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Huffman A, Shum H. Boundary-bound reactions: Pattern formation with and without hydrodynamics. Phys Rev E 2023; 108:055103. [PMID: 38115506 DOI: 10.1103/physreve.108.055103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 10/13/2023] [Indexed: 12/21/2023]
Abstract
We study chemical pattern formation in a fluid between two flat plates and the effect of such patterns on the formation of convective cells. This patterning is made possible by assuming the plates are chemically reactive or release reagents into the fluid, both of which we model as chemical fluxes. We consider this as a specific example of boundary-bound reactions. In the absence of coupling with fluid flow, we show that the two-reagent system with nonlinear reactions admits chemical instabilities equivalent to diffusion-driven Turing instabilities. In the other extreme, when chemical fluxes at the two bounding plates are constant, diffusion-driven instabilities do not occur but hydrodynamic phenomena analogous to Rayleigh-Bénard convection are possible. Assuming we can influence the chemical fluxes along the domain and select suitable reaction systems, this presents a mechanism for the control of chemical and hydrodynamic instabilities and pattern formation. We study a generic class of models and find necessary conditions for a bifurcation to pattern formation. Afterwards, we present two examples derived from the Schnakenberg-Selkov reaction. Unlike the classical Rayleigh-Bénard instability, which requires a sufficiently large unstable density gradient, a chemohydrodynamic instability based on Turing-style pattern formation can emerge from a state that is uniform in density. We also find parameter combinations that result in the formation of convective cells whether gravity acts upwards or downwards relative to the reactive plate. The wave number of the cells and the direction of the flow at regions of high/low concentration depend on the orientation, hence, different patterns can be elicited by simply inverting the device. More generally, our results suggest methods for controlling pattern formation and convection by tuning reaction parameters. As a consequence, we can drive and alter fluid flow in a chamber without mechanical pumps by influencing the chemical instabilities.
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Affiliation(s)
- Aiden Huffman
- Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada
| | - Henry Shum
- Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada
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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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Bigaj A, Budroni MA, Escala DM, Rongy L. Marangoni- vs. buoyancy-driven flows: competition for spatio-temporal oscillations in A + B → C systems. Phys Chem Chem Phys 2023; 25:11707-11716. [PMID: 37060119 DOI: 10.1039/d3cp00637a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/16/2023]
Abstract
The emergence of self-organized behaviors such as spatio-temporal oscillations is well-known for complex reactions involving nonlinear chemical or thermal feedback. Recently, it was shown that local oscillations of the chemical species concentration can be induced under isothermal batch conditions for simple bimolecular A + B → C reactions, provided they are actively coupled with hydrodynamics. When two reactants A and B, initially separated in space, react upon diffusive contact, damped spatio-temporal oscillations could develop when the surface tension increases sufficiently in the reaction zone. Additionally, if the density decreases, the coupling of both surface tension- and buoyancy-driven contributions to the flow can further sustain this oscillatory instability. Here, we investigate the opposite case of a reaction inducing a localized decrease in surface tension and an increase in density in the reacting zones. In this case, the competition arising from the two antagonistic flows is needed to create oscillatory dynamics, i.e., no oscillations are observed for pure chemically driven Marangoni flows. We study numerically these scenarios in a 2-dimensional system and show how they are controlled by the following key parameters: (i) ΔM and ΔR governing the surface tension and density variation during the reaction, respectively, (ii) the layer thickness of the system, and (iii) its lateral length. This work is a further step toward inducing and controlling chemical oscillations in simple reactions.
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Affiliation(s)
- Adam Bigaj
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université libre de Bruxelles (ULB), CP 231 - Campus Plaine, 1050 Brussels, Belgium.
| | - Marcello A Budroni
- Department of Chemistry and Pharmacy, University of Sassari, Via Vienna 2, 07100 Sassari, Italy.
| | - Darío Martín Escala
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université libre de Bruxelles (ULB), CP 231 - Campus Plaine, 1050 Brussels, Belgium.
| | - Laurence Rongy
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université libre de Bruxelles (ULB), CP 231 - Campus Plaine, 1050 Brussels, Belgium.
