1
|
Castellini S, Brizioli M, Giraudet C, Carpineti M, Croccolo F, Giavazzi F, Vailati A. Modeling and correction of image drift in dynamic shadowgraphy experiments. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:25. [PMID: 38587607 DOI: 10.1140/epje/s10189-024-00413-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Accepted: 03/03/2024] [Indexed: 04/09/2024]
Abstract
The study of phoretic transport phenomena under non-stationary conditions presents several challenges, mostly related to the stability of the experimental apparatus. This is particularly true when investigating with optical means the subtle temperature and concentration fluctuations that arise during diffusion processes, superimposed to the macroscopic state of the system. Under these conditions, the tenuous signal from fluctuations is easily altered by the presence of artifacts. Here, we address an experimental issue frequently reported in the investigation by means of dynamic shadowgraphy of the non-equilibrium fluctuations arising in liquid mixtures under non-stationary conditions, such as those arising after the imposition or removal of a thermal stress, where experiments show systematically the presence of a spurious contribution in the reconstructed structure function of the fluctuations, which depends quadratically from the time delay. We clarify the mechanisms responsible for this artifact, showing that it is caused by the imperfect alignment of the sample cell with respect to gravity, which couples the temporal evolution of the concentration profile within the sample with the optical signal collected by the shadowgraph diagnostics. We propose a data analysis protocol that enables disentangling the spurious contributions and the genuine dynamics of the fluctuations, which can be thus reliably reconstructed.
Collapse
Affiliation(s)
- Stefano Castellini
- Dipartimento di Fisica"A. Pontremoli", Università degli Studi di Milano, Milan, Italy
| | - Matteo Brizioli
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, Segrate, Italy
| | - Cédric Giraudet
- LFCR UMR5150, E2S UPPA, CNRS, Universite de Pau et des Pays de l'Adour, Anglet, France
| | - Marina Carpineti
- Dipartimento di Fisica"A. Pontremoli", Università degli Studi di Milano, Milan, Italy
| | - Fabrizio Croccolo
- LFCR UMR5150, E2S UPPA, CNRS, Universite de Pau et des Pays de l'Adour, Anglet, France
| | - Fabio Giavazzi
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, Segrate, Italy.
| | - Alberto Vailati
- Dipartimento di Fisica"A. Pontremoli", Università degli Studi di Milano, Milan, Italy
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
Diffusion in liquid mixtures. NPJ Microgravity 2023; 9:1. [PMID: 36646718 PMCID: PMC9842720 DOI: 10.1038/s41526-022-00246-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Accepted: 12/19/2022] [Indexed: 01/18/2023] Open
Abstract
The understanding of transport and mixing in fluids in the presence and in the absence of external fields and reactions represents a challenging topic of strategic relevance for space exploration. Indeed, mixing and transport of components in a fluid are especially important during long-term space missions where fuels, food and other materials, needed for the sustainability of long space travels, must be processed under microgravity conditions. So far, the processes of transport and mixing have been investigated mainly at the macroscopic and microscopic scale. Their investigation at the mesoscopic scale is becoming increasingly important for the understanding of mass transfer in confined systems, such as porous media, biological systems and microfluidic systems. Microgravity conditions will provide the opportunity to analyze the effect of external fields and reactions on optimizing mixing and transport in the absence of the convective flows induced by buoyancy on Earth. This would be of great practical applicative relevance to handle complex fluids under microgravity conditions for the processing of materials in space.
Collapse
|
4
|
Srivastava I, Ladiges DR, Nonaka AJ, Garcia AL, Bell JB. Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures. Phys Rev E 2023; 107:015305. [PMID: 36797914 DOI: 10.1103/physreve.107.015305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
We present a numerical formulation for the solution of nonisothermal, compressible Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are that it significantly simplifies the discretization of diffusive and stochastic momentum fluxes into a more compact form, and it provides an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously by Balakrishnan et al. [Phys. Rev. E 89, 013017 (2014)1539-375510.1103/PhysRevE.89.013017]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo method.
Collapse
Affiliation(s)
- Ishan Srivastava
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Daniel R Ladiges
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Andy J Nonaka
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Alejandro L Garcia
- Department of Physics and Astronomy, San Jose State University, 1 Washington Square, San Jose, California 95192, USA
| | - John B Bell
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
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.
