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Kabbadj S, Rongy L, De Wit A. Effect of variable solubility on reactive dissolution in partially miscible systems. Phys Rev E 2023; 107:065109. [PMID: 37464620 DOI: 10.1103/physreve.107.065109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 06/07/2023] [Indexed: 07/20/2023]
Abstract
When two partially miscible systems are put in contact, one phase, A, can dissolve into the other one with a given solubility. Chemical reactions in the host phase can impact this dissolution by consuming A and by generating products that impact the solubility of A. Here, we study theoretically the optimal conditions for transfer of a reactant A in a host phase containing a species B when a bimolecular A + B → C reaction generates a product C that linearly decreases the solubility of A. We have quantified numerically the influence of this variable solubility on the reaction-diffusion (RD) concentration profiles of all species in the host phase, on the temporal evolution of the position of the reaction front, and on the flux of A through the interface. We have also computed the analytical asymptotic concentration profiles, solutions at long times of the RD governing equations. For a fixed negative effect of C on the solubility of A, an increase in the initial concentration of reactant B or an increase in the diffusion rate of species B and C results in a larger flux of A and hence a larger amount of A dissolved in the host solution at a given time. However, when the influence of C on the solubility increases, the mass transfer decreases. Our results help understand to what extent a chemical reaction can optimize the reactive transfer of a solute to a host phase with application to, among other things, the geological sequestration of carbon dioxide in an aquifer.
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Affiliation(s)
- S Kabbadj
- Nonlinear Physical Chemistry Unit, Université libre de Bruxelles, CP231, Boulevard du Triomphe, 1050 Bruxelles, Belgium
| | - L Rongy
- Nonlinear Physical Chemistry Unit, Université libre de Bruxelles, CP231, Boulevard du Triomphe, 1050 Bruxelles, Belgium
| | - A De Wit
- Nonlinear Physical Chemistry Unit, Université libre de Bruxelles, CP231, Boulevard du Triomphe, 1050 Bruxelles, Belgium
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2
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Tiani R, Rongy L. Marangoni-driven nonlinear dynamics of bimolecular frontal systems: a general classification for equal diffusion coefficients. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220080. [PMID: 36842981 DOI: 10.1098/rsta.2022.0080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2022] [Accepted: 11/14/2022] [Indexed: 06/18/2023]
Abstract
When bimolecular fronts form in solutions, their dynamics is likely to be affected by chemically driven convection such as buoyancy- and Marangoni-driven flows. It is known that front dynamics in the presence of buoyancy-driven convection can be predicted solely on the basis of the one-dimensional reaction-diffusion concentration profiles but that those predictions fail for Marangoni-driven convection. With a two-dimensional reaction-diffusion-Marangoni convection model, we analyze here convective effects on the time scalings of the front properties, together with the influence of reaction reversibility and of the ratio of initial reactants' concentrations on the front dynamics. The effect of buoyancy forces is here neglected by assuming the reactive system to be in zero-gravity condition and/or the solution density to be spatially homogenous. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.
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Affiliation(s)
- R Tiani
- Nonlinear Physical Chemistry Unit, Université libre de Bruxelles (ULB), Faculté des Sciences, CP231, 1050 Brussels, Belgium
| | - L Rongy
- Nonlinear Physical Chemistry Unit, Université libre de Bruxelles (ULB), Faculté des Sciences, CP231, 1050 Brussels, Belgium
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3
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Stergiou Y, Hauser MJ, Comolli A, Brau F, De Wit A, Schuszter G, Papp P, Horváth D, Roux C, Pimienta V, Eckert K, Schwarzenberger K. Effects of gravity modulation on the dynamics of a radial A+B→C reaction front. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.117703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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4
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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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5
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Loodts V, Knaepen B, Rongy L, De Wit A. Enhanced steady-state dissolution flux in reactive convective dissolution. Phys Chem Chem Phys 2017; 19:18565-18579. [PMID: 28686243 DOI: 10.1039/c7cp01372h] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Chemical reactions can accelerate, slow down or even be at the very origin of the development of dissolution-driven convection in partially miscible stratifications when they impact the density profile in the host fluid phase. We numerically analyze the dynamics of this reactive convective dissolution in the fully developed non-linear regime for a phase A dissolving into a host layer containing a dissolved reactant B. We show for a general A + B → C reaction in solution, that the dynamics vary with the Rayleigh numbers of the chemical species, i.e. with the nature of the chemicals in the host phase. Depending on whether the reaction slows down, accelerates or is at the origin of the development of convection, the spatial distributions of species A, B or C, the dissolution flux and the reaction rate are different. We show that chemical reactions can enhance the steady-state flux as they consume A and can induce more intense convection than in the non-reactive case. This result is important in the context of CO2 geological sequestration where quantifying the storage rate of CO2 dissolving into the host oil or aqueous phase is crucial to assess the efficiency and the safety of the project.
