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Schmidt PS, Wu W, Rausch MH, Fröba AP. Fick diffusion coefficients probed by the shadowgraph method considering confinement and advection. J Chem Phys 2023; 158:094502. [PMID: 36889943 DOI: 10.1063/5.0143400] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2023] Open
Abstract
The present work contributes to the development of the shadowgraph method for its routine application for an accurate determination of the Fick diffusion coefficient D11 of binary fluid mixtures. In this context, measurement and data evaluation strategies for thermodiffusion experiments where confinement and advection are potentially present are elaborated by studying two binary liquid mixtures with positive and negative Soret coefficients, i.e., 1,2,3,4-tetrahydronaphthalene/n-dodecane and acetone/cyclohexane. For obtaining accurate D11 data, the dynamics of non-equilibrium fluctuations in concentration is analyzed considering recent theory by data evaluation procedures that are demonstrated to be suitable for different experimental configurations.
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Affiliation(s)
- P S Schmidt
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
| | - W Wu
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
| | - M H Rausch
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
| | - A P Fröba
- Institute of Advanced Optical Technologies - Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 8, 91052 Erlangen, Germany
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2
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García-Fernández L, Bataller H, Fruton P, Giraudet C, Vailati A, Croccolo F. Stabilized convection in a ternary mixture with two Soret coefficients of opposite sign. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:52. [PMID: 35633426 PMCID: PMC9148296 DOI: 10.1140/epje/s10189-022-00202-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Accepted: 04/27/2022] [Indexed: 06/15/2023]
Abstract
We performed ground-based experiments on the sample polystyrene-toluene-cyclohexane in order to complement the experimental activities in microgravity conditions related to the ESA projects DCMIX4 and Giant Fluctuations. After applying a stabilizing thermal gradient by heating from above a layer of the fluid mixture, we studied over many hours the density variations in the bidimensional horizontal field by means of a Shadowgraph optical setup. The resulting images evidence the appearance of convective instability after a diffusive time associated with the binary molecular solvent consisting of toluene and cyclohexane, confirming the negative sign of the Soret coefficient of this mixture. After a larger diffusive time related to mass diffusion of the polystyrene in the binary solvent, convection was suppressed by the increasing stabilizing density gradient originated by the Soret-induced concentration gradient of the polymer. This is compatible with a positive sign of the Soret coefficient of the polymer in the binary solvent.
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Affiliation(s)
- Loreto García-Fernández
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Universite de Pau et des Pays de l’Adour, Anglet, France
- Centre National d’Études Spatiales (CNES), 2, Place Maurice Quentin, Paris, France
- Department of Structure of Matter, Thermal Physics and Electronics, Faculty of Physics, University Complutense of Madrid, Madrid, Spain
| | - Henri Bataller
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Universite de Pau et des Pays de l’Adour, Anglet, France
| | - Paul Fruton
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Universite de Pau et des Pays de l’Adour, Anglet, France
| | - Cédric Giraudet
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Universite de Pau et des Pays de l’Adour, Anglet, France
| | - Alberto Vailati
- Dipartimento di Fisica “A. Pontremoli”, Università degli Studi di Milano, Milan, Italy
| | - Fabrizio Croccolo
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Universite de Pau et des Pays de l’Adour, Anglet, France
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Zapf D, Kantelhardt J, Köhler W. Nonlinearities in shadowgraphy experiments on non-equilibrium fluctuations in polymer solutions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:40. [PMID: 35471468 PMCID: PMC9043008 DOI: 10.1140/epje/s10189-022-00195-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 04/11/2022] [Indexed: 06/14/2023]
Abstract
Giant thermal and solutal non-equilibrium fluctuations are observed in shadowgraphy experiments on liquid mixtures subjected to a temperature gradient. For large temperature differences, both the temperature and the composition dependence of the relevant thermophysical parameters and the nonlinear terms in the diffusion equation need to be taken into account, leading to a nonlinear concentration profile. For temperature differences exceeding the inverse of the Soret coefficient, in our example approximately 10 K, the usual data evaluation yields increasingly wrong diffusion and Soret coefficients that are off by almost a factor of two for a temperature difference of 50 K. A local model that treats the measured shadowgraph signal as a superposition of the contributions from every layer of the sample is able to capture the essential trend and yields a good agreement with experimental data. The results are important for the application of shadowgraphy as a tool for the measurement of Soret and diffusion coefficients, where large temperature gradients promise a good signal-to-noise ratio.
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Affiliation(s)
- D Zapf
- Physikalisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany
| | - J Kantelhardt
- Physikalisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany
| | - W Köhler
- Physikalisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany.