Collapse
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.
| |
Collapse
|
7
|
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.
Collapse
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.
| |
Collapse
|
8
|
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.
Collapse
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
| |
Collapse
|
9
|
Schraml M, Bataller H, Bauer C, Bou-Ali MM, Croccolo F, Lapeira E, Mialdun A, Möckel P, Ndjaka AT, Shevtsova V, Köhler W. The Soret coefficients of the ternary system water/ethanol/triethylene glycol and its corresponding binary mixtures. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:128. [PMID: 34661786 PMCID: PMC8523436 DOI: 10.1140/epje/s10189-021-00134-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 10/02/2021] [Indexed: 06/13/2023]
Abstract
Thermodiffusion in ternary mixtures is considered prototypic for the Soret effect of truly multicomponent systems. We discuss ground-based measurements of the Soret coefficient along the binary borders of the Gibbs triangle of the highly polar and hydrogen bonding ternary DCMIX3-system water/ethanol/triethylene glycol. All three Soret coefficients decay with increasing concentration, irrespective of the choice of the independent component, and show a characteristic sign change as a function of temperature and/or composition. With the exception of triethylene glycol/ethanol at high temperatures, the minority component always migrates toward the cold side. All three binaries exhibit temperature-independent fixed points of the Soret coefficient. The decay of the Soret coefficient with concentration can be related to negative excess volumes of mixing. The sign changes of the Soret coefficients of the binaries allow to draw far-reaching conclusions about the signs of the Soret coefficients of the corresponding ternary mixtures. In particular, we show that at least one ternary composition must exist, where all three Soret coefficients vanish simultaneously and no steady-state separation is observable.
Collapse
Affiliation(s)
- M Schraml
- Physikalisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany
| | - H Bataller
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Anglet, France
| | - C Bauer
- Physikalisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany
| | - M M Bou-Ali
- Mondragon Unibertsitatea, 20500, Arrasate-Mondragon, Spain
| | - F Croccolo
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Anglet, France
| | - E Lapeira
- Mondragon Unibertsitatea, 20500, Arrasate-Mondragon, Spain
| | - A Mialdun
- MRC, CP 165/62, Université libre de Bruxelles (ULB), 50, Ave. F.D. Roosevelt, B-1050, Brussels, Belgium
| | - P Möckel
- Physikalisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany
| | - A T Ndjaka
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, TotalEnergies, LFCR UMR5150, Anglet, France
- BRGM, Orléans, France
| | - V Shevtsova
- Mondragon Unibertsitatea, 20500, Arrasate-Mondragon, Spain
- Ikerbasque, Basque Foundation for Science, Bilbao, Spain
| | - W Köhler
- Physikalisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany.
| |
Collapse
|
10
|
Zapf D, Köhler W. Thermal and solutal non-equilibrium fluctuations in a polymer solution. J Chem Phys 2020; 153:224902. [PMID: 33317316 DOI: 10.1063/5.0030854] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have performed shadowgraphy experiments on a dilute polymer solution subjected to a temperature gradient in order to investigate simultaneous thermal and solutal non-equilibrium fluctuations (NEFs). The gravitational quenching of the NEFs at small q-vectors defines the thermal and solutal roll-off wavevectors, which can be extracted from both the static structure function and the time correlation functions. Both methods yield good agreement, and the ∼10% larger static solutal roll-off wavevector coincides with a similar observation reported in the literature. The thermal diffusivity of the solution and the diffusion, thermodiffusion, and Soret coefficients of the polymer can be obtained from the q-dependence of the relaxation times and from the thermal and solutal roll-off wavevectors without explicit knowledge of the optical contrast factors. This provides an alternative route for the measurement of diffusive transport coefficients, albeit with an unfavorable error propagation.
