PHYSICAL REVIEW LETTERS 2018; 121:024501. [PMID: 30085731 DOI: 10.1103/physrevlett.121.024501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2017] [Revised: 01/30/2018] [Indexed: 06/08/2023]
Abstract
A reactive interface in the form of an autocatalytic reaction front propagating in a bulk phase can generate a dynamic contact line upon reaching the free surface when a surface tension gradient builds up due to the change in chemical composition. Experiments in microgravity evidence the existence of a self-organized autonomous and localized coupling of a pure Marangoni flow along the surface with the reaction in the bulk. This dynamics results from the advancement of the contact line at the surface that acts as a moving source of the reaction, leading to the reorientation of the front propagation. Microgravity conditions allow one to isolate the transition regime during which the surface propagation is enhanced, whereas diffusion remains the main mode of transport in the bulk with negligible convective mixing, a regime typically concealed on Earth because of buoyancy-driven convection.
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Affiliation(s)
- P Bába
- Department of Physical Chemistry and Materials Science, University of Szeged, Aradi vértanúk tere 1, Szeged H-6720, Hungary
| | - L Rongy
- Nonlinear Physical Chemistry Unit, Université libre de Bruxelles (ULB), Campus Plaine, C.P. 231, 1050 Brussels, Belgium
| | - A De Wit
- Nonlinear Physical Chemistry Unit, Université libre de Bruxelles (ULB), Campus Plaine, C.P. 231, 1050 Brussels, Belgium
| | - M J B Hauser
- Institute of Biometry and Medical Informatics, Otto von Guericke Universität Magdeburg, Leipziger Straße 44, D-39120 Magdeburg, Germany and Institute of Physics, Otto von Guericke-Universität Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
| | - Á Tóth
- Department of Physical Chemistry and Materials Science, University of Szeged, Aradi vértanúk tere 1, Szeged H-6720, Hungary
| | - D Horváth
- Department of Applied and Environmental Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
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Tiani R, De Wit A, Rongy L. Surface tension- and buoyancy-driven flows across horizontally propagating chemical fronts. Adv Colloid Interface Sci 2018; 255:76-83. [PMID: 28826815 DOI: 10.1016/j.cis.2017.07.020] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2017] [Revised: 07/07/2017] [Accepted: 07/17/2017] [Indexed: 11/17/2022]
Abstract
Chemical reactions can interplay with hydrodynamic flows to generate various complex phenomena. Because of their relevance in many research areas, chemically-induced hydrodynamic flows have attracted increasing attention in the last decades. In this context, we propose to give a review of the past and recent theoretical and experimental works which have considered the interaction of such flows with chemical fronts, i.e. reactive interfaces, formed between miscible solutions. We focus in particular on the influence of surface tension- (Marangoni) and buoyancy-driven flows on the dynamics of chemical fronts propagating horizontally in the gravity field.
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Affiliation(s)
- R Tiani
- Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, Brussels 1050, Belgium.
| | - A De Wit
- Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, Brussels 1050, Belgium
| | - L Rongy
- Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, Brussels 1050, Belgium
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Liu Y, Zhou W, Zheng T, Zhao Y, Gao Q, Pan C, Horváth AK. Convection-Induced Fingering Fronts in the Chlorite-Trithionate Reaction. J Phys Chem A 2016; 120:2514-20. [PMID: 27059304 DOI: 10.1021/acs.jpca.6b01192] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Based upon a former study, the chlorite-trithionate reaction can avoid the side reactions arising from the well-known alkaline decomposition of polythionates, making it a suitable candidate for investigating spatial front instabilities in a reaction-diffusion-convection system. In this work, the chlorite-trithionate reaction was investigated in a Hele-Shaw cell, in which fingering patterns were observed over a wide range of reactant concentrations. A significant density increment crossing the propagating front indicates that the fingering pattern is generated as a consequence of the buoyancy-driven instability due to the density changes of solute when the gap thickness is less than 4 mm. The velocity of the steepest descent in the propagating front depends almost linearly on the gap thickness but displays a saturation-like profile on the trithionate concentration as well as a maximum on the chlorite concentration. Numerical simulation using the Stokes-Brinkman Equation coupled to the reaction-diffusion processes, including hydrogen ion autocatalysis and consumption, reproduces the observed fingering fronts.