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Affiliation(s)
- V Loodts
- Université libre de Bruxelles (ULB), Faculté des Sciences, Nonlinear Physical Chemistry Unit, CP231, 1050 Brussels, Belgium.
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6
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Budroni MA, Thomas C, De Wit A. Chemical control of dissolution-driven convection in partially miscible systems: nonlinear simulations and experiments. Phys Chem Chem Phys 2017; 19:7936-7946. [DOI: 10.1039/c6cp08434f] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Numerical simulations combined with experimental results from two laboratory-scale model systems show how to control convective dissolution by chemical reactions.
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Affiliation(s)
- M. A. Budroni
- Université libre de Bruxelles (ULB)
- Nonlinear Physical Chemistry Unit
- Faculté des Sciences
- CP231
- 1050 Brussels
| | - C. Thomas
- Université libre de Bruxelles (ULB)
- Nonlinear Physical Chemistry Unit
- Faculté des Sciences
- CP231
- 1050 Brussels
| | - A. De Wit
- Université libre de Bruxelles (ULB)
- Nonlinear Physical Chemistry Unit
- Faculté des Sciences
- CP231
- 1050 Brussels
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De Wit A. Chemo-hydrodynamic patterns in porous media. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2016; 374:rsta.2015.0419. [PMID: 27597788 PMCID: PMC5014293 DOI: 10.1098/rsta.2015.0419] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 07/24/2016] [Indexed: 05/07/2023]
Abstract
Chemical reactions can interplay with hydrodynamic flows to generate chemo-hydrodynamic instabilities affecting the spatio-temporal evolution of the concentration of the chemicals. We review here such instabilities for porous media flows. We describe the influence of chemical reactions on viscous fingering, buoyancy-driven fingering in miscible systems, convective dissolution as well as precipitation patterns. Implications for environmental systems are discussed.This article is part of the themed issue 'Energy and the subsurface'.
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Affiliation(s)
- A De Wit
- Nonlinear Physical Chemistry Unit, Université Libre de Bruxelles, CP 231, 1050 Brussels, Belgium
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Loodts V, Trevelyan PMJ, Rongy L, De Wit A. Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification. Phys Rev E 2016; 94:043115. [PMID: 27841615 DOI: 10.1103/physreve.94.043115] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Indexed: 06/06/2023]
Abstract
Various spatial density profiles can develop in partially miscible stratifications when a phase A dissolves with a finite solubility into a host phase containing a dissolved reactant B. We investigate theoretically the impact of an A+B→C reaction on such density profiles in the host phase and classify them in a parameter space spanned by the ratios of relative contributions to density and diffusion coefficients of the chemical species. While the density profile is either monotonically increasing or decreasing in the nonreactive case, reactions combined with differential diffusivity can create eight different types of density profiles featuring up to two extrema in density, at the reaction front or below it. We use this framework to predict various possible hydrodynamic instability scenarios inducing buoyancy-driven convection around such reaction fronts when they propagate parallel to the gravity field.