Collapse
Affiliation(s)
- D Zapf
- Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - W Köhler
- Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
11
|
Galand Q, Van Vaerenbergh S, Köhler W, Khlybov O, Lyubimova T, Mialdun A, Ryzhkov I, Shevtsova V, Triller T. Results of the DCMIX1 experiment on measurement of Soret coefficients in ternary mixtures of hydrocarbons under microgravity conditions on the ISS. J Chem Phys 2019; 151:134502. [DOI: 10.1063/1.5100595] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Quentin Galand
- MRC, Université libre de Bruxelles, Department of Chemical Physics, Avenue F. D. Roosevelt, CP165/32, B-1050 Brussels, Belgium
| | - Stéfan Van Vaerenbergh
- MRC, Université libre de Bruxelles, Department of Chemical Physics, Avenue F. D. Roosevelt, CP165/32, B-1050 Brussels, Belgium
| | - Werner Köhler
- Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
| | - Oleg Khlybov
- Institute of Continuous Media Mechanics UB RAS, Koroleva, 1, 614013 Perm, Russia
| | - Tatyana Lyubimova
- Institute of Continuous Media Mechanics UB RAS, Koroleva, 1, 614013 Perm, Russia
| | - Aliaksandr Mialdun
- MRC, Université libre de Bruxelles, Department of Chemical Physics, Avenue F. D. Roosevelt, CP165/32, B-1050 Brussels, Belgium
| | - Ilya Ryzhkov
- Institute of Computational Modelling SB RAS, 660036 Krasnoyarsk, Russia
- Siberian Federal University, Svobodny 79, 660041 Krasnoyarsk, Russia
| | - Valentina Shevtsova
- MRC, Université libre de Bruxelles, Department of Chemical Physics, Avenue F. D. Roosevelt, CP165/32, B-1050 Brussels, Belgium
| | - Thomas Triller
- Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
| |
Collapse
|
12
|
García-Fernández L, Fruton P, Bataller H, Ortiz de Zárate JM, Croccolo F. Coupled non-equilibrium fluctuations in a polymeric ternary mixture. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:124. [PMID: 31511999 DOI: 10.1140/epje/i2019-11889-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Accepted: 08/14/2019] [Indexed: 06/10/2023]
Abstract
We investigate by dynamic shadowgraphy the non-equilibrium fluctuations at the steady state of a thermodiffusion experiment in a polymeric ternary mixture of polystyrene-toluene-n-hexane. The structure function of the refractive index reveals the existence of quite different decay times, thus requiring the analysis of a wide range of correlation times. This is related to the simultaneous presence of three distinct decay modes corresponding to (from fastest to slowest) the relaxation of temperature fluctuations, of the concentration fluctuations of the mixed solvent, and of the concentration fluctuations of the polymer in the binary solvent. An investigation of the decay times at the corresponding diffusive regimes provides a measurement of the thermal diffusivity and the two eigenvalues of the mass diffusion matrix of the ternary mixture. Similar experiments were performed in the past but here, to suppress the confinement effect and obtain a more direct comparison with the theory, a thicker sample is studied. Moreover, also a faster camera is used allowing the experimental observation of faster modes, like the propagative ones. The experimental values of the decay times are eventually compared with those predicted by different available theories. Finally, we present a more complete theoretical model to describe the non-equilibrium fluctuations in the bulk of a ternary mixture at the steady state of a thermodiffusion experiment.
Collapse
Affiliation(s)
- L García-Fernández
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 1 Allée du Parc Montaury, 64600, Anglet, France.
- Centre National d'Études Spatiales (CNES), 2, Place Maurice Quentin, 75001, Paris, France.
| | - P Fruton
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 1 Allée du Parc Montaury, 64600, Anglet, France
| | - H Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 1 Allée du Parc Montaury, 64600, Anglet, France
| | - J M Ortiz de Zárate
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Plaza de las Ciencias 1, 28040, Madrid, Spain
| | - F Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 1 Allée du Parc Montaury, 64600, Anglet, France
| |
Collapse
|
13
|
Croccolo F, Brogioli D, Vailati A. Cylindrical flowing-junction cell for the investigation of fluctuations and pattern-formation in miscible fluids. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:085109. [PMID: 31472663 DOI: 10.1063/1.5112778] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2019] [Accepted: 08/05/2019] [Indexed: 06/10/2023]
Abstract
We describe a flowing-junction cell with cylindrical symmetry suitable to investigate fluctuations and pattern formation at the diffusing interface between two miscible phases of a liquid mixture. The continuous outflow of the remixed fluid through a thin slit located at the midheight of the sample allows the preparation of an initially sharp interface. The system can be used in both gravity-stable and unstable conditions. In the stable case, the denser liquid is on the bottom of the cell and mass diffusion is the only active process for remixing the two liquids. Once the flow is stopped, one can investigate nonequilibrium fluctuations during free-diffusion in a binary mixture or double diffusive instabilities in multicomponent mixtures. Two horizontal transparent windows allow vertical mapping of the fluid flow by using shadowgraphy. In the unstable condition, with the denser fluid on top, stopping the radial flow at the interface gives rise to a Rayleigh-Taylor instability, which drives the denser liquid toward the bottom of the cell. The fact that the cell can maintain the system in the unstable condition shows that it is suitable to perform experiments under microgravity conditions. With respect to other free-diffusion cells, the proposed configuration has the advantage that the interface is extremely stable and flat, and that the experiments can be repeated by just flowing the cell with fresh liquids.