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4
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Budroni MA, Lemaigre L, Escala DM, Wit AD. Buoyancy-Driven Chemohydrodynamic Patterns in A + B → Oscillator Two-Layer Stratifications. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:997-1009. [PMID: 36623172 PMCID: PMC9940852 DOI: 10.1021/acs.langmuir.2c02548] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Revised: 12/13/2022] [Indexed: 06/17/2023]
Abstract
Chemohydrodynamic patterns due to the interplay of buoyancy-driven instabilities and reaction-diffusion patterns are studied experimentally in a vertical quasi-two-dimensional reactor in which two solutions A and B containing separate reactants of the oscillating Belousov-Zhabotinsky system are placed in contact along a horizontal contact line where excitable or oscillating dynamics can develop. Different types of buoyancy-driven instabilities are selectively induced in the reactive zone depending on the initial density jump between the two layers, controlled here by the bromate salt concentration. Starting from a less dense solution above a denser one, two possible differential diffusion instabilities are triggered depending on whether the fast diffusing sulfuric acid is in the upper or lower solution. Specifically, when the solution containing malonic acid and sulfuric acid is stratified above the one containing the slow-diffusing bromate salt, a diffusive layer convection (DLC) instability is observed with localized convective rolls around the interface. In that case, the reaction-diffusion wave patterns remain localized above the initial contact line, scarcely affected by the flow. If, on the contrary, sulfuric acid diffuses upward because it is initially dissolved in the lower layer, then a double-diffusion (DD) convective mode develops. This triggers fingers across the interface that mix the reactants such that oscillatory dynamics and rippled waves develop throughout the whole reactor. If the denser solution is put on top of the other one, then a fast developing Rayleigh-Taylor (RT) instability induces fast mixing of all reactants such that classical reaction-diffusion waves develop later on in the convectively mixed solutions.
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Affiliation(s)
- M. A. Budroni
- Department
of Chemical, Physical, Mathematical and Natural Sciences, University of Sassari, Via Vienna 2, 07100 Sassari, Italy
| | - L. Lemaigre
- Université
Libre de Bruxelles (ULB), Nonlinear Physical
Chemistry Unit, Faculté des Sciences, CP231, 1050 Brussels, Belgium
| | - D. M. Escala
- Université
Libre de Bruxelles (ULB), Nonlinear Physical
Chemistry Unit, Faculté des Sciences, CP231, 1050 Brussels, Belgium
| | - A. De Wit
- Université
Libre de Bruxelles (ULB), Nonlinear Physical
Chemistry Unit, Faculté des Sciences, CP231, 1050 Brussels, Belgium
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Gao Y, Paul JE, Chen M, Hong L, Chamorro LP, Sottos NR, Geubelle PH. Buoyancy-Induced Convection Driven by Frontal Polymerization. PHYSICAL REVIEW LETTERS 2023; 130:028101. [PMID: 36706389 DOI: 10.1103/physrevlett.130.028101] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Revised: 10/17/2022] [Accepted: 12/05/2022] [Indexed: 06/18/2023]
Abstract
In this Letter, we study the interaction between a self-sustaining exothermic reaction front propagating in a direction perpendicular to that of gravity and the buoyancy-driven convective flow during frontal polymerization (FP) of a low-viscosity monomer resin. As the polymerization front transforms the liquid monomer into the solid polymer, the large thermal gradients associated with the propagating front sustain a natural convection of the fluid ahead of the front. The fluid convection in turn affects the reaction-diffusion (RD) dynamics and the shape of the front. Detailed multiphysics numerical analyses and particle image velocimetry experiments reveal this coupling between natural convection and frontal polymerization. The frontal Rayleigh (Ra) number affects the magnitude of the velocity field and the inclination of the front. A higher Ra number drives instability during FP, leading to the observation of thermal-chemical patterns with tunable wavelengths and magnitudes.
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Affiliation(s)
- Y Gao
- Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, USA
- Department of Aerospace Engineering, University of Illinois, Urbana, Illinois 61801, USA
| | - J E Paul
- Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, USA
- Department of Material Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA
| | - M Chen
- Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, USA
- Department of Aerospace Engineering, University of Illinois, Urbana, Illinois 61801, USA
| | - L Hong
- Department of Mechanical Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA
| | - L P Chamorro
- Department of Mechanical Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA
| | - N R Sottos
- Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, USA
- Department of Material Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA
| | - P H Geubelle
- Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, USA
- Department of Aerospace Engineering, University of Illinois, Urbana, Illinois 61801, USA
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6
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Nguindjel ADC, de Visser PJ, Winkens M, Korevaar PA. Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics. Phys Chem Chem Phys 2022; 24:23980-24001. [PMID: 36172850 DOI: 10.1039/d2cp02542f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.
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Affiliation(s)
| | - Pieter J de Visser
- Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands.
| | - Mitch Winkens
- Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands.
| | - Peter A Korevaar
- Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands.
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Basilio Hazas M, Ziliotto F, Rolle M, Chiogna G. Linking mixing and flow topology in porous media: An experimental proof. Phys Rev E 2022; 105:035105. [PMID: 35428141 DOI: 10.1103/physreve.105.035105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2021] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.