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Affiliation(s)
- V Loodts
- Université libre de Bruxelles (ULB), Faculté des Sciences, Nonlinear Physical Chemistry Unit, Campus de la Plaine - Boulevard du Triomphe CP231 1050 Bruxelles, Belgium
| | - P M J Trevelyan
- Division of Mathematics and Statistics, University of South Wales, Pontypridd CF37 1DL, United Kingdom
| | - L Rongy
- Université libre de Bruxelles (ULB), Faculté des Sciences, Nonlinear Physical Chemistry Unit, Campus de la Plaine - Boulevard du Triomphe CP231 1050 Bruxelles, Belgium
| | - A De Wit
- Université libre de Bruxelles (ULB), Faculté des Sciences, Nonlinear Physical Chemistry Unit, Campus de la Plaine - Boulevard du Triomphe CP231 1050 Bruxelles, Belgium
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Tiani R, Rongy L. Influence of Marangoni flows on the dynamics of isothermal A + B → C reaction fronts. J Chem Phys 2016; 145:124701. [DOI: 10.1063/1.4962580] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. Tiani
- Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
| | - L. Rongy
- Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
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Loodts V, Rongy L, De Wit A. Chemical control of dissolution-driven convection in partially miscible systems: theoretical classification. Phys Chem Chem Phys 2015; 17:29814-23. [PMID: 26486608 DOI: 10.1039/c5cp03082j] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Dissolution-driven convection occurs in the host phase of a partially miscible system when a buoyantly unstable density stratification develops upon dissolution. Reactions can impact such convection by changing the composition and thus the density of the host phase. Here we study the influence of A + B → C reactions on such convective dissolution when A is the dissolving species and B a reactant initially in solution in the host phase. We perform a linear stability analysis of related reaction-diffusion density profiles to compare the growth rate of the instability in the reactive case to its non reactive counterpart when all species diffuse at the same rate. We classify the stabilizing or destabilizing influence of reactions on the buoyancy-driven convection in a parameter space spanned by the solutal Rayleigh numbers RA,B,C of chemical species A, B, C and by the ratio β of initial concentrations of the reactants. For RA > 0, the non reactive dissolution of A in the host phase is buoyantly unstable. In that case, we show that the reaction is enhancing convection provided C is sufficiently denser than B. Increasing the ratio β of initial reactant concentrations increases the effect of chemistry but does not significantly impact the stabilizing/destabilizing classification. When the non reactive case is buoyantly stable (RA≤ 0), reactions can create in time an unstable density stratification and trigger convection if RC > RB. Our theoretical approach allows classifying previous results in a unifying picture and developing strategies for the chemical control of convective dissolution.
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Affiliation(s)
- V Loodts
- Université libre de Bruxelles (ULB), Faculté des Sciences, Nonlinear Physical Chemistry Unit, CP231, 1050 Brussels, Belgium.
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Trevelyan PMJ, Almarcha C, De Wit A. Buoyancy-driven instabilities around miscible A+B→C reaction fronts: a general classification. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023001. [PMID: 25768591 DOI: 10.1103/physreve.91.023001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Indexed: 05/07/2023]
Abstract
Upon contact between miscible solutions of reactants A and B along a horizontal interface in the gravity field, various buoyancy-driven instabilities can develop when an A+B→C reaction takes place and the density varies with the concentrations of the various chemicals. To classify the possible convective instability scenarios, we analyze the spatial dependence of the large time asymptotic density profiles as a function of the key parameters of the problem, which are the ratios of diffusion coefficients and of solutal expansion coefficients of species A, B, and C. We find that 62 different density profiles can develop in the reactive problem, whereas only 6 of them can be obtained in the nonreactive one.
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Affiliation(s)
- P M J Trevelyan
- Nonlinear Physical Chemistry Unit, Center for Nonlinear Phenomena and Complex Systems, Faculté des Sciences, Université libre de Bruxelles (ULB), CP 231, 1050 Brussels, Belgium
| | - C Almarcha
- Nonlinear Physical Chemistry Unit, Center for Nonlinear Phenomena and Complex Systems, Faculté des Sciences, Université libre de Bruxelles (ULB), CP 231, 1050 Brussels, Belgium
| | - A De Wit
- Nonlinear Physical Chemistry Unit, Center for Nonlinear Phenomena and Complex Systems, Faculté des Sciences, Université libre de Bruxelles (ULB), CP 231, 1050 Brussels, Belgium
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12
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Loodts V, Thomas C, Rongy L, De Wit A. Control of convective dissolution by chemical reactions: general classification and application to CO(2) dissolution in reactive aqueous solutions. PHYSICAL REVIEW LETTERS 2014; 113:114501. [PMID: 25259984 DOI: 10.1103/physrevlett.113.114501] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2014] [Indexed: 05/23/2023]
Abstract
In partially miscible two-layer systems within a gravity field, buoyancy-driven convective motions can appear when one phase dissolves with a finite solubility into the other one. We investigate the influence of chemical reactions on such convective dissolution by a linear stability analysis of a reaction-diffusion-convection model. We show theoretically that a chemical reaction can either enhance or decrease the onset time of the convection, depending on the type of density profile building up in time in the reactive solution. We classify the stabilizing and destabilizing scenarios in a parameter space spanned by the solutal Rayleigh numbers. As an example, we experimentally demonstrate the possibility to enhance the convective dissolution of gaseous CO_{2} in aqueous solutions by a classical acid-base reaction.