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Affiliation(s)
- Yang Liu
- College of Chemical Engineering, China University of Mining and Technology , Xuzhou 221116, People's Republic of China
| | - Wenxiu Zhou
- College of Chemical Engineering, China University of Mining and Technology , Xuzhou 221116, People's Republic of China
| | - Ting Zheng
- College of Chemical Engineering, China University of Mining and Technology , Xuzhou 221116, People's Republic of China
| | - Yuemin Zhao
- College of Chemical Engineering, China University of Mining and Technology , Xuzhou 221116, People's Republic of China
| | - Qingyu Gao
- College of Chemical Engineering, China University of Mining and Technology , Xuzhou 221116, People's Republic of China
| | - Changwei Pan
- College of Chemical Engineering, China University of Mining and Technology , Xuzhou 221116, People's Republic of China
| | - Attila K Horváth
- Department of Inorganic Chemistry, University of Pécs , Ifjúság útja 6., H-7624 Pécs, Hungary
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Gueudré T, Dubey AK, Talon L, Rosso A. Strong pinning of propagation fronts in adverse flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:041004. [PMID: 24827180 DOI: 10.1103/physreve.89.041004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2014] [Indexed: 06/03/2023]
Abstract
Reaction fronts evolving in a porous medium exhibit a rich dynamical behavior. In the presence of an adverse flow, experiments show that the front slows down and eventually gets pinned, displaying a particular sawtooth shape. Extensive numerical simulations of the hydrodynamic equations confirm the experimental observations. Here we propose a stylized model, predicting two possible outcomes of the experiments for large adverse flow: either the front develops a sawtooth shape or it acquires a complicated structure with islands and overhangs. A simple criterion allows one to distinguish between the two scenarios and its validity is reproduced by direct hydrodynamical simulations. Our model gives a better understanding of the transition and is relevant in a variety of domains, when the pinning regime is strong and only relies on a small number of sites.
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Affiliation(s)
- Thomas Gueudré
- CNRS-LPT, Ecole Normale Supérieure, 75231 Cedex 05 Paris, France
| | | | - Laurent Talon
- Université Paris-Sud, CNRS, Laboratoire FAST, UMR 7608, Orsay F-91405, France
| | - Alberto Rosso
- Université Paris-Sud, CNRS, LPTMS, UMR 8626, Orsay F-91405, France
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Horváth D, Budroni MA, Bába P, Rongy L, De Wit A, Eckert K, Hauser MJB, Tóth Á. Convective dynamics of traveling autocatalytic fronts in a modulated gravity field. Phys Chem Chem Phys 2014; 16:26279-87. [DOI: 10.1039/c4cp02480j] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Modulation of the gravity field, spanning from the hyper-gravity to micro-gravity of a parabolic flight, reveals the contribution of Marangoni flow in a propagating reaction front with an open air–liquid interface.
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Affiliation(s)
- Dezső Horváth
- Department of Physical Chemistry and Materials Science
- University of Szeged
- Szeged, Hungary
- Department of Applied and Environmental Chemistry
- University of Szeged
| | - Marcello A. Budroni
- Nonlinear Physical Chemistry Unit
- CP 231
- Faculté des Sciences
- Université libre de Bruxelles (ULB)
- 1050 Brussels, Belgium
| | - Péter Bába
- Department of Physical Chemistry and Materials Science
- University of Szeged
- Szeged, Hungary
| | - Laurence Rongy
- Nonlinear Physical Chemistry Unit
- CP 231
- Faculté des Sciences
- Université libre de Bruxelles (ULB)
- 1050 Brussels, Belgium
| | - Anne De Wit
- Nonlinear Physical Chemistry Unit
- CP 231
- Faculté des Sciences
- Université libre de Bruxelles (ULB)
- 1050 Brussels, Belgium
| | - Kerstin Eckert
- Institute of Fluid Mechanics
- Technische Universität Dresden
- D-01062 Dresden, Germany
| | - Marcus J. B. Hauser
- Biophysics Group
- Otto-von-Guericke-Universität Magdeburg
- D-39106 Magdeburg, Germany
| | - Ágota Tóth
- Department of Physical Chemistry and Materials Science
- University of Szeged
- Szeged, Hungary
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Sebestíková L. Relation between shape of liquid-gas interface and evolution of buoyantly unstable three-dimensional chemical fronts. Phys Rev E 2013; 88:033023. [PMID: 24125360 DOI: 10.1103/physreve.88.033023] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2012] [Revised: 08/08/2013] [Indexed: 11/07/2022]
Abstract
Buoyantly unstable 3D chemical fronts were seen traveling through an iodate-arsenous acid reaction solution. The experiments were performed in channel reactors with rectangular cross sections, where the top of the reaction solution was in contact with air. A concave or convex meniscus was pinned to reactor lateral walls. Influence of the meniscus shape on front development was investigated. For the concave meniscus, an asymptotic shape of fronts holding negative curvature was observed. On the other hand, fronts propagating in the solution with the convex meniscus kept only positive curvature. Those fronts were also a bit faster than fronts propagating in the solution with the concave meniscus. A relation between the meniscus shape, flow distribution, velocity, and shape is discussed.