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Ndjaka AT, García-Fernández L, Bouyou DEB, Lassin A, Azaroual M, Croccolo F, Bataller H. Mass diffusion and Soret coefficient measurements of triethylene glycol/water binary mixtures by dynamic shadowgraphy. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:20. [PMID: 35254520 DOI: 10.1140/epje/s10189-022-00171-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
The investigation of the transport properties of binary fluid mixtures remains a topic of interest in relation to the more challenging studies of ternary mixtures. In fact, the study of the phase boundary limits of the Gibbs composition triangle can be the initial step for a more complete analysis of ternary mixtures. In this paper, we apply the dynamic shadowgraphy optical technique to study non-equilibrium fluctuations induced by the presence of a gradient of temperature and/or concentration in the triethylene glycol (TEG)/water system. These thermodiffusion and free-diffusion experiments aim at measuring the transport properties of samples of the studied system at different experimental conditions. We scan both the average temperature and the TEG concentration, which allows us investigating both positive and negative thermodiffusive behaviours. The obtained values of mass diffusion coefficient are consistent with data available in the literature in the range of temperature investigated in this study. The mass diffusion coefficient of the sample prepared at 0.7 w/w TEG concentration are characterised by shadowgraphy following the two proposed methods, exhibiting consistent results. An increase of the mass diffusion coefficient as a function of the average temperature is highlighted. On the other hand, the thermodiffusion coefficient appears to be independent of the average temperature of the sample at 0.3 w/w TEG concentration.
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Affiliation(s)
- A T Ndjaka
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR 5150, Universite de Pau et des Pays de l'Adour, Anglet, France
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR 5150, BRGM, F-45060, Orléans, France
| | - L García-Fernández
- Department of Structure of Matter, Thermal Physics and Electronics, Faculty of Physics, University Complutense of Madrid, Avda. Complutense s/n, 28040, Madrid, Spain
| | - D E Bouyou Bouyou
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR 5150, Universite de Pau et des Pays de l'Adour, Anglet, France
| | - A Lassin
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR 5150, BRGM, F-45060, Orléans, France
| | - M Azaroual
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR 5150, BRGM, F-45060, Orléans, France
- CNRS, BRGM, ISTO, Univ. Orléans, UMR 7327, F-45071, Orléans, France
| | - F Croccolo
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR 5150, Universite de Pau et des Pays de l'Adour, Anglet, France
| | - H Bataller
- E2S UPPA, CNRS, TotalEnergies, LFCR UMR 5150, Universite de Pau et des Pays de l'Adour, Anglet, France.
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Norouzisadeh M, Chraga M, Cerchiari G, Croccolo F. The modern structurator: increased performance for calculating the structure function. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:146. [PMID: 34855019 PMCID: PMC8639561 DOI: 10.1140/epje/s10189-021-00146-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 10/31/2021] [Indexed: 06/13/2023]
Abstract
The autocorrelation function is a statistical tool that is often combined with dynamic light scattering (DLS) techniques to investigate the dynamical behavior of the scattered light fluctuations in order to measure, for example, the diffusive behavior of transparent particles dispersed in a fluid. An alternative approach to the autocorrelation function for the analysis of DLS data has been proposed decades ago and consists of calculating the autocorrelation function starting from difference of the signal at different times by using the so-called structure function. The structure function approach has been proven to be more robust than the autocorrelation function method in terms of noise and drift rejection. Therefore, the structure function analysis has gained visibility, in particular in combination with imaging techniques such as dynamic shadowgraphy and differential dynamic microscopy. Here, we show how the calculation of the structure function over thousands of images, typical of such techniques, can be accelerated, with the aim of achieving real-time analysis. The acceleration is realized by taking advantage of the Wiener-Khinchin theorem, i.e., by calculating the difference of images through Fourier transform in time. The new algorithm was tested both on CPU and GPU hardware, showing that the acceleration is particularly large in the case of CPU.
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Affiliation(s)
- Mojtaba Norouzisadeh
- E2S UPPA, CNRS, TOTAL, LFCR UMR5150, Universite de Pau et des Pays de l'Adour, Anglet, France
- Institut des Sciences de la Terre d'Orléans, CNRS, Université Orléans, 1A rue de la Férollerie, 45071, Orléans, France
| | - Mohammed Chraga
- E2S UPPA, CNRS, TOTAL, LFCR UMR5150, Universite de Pau et des Pays de l'Adour, Anglet, France
| | - Giovanni Cerchiari
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020, Innsbruck, Austria.
| | - Fabrizio Croccolo
- E2S UPPA, CNRS, TOTAL, LFCR UMR5150, Universite de Pau et des Pays de l'Adour, Anglet, France
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Bresme F, Vesovic V, Bataller H, Croccolo F. Topical Issue on Thermal Non-Equilibrium Phenomena in Soft Matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:148. [PMID: 31754843 DOI: 10.1140/epje/i2019-11918-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 11/20/2019] [Indexed: 06/10/2023]
Affiliation(s)
- Fernando Bresme
- Department of Chemistry, Imperial College London, White City Campus, W12 0BZ, London, UK
| | - Velisa Vesovic
- Department of Earth Science & Engineering, Imperial College London, South Kensington Campus, SW7 2AZ, London, UK
| | - Henri Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs, IPRA, UMR5150, E2S-Univ Pau and Pays Adour/CNRS/Total, 1 Allée du Parc Montaury, 64600, Anglet, France
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs, IPRA, UMR5150, E2S-Univ Pau and Pays Adour/CNRS/Total, 1 Allée du Parc Montaury, 64600, Anglet, France
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