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Affiliation(s)
- V Loodts
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
| | - C Thomas
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
| | - L Rongy
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
| | - A De Wit
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
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13
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Kim MC. Effect of the irreversible A+B →C reaction on the onset and the growth of the buoyancy-driven instability in a porous medium. Chem Eng Sci 2014. [DOI: 10.1016/j.ces.2014.03.017] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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14
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Almarcha C, Trevelyan PMJ, Grosfils P, De Wit A. Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:033009. [PMID: 24125346 DOI: 10.1103/physreve.88.033009] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2013] [Indexed: 06/02/2023]
Abstract
A buoyancy-driven hydrodynamic instability appearing when an aqueous acid solution of HCl overlies a denser alkaline aqueous solution of NaOH in a vertically oriented Hele-Shaw cell is studied both experimentally and theoretically. The peculiarity of this reactive convection pattern is its asymmetry with regard to the initial contact line between the two solutions as convective plumes develop in the acidic solution only. We investigate here by a linear stability analysis (LSA) of a reaction-diffusion-convection model of a simple A+B→C reaction the relative role of solutal versus thermal effects in the origin and location of this instability. We show that heat effects are much weaker than concentration-related ones such that the heat of reaction only plays a minor role on the dynamics. Computation of density profiles and of the stability analysis eigenfunctions confirm that the convective motions result from a diffusive layer convection mechanism whereby a locally unstable density stratification develops in the upper acidic layer because of the difference in the diffusion coefficients of the chemical species. The growth rate and wavelength of the pattern are determined experimentally as a function of the Brinkman parameter of the problem and compare favorably with the theoretical predictions of both LSA and nonlinear simulations.
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Affiliation(s)
- C Almarcha
- Nonlinear Physical Chemistry Unit, CP231, Faculté des Sciences, Université Libre de Bruxelles (ULB), 1050 Brussels, Belgium and Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, F-13384, Marseille, France
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15
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Eckert K, Rongy L, Wit AD. A + B → C reaction fronts in Hele-Shaw cells under modulated gravitational acceleration. Phys Chem Chem Phys 2012; 14:7337-45. [DOI: 10.1039/c2cp40132k] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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16
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Almarcha C, R'Honi Y, De Decker Y, Trevelyan PMJ, Eckert K, De Wit A. Convective mixing induced by acid-base reactions. J Phys Chem B 2011; 115:9739-44. [PMID: 21793552 DOI: 10.1021/jp202201e] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
When two miscible solutions, each containing a reactive species, are put in contact in the gravity field, local variations in the density due to the reaction can induce convective motion and mixing. We characterize here both experimentally and theoretically such buoyancy-driven instabilities induced by the neutralization of a strong acid by a strong base in aqueous solutions. The diverse patterns obtained are shown to depend on the type of reactants used and on their relative concentrations. They have their origin in a combination of classical hydrodynamic instabilities including differential diffusion of the solutes involved while temperature effects only play a marginal role.
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Affiliation(s)
- C Almarcha
- IRPHE, UMR 6594, CNRS, Université d'Aix-Marseille 1, 49, rue F. Joliot Curie, 13384 Marseille, France.
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Kuster S, Riolfo LA, Zalts A, El Hasi C, Almarcha C, Trevelyan PMJ, De Wit A, D'Onofrio A. Differential diffusion effects on buoyancy-driven instabilities of acid–base fronts: the case of a color indicator. Phys Chem Chem Phys 2011; 13:17295-303. [DOI: 10.1039/c1cp21185d] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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