Collapse
Affiliation(s)
- Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs (LFCR), IPRA, UMR5150 E2S-Univ Pau & Pays Adour, CNRS, TOTAL, 64600 Anglet, France
| | - Doriano Brogioli
- Universität Bremen, Energiespeicher-und Energiewandlersysteme, Bibliothekstraße 1, 28359 Bremen, Germany
| | - Alberto Vailati
- Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, I-20133, Milano, Italy
| |
Collapse
|
14
|
Braibanti M, Artola PA, Baaske P, Bataller H, Bazile JP, Bou-Ali MM, Cannell DS, Carpineti M, Cerbino R, Croccolo F, Diaz J, Donev A, Errarte A, Ezquerro JM, Frutos-Pastor A, Galand Q, Galliero G, Gaponenko Y, García-Fernández L, Gavaldá J, Giavazzi F, Giglio M, Giraudet C, Hoang H, Kufner E, Köhler W, Lapeira E, Laverón-Simavilla A, Legros JC, Lizarraga I, Lyubimova T, Mazzoni S, Melville N, Mialdun A, Minster O, Montel F, Molster FJ, Ortiz de Zárate JM, Rodríguez J, Rousseau B, Ruiz X, Ryzhkov II, Schraml M, Shevtsova V, Takacs CJ, Triller T, Van Vaerenbergh S, Vailati A, Verga A, Vermorel R, Vesovic V, Yasnou V, Xu S, Zapf D, Zhang K. European Space Agency experiments on thermodiffusion of fluid mixtures in space. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:86. [PMID: 31289962 DOI: 10.1140/epje/i2019-11849-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2019] [Accepted: 06/05/2019] [Indexed: 06/09/2023]
Abstract
This paper describes the European Space Agency (ESA) experiments devoted to study thermodiffusion of fluid mixtures in microgravity environment, where sedimentation and convection do not affect the mass flow induced by the Soret effect. First, the experiments performed on binary mixtures in the IVIDIL and GRADFLEX experiments are described. Then, further experiments on ternary mixtures and complex fluids performed in DCMIX and planned to be performed in the context of the NEUF-DIX project are presented. Finally, multi-component mixtures studied in the SCCO project are detailed.
Collapse
Affiliation(s)
- M Braibanti
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands.
| | - P -A Artola
- Laboratoire de Chimie-Physique, UMR 8000 CNRS, Université Paris-Sud, Orsay, France
| | - P Baaske
- Nanotemper Technologies GmbH, Munich, Germany
| | - H Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 1 Allée du Parc Montaury, 64600, Anglet, France
| | - J -P Bazile
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 64000, Pau, France
| | - M M Bou-Ali
- MGEP Mondragon GoiEskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Mondragon, Spain
| | - D S Cannell
- Department of Physics, University of California at Santa Barbara, 93106, Santa Barbara, CA, USA
| | - M Carpineti
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| | - R Cerbino
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, 20090, Segrate, Italy
| | - F Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 1 Allée du Parc Montaury, 64600, Anglet, France
| | - J Diaz
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 64000, Pau, France
| | - A Donev
- Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA
| | - A Errarte
- MGEP Mondragon GoiEskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Mondragon, Spain
| | - J M Ezquerro
- E-USOC. ETSIAE, Universidad Politécnica de Madrid, Madrid, Spain
| | - A Frutos-Pastor
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands
| | - Q Galand
- MRC, Université libre de Bruxelles, Av. F.D. Roosevelt, 50, CP165/62, 1050, Brussels, Belgium
| | - G Galliero
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 64000, Pau, France
| | - Y Gaponenko
- MRC, Université libre de Bruxelles, Av. F.D. Roosevelt, 50, CP165/62, 1050, Brussels, Belgium
| | - L García-Fernández
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 1 Allée du Parc Montaury, 64600, Anglet, France
- Centre National d'Etudes Spatiales (CNES), 2, Place Maurice Quentin, 75001, Paris, France
| | - J Gavaldá
- Departament de Química Física i Inòrganica, Universitat Rovira i Virgili, Tarragona, Spain
| | - F Giavazzi
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, 20090, Segrate, Italy
| | - M Giglio
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| | - C Giraudet
- Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany
| | - H Hoang
- Institute of Fundamental and Applied Sciences, Duy Tan University, 10C Tran Nhat Duat Street, District 1, 700000, Ho Chi Minh City, Vietnam