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Affiliation(s)
- L Sebestíková
- Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, Pod Patankou 30/5, 16612 Praha 6, Czech Republic
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Saha S, Salin D, Talon L. Low Reynolds number suspension gravity currents. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:85. [PMID: 23933985 DOI: 10.1140/epje/i2013-13085-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2013] [Revised: 06/03/2013] [Accepted: 06/18/2013] [Indexed: 06/02/2023]
Abstract
The extension of a gravity current in a lock-exchange problem, proceeds as square root of time in the viscous-buoyancy phase, where there is a balance between gravitational and viscous forces. In the presence of particles however, this scenario is drastically altered, because sedimentation reduces the motive gravitational force and introduces a finite distance and time at which the gravity current halts. We investigate the spreading of low Reynolds number suspension gravity currents using a novel approach based on the Lattice-Boltzmann (LB) method. The suspension is modeled as a continuous medium with a concentration-dependent viscosity. The settling of particles is simulated using a drift flux function approach that enables us to capture sudden discontinuities in particle concentration that travel as kinematic shock waves. Thereafter a numerical investigation of lock-exchange flows between pure fluids of unequal viscosity, reveals the existence of wall layers which reduce the spreading rate substantially compared to the lubrication theory prediction. In suspension gravity currents, we observe that the settling of particles leads to the formation of two additional fronts: a horizontal front near the top that descends vertically and a sediment layer at the bottom which aggrandises due to deposition of particles. Three phases are identified in the spreading process: the final corresponding to the mutual approach of the two horizontal fronts while the laterally advancing front halts indicating that the suspension current stops even before all the particles have settled. The first two regimes represent a constant and a decreasing spreading rate respectively. Finally we conduct experiments to substantiate the conclusions of our numerical and theoretical investigation.
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Affiliation(s)
- Sandeep Saha
- UPMC Univ Paris 06, Univ Paris-Sud, CNRS, F-91405, Paris, France
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Atis S, Saha S, Auradou H, Martin J, Rakotomalala N, Talon L, Salin D. CHEMO-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. CHAOS (WOODBURY, N.Y.) 2012; 22:037108. [PMID: 23020499 DOI: 10.1063/1.4734489] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow experiments around a single obstacle were used to delineate the range of steady state behavior. A model using the "eikonal thin front limit" explains the observed steady states.
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Affiliation(s)
- S Atis
- Laboratoire Fluides Automatique et Systèmes Thermiques, Universités P. et M. Curie and Paris Sud, C.N.R.S. (UMR7608), Bâtiment 502, Campus Universitaire, 91405 Orsay Cedex, France
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Schuszter G, Horváth D, Tóth Á. Convective instabilities of chemical fronts in close-packed porous media. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.07.038] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Pópity-Tóth É, Horváth D, Tóth Á. Horizontally propagating three-dimensional chemo-hydrodynamic patterns in the chlorite-tetrathionate reaction. CHAOS (WOODBURY, N.Y.) 2012; 22:037105. [PMID: 23020496 DOI: 10.1063/1.4740464] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Planar reaction fronts resulting from the coupling of exothermic autocatalytic reactions and transport processes can be deformed by convection in the presence of gravity field. We have experimentally investigated how buoyancy affects the spatiotemporal pattern formation at various solution thicknesses in three-dimensional medium. In the chlorite-tetrathionate reaction, a stable structure propagating horizontally with constant velocity and geometry develops when appropriately thick solutions are studied. Both the horizontal and the vertical projections of the resulting three-dimensional structures are quantitatively characterized: the smooth leading edge of the front is independent of the solution thickness and the structured trailing edge ends in a center cusp with a constant angle.
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Affiliation(s)
- Éva Pópity-Tóth
- Department of Physical Chemistry and Materials Science, University of Szeged, Aradi vértanúk tere 1., Szeged H-6720, Hungary
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Rongy L, Assemat P, De Wit A. Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers. CHAOS (WOODBURY, N.Y.) 2012; 22:037106. [PMID: 23020497 DOI: 10.1063/1.4747711] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Gradients of concentration and temperature across exothermic chemical fronts propagating in free-surface solution layers can initiate Marangoni-driven convection. We investigate here the dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and Marangoni-driven flows. To this end, we numerically integrate the incompressible Navier-Stokes equations coupled through the tangential stress balance to evolution equations for the concentration of the autocatalytic product and for the temperature. A solutal and a thermal Marangoni numbers measure the coupling between reaction-diffusion processes and surface-driven convection. In the case of an isothermal system, the asymptotic dynamics is characterized by a steady fluid vortex traveling at a constant speed with the front, deforming and accelerating it [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)]. We analyze here the influence of the reaction exothermicity on the dynamics of the system in both cases of cooperative and competitive solutal and thermal effects. We show that exothermic fronts can exhibit new unsteady spatio-temporal dynamics when the solutal and thermal effects are antagonistic. The influence of the solutal and thermal Marangoni numbers, of the Lewis number (ratio of thermal diffusivity over molecular diffusivity), and of the height of the liquid layer on the spatio-temporal front evolution are investigated.
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Affiliation(s)
- L Rongy
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), CP 231, 1050 Brussels, Belgium
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Budroni MA, Rongy L, De Wit A. Dynamics due to combined buoyancy- and Marangoni-driven convective flows around autocatalytic fronts. Phys Chem Chem Phys 2012; 14:14619-29. [DOI: 10.1039/c2cp41962a] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Pópity-Tóth É, Horváth D, Tóth Á. The dependence of scaling law on stoichiometry for horizontally propagating vertical chemical fronts. J Chem Phys 2011; 135:074506. [DOI: 10.1063/1.3626217] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Malham IB, Jarrige N, Martin J, Rakotomalala N, Talon L, Salin D. Lock-exchange experiments with an autocatalytic reaction front. J Chem Phys 2010; 133:244505. [DOI: 10.1063/1.3507899] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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