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Affiliation(s)
- Mónica Basilio Hazas
- Chair of Hydrology and River Basin Management, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany
| | - Francesca Ziliotto
- Chair of Hydrology and River Basin Management, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany
| | - Massimo Rolle
- Department of Environmental Engineering, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | - Gabriele Chiogna
- Chair of Hydrology and River Basin Management, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany
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Budroni MA, Rossi F, Rongy L. From Transport Phenomena to Systems Chemistry: Chemohydrodynamic Oscillations in A+B→C Systems. CHEMSYSTEMSCHEM 2021. [DOI: 10.1002/syst.202100023] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Affiliation(s)
- Marcello A. Budroni
- Department of Chemistry and Pharmacy University of Sassari Via Vienna 2 Sassari 07100 Italy
| | - Federico Rossi
- Department of Physical Science, Earth and Environment University of Siena Pian dei Mantellini 44-53100 Siena SI Italy
| | - Laurence Rongy
- Nonlinear Physical Chemistry Unit Faculté des Sciences Université libre de Bruxelles (ULB) CP231, 1050 Brussels Belgium
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9
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Budroni MA, Polo A, Upadhyay V, Bigaj A, Rongy L. Chemo-hydrodynamic pulsations in simple batch A + B → C systems. J Chem Phys 2021; 154:114501. [PMID: 33752375 DOI: 10.1063/5.0042560] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Spatio-temporal oscillations can be induced under batch conditions with ubiquitous bimolecular reactions in the absence of any nonlinear chemical feedback, thanks to an active interplay between the chemical process and chemically driven hydrodynamic flows. When two reactants A and B, initially separated in space, react upon diffusive contact, they can power convective flows by inducing a localized variation of surface tension and density at the mixing interface. These flows feedback with the reaction-diffusion dynamics, bearing damped or sustained spatio-temporal oscillations of the concentrations and flow field. By means of numerical simulations, we detail the mechanism underlying these chemohydrodynamic oscillations and classify the main dynamical scenarios in the relevant space drawn by parameters ΔM and ΔR, which rule the surface tension- and buoyancy-driven contributions to convection, respectively. The reactor height is found to play a critical role in the control of the dynamics. The analysis reveals the intimate nature of these oscillatory phenomena and the hierarchy among the different phenomena at play: oscillations are essentially hydrodynamic and the chemical process features the localized trigger for Marangoni flows unstable toward oscillatory instabilities. The characteristic size of Marangoni convective rolls mainly determines the critical conditions and properties of the oscillations, which can be further tuned or suppressed by the buoyancy competition. We finally discuss the possible experimental implementation of such a class of chemo-hydrodynamic oscillator and its implications in fundamental and applied terms.
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Affiliation(s)
- Marcello A Budroni
- Department of Chemistry and Pharmacy, University of Sassari, Via Vienna 2, 07100 Sassari, Italy
| | - Alessandro Polo
- Department of Chemistry and Pharmacy, University of Sassari, Via Vienna 2, 07100 Sassari, Italy
| | - Virat Upadhyay
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université Libre de Bruxelles, CP 231 - Campus Plaine, 1050 Brussels, Belgium
| | - Adam Bigaj
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université Libre de Bruxelles, CP 231 - Campus Plaine, 1050 Brussels, Belgium
| | - Laurence Rongy
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Université Libre de Bruxelles, CP 231 - Campus Plaine, 1050 Brussels, Belgium
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10
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Budroni MA, Rossi F, Marchettini N, Wodlei F, Lo Nostro P, Rustici M. Hofmeister Effect in Self-Organized Chemical Systems. J Phys Chem B 2020; 124:9658-9667. [PMID: 32989990 DOI: 10.1021/acs.jpcb.0c06956] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
We studied the effect of spectator ions in the prototype of far-from-equilibrium self-organized chemical systems, the Belousov-Zhabotinsky (BZ) reaction. In particular, we investigated the specific ion effect of alkali metal cations, connoted for their kosmotropic and chaotropic properties. By means of combined experimental and numerical approaches, we could show a neat and robust evidence for the Hofmeister effect in this system. Spectator cations induce a marked increment of the induction period that preludes regular oscillations and decrease the oscillation amplitude following the sequence Li+ < Na+ ≪ K+ ∼ Cs+. These ions affect the system kinetics by interfering in the interaction between the oxidized form of the catalyst and the organic substrate, responsible for resetting the BZ system to pre-autocatalytic (reduced) conditions. The specific ion effect on these key reactive steps is systematically characterized and correlated with different parameters which describe the interaction of the cations with the solvent.
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Affiliation(s)
- Marcello A Budroni
- Department of Chemistry and Pharmacy, University of Sassari, Sassari (SS) 07100, Italy
| | - Federico Rossi
- Department of Earth, Environmental and Physical Sciences-DEEP Sciences, University of Siena, Siena (SI) 53100, Italy
| | - Nadia Marchettini
- Department of Earth, Environmental and Physical Sciences-DEEP Sciences, University of Siena, Siena (SI) 53100, Italy
| | - Florian Wodlei
- Department of Chemistry and Pharmacy, University of Sassari, Sassari (SS) 07100, Italy
| | - Pierandrea Lo Nostro
- Department of Chemistry, University of Florence, Sesto Fiorentino (FI) 50019, Italy
| | - Mauro Rustici
- Department of Chemistry and Pharmacy, University of Sassari, Sassari (SS) 07100, Italy
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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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