| | - E Kufner
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands
| | - W Köhler
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - E Lapeira
- MGEP Mondragon GoiEskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Mondragon, Spain
| | | | - J -C Legros
- MRC, Université libre de Bruxelles, Av. F.D. Roosevelt, 50, CP165/62, 1050, Brussels, Belgium
| | - I Lizarraga
- MGEP Mondragon GoiEskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Mondragon, Spain
| | - T Lyubimova
- Institute of Continuous Media Mechanics UB RAS, 614013, Perm, Russia
| | - S Mazzoni
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| | - N Melville
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands
| | - A Mialdun
- MRC, Université libre de Bruxelles, Av. F.D. Roosevelt, 50, CP165/62, 1050, Brussels, Belgium
| | - O Minster
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands
| | - F Montel
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 64000, Pau, France
| | - F J Molster
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands
| | - J M Ortiz de Zárate
- Departamento de Estructura de la Materia, Facultad de Fisica, Universidad Complutense, Plaza de las Ciencias 1, 28040, Madrid, Spain
| | - J Rodríguez
- E-USOC. ETSIAE, Universidad Politécnica de Madrid, Madrid, Spain
| | - B Rousseau
- Laboratoire de Chimie-Physique, UMR 8000 CNRS, Université Paris-Sud, Orsay, France
| | - X Ruiz
- Centre National d'Etudes Spatiales (CNES), 2, Place Maurice Quentin, 75001, Paris, France
| | - I I Ryzhkov
- Institute of Computational Modelling SB RAS, 660036, Akademgorodok, Krasnoyarsk, Russia
| | - M Schraml
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - V Shevtsova
- MRC, Université libre de Bruxelles, Av. F.D. Roosevelt, 50, CP165/62, 1050, Brussels, Belgium
| | - C J Takacs
- Department of Physics, University of California at Santa Barbara, 93106, Santa Barbara, CA, USA
| | - T Triller
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - S Van Vaerenbergh
- MRC, Université libre de Bruxelles, Av. F.D. Roosevelt, 50, CP165/62, 1050, Brussels, Belgium
| | - A Vailati
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| | - A Verga
- European Space Agency (ESA), ESTEC, Noordwijk, The Netherlands
| | - R Vermorel
- Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour / CNRS / TOTAL, 64000, Pau, France
| | - V Vesovic
- Department of Earth Science and Engineering, Imperial College London, London, UK
| | - V Yasnou
- MRC, Université libre de Bruxelles, Av. F.D. Roosevelt, 50, CP165/62, 1050, Brussels, Belgium
| | - S Xu
- Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Science, Beijing, China
| | - D Zapf
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - K Zhang
- State Key Laboratory of Enhanced Oil Recovery (Research Institute of Petroleum Exploration & Development), CNPC, Beijing, China
| |
Collapse
|
15
|
Brogioli D, Croccolo F, Vailati A. Asymmetric time-cross-correlation of nonequilibrium concentration fluctuations in a ternary liquid mixture. Phys Rev E 2019; 99:053115. [PMID: 31212452 DOI: 10.1103/physreve.99.053115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Indexed: 11/07/2022]
Abstract
Equilibrium phenomena are characterized by time symmetry. Thermodynamic fluctuations are also time-symmetric at equilibrium. Conversely, diffusion of a solute in a liquid in the presence of a gradient is a nonequilibrium phenomenon, which gives rise to long-range fluctuations with amplitude much larger than the equilibrium one for small enough wave number. In the case of diffusion in binary mixtures such fluctuations are time-symmetric, notwithstanding the fact that they are generated by a nonequilibrium condition. In this paper, we investigate diffusion of two solutes in a ternary liquid mixture by means of fluctuating hydrodynamics theory. We show that the time-cross-correlation function of the concentrations is not time-symmetric, hence showing that time symmetry is violated for such nonequilibrium fluctuations. We discuss the feasibility of experiments aimed at the detection of the asymmetry of the cross-correlation function of nonequilibrium concentration fluctuations in ternary mixtures, as envisaged in the Giant Fluctuations (NEUF-DIX) microgravity project of the European Space Agency.
Collapse
Affiliation(s)
- Doriano Brogioli
- Universität Bremen, Energiespeicher- und Energiewandlersysteme, Bibliothekstraße 1, 28359 Bremen, Germany
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs (LFCR), IPRA, UMR5150 E2S-Univ Pau & Pays Adour, CNRS, TOTAL, 64600 Anglet, France
| | - Alberto Vailati
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| |
Collapse
|
16
|
Ortiz de Zárate JM. Definition of frame-invariant thermodiffusion and Soret coefficients for ternary mixtures. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:43. [PMID: 30953207 DOI: 10.1140/epje/i2019-11803-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Accepted: 03/05/2019] [Indexed: 06/09/2023]
Abstract
The definitions of thermodiffusion and Soret coefficients for a binary mixture include a concentration prefactor x(1 - x), when mole fraction x is used, or w(1 - w), when mass fraction w is used. In this paper the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the thermodiffusion and the Soret coefficients invariant upon changing in the concentration representation, using either mole fraction or mass faction. Then, it is shown how this invariance property can be extended to ternary mixtures by using appropriate concentration prefactors in matrix form. The paper is completed with some considerations about alternative definitions of thermodiffusion coefficients, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, use of molar concentrations and, finally, extension to multi-component mixtures.
Collapse
Affiliation(s)
- José M Ortiz de Zárate
- Facultad de Ciencias Físicas, Universidad Complutense, Plaza de las Ciencias 1, 28040, Madrid, Spain.
| |
Collapse
|
17
|
Croccolo F, García-Fernández L, Bataller H, Vailati A, Ortiz de Zárate JM. Propagating modes in a binary liquid mixture under thermal stress. Phys Rev E 2019; 99:012602. [PMID: 30780374 DOI: 10.1103/physreve.99.012602] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2018] [Indexed: 11/07/2022]
Abstract
Nonequilibrium temperature and concentration fluctuations inside a binary liquid mixture under the action of a temperature gradient relax back to equilibrium either due to conduction and diffusion at large wave numbers, or due to the quenching determined by gravity at small wave numbers. We investigate the dynamics of nonequilibrium fluctuations in a binary liquid mixture of polystyrene and toluene heated from above under stationary conditions in a thermodiffusion experiment. We show that the strong gravitational stabilization at small wave numbers determines the appearance of propagating modes of nonequilibrium fluctuations as detected through the structure function of shadowgraph images. The propagating modes are the combined effect of temperature and velocity nonequilibrium fluctuations induced by the buoyancy force. The experimental results are in good agreement with a fluctuating hydrodynamics theroretical model including the coupling of fluctuations of velocity, temperature and concentration.
Collapse
Affiliation(s)
- Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs, IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 64600 Anglet, France
| | - Loreto García-Fernández
- Laboratoire des Fluides Complexes et leurs Réservoirs, IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 64600 Anglet, France
| | - Henri Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs, IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 64600 Anglet, France
| | - Alberto Vailati
- Universitá degli Studi di Milano, Via Celoria 13, 20013 Milano, Italy
| | - José María Ortiz de Zárate
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| |
Collapse
|
18
|
Bataller H, Triller T, Pur B, Köhler W, Ortiz de Zárate JM, Croccolo F. Dynamic analysis of the light scattered by the non-equilibrium fluctuations of a ternary mixture of polystyrene-toluene-n-hexane. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:35. [PMID: 28352991 DOI: 10.1140/epje/i2017-11522-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2016] [Accepted: 03/01/2017] [Indexed: 06/06/2023]
Abstract
Dynamic analysis of the light scattered by non-equilibrium fluctuations in a thermodiffusion experiment has been performed on a sample of polystyrene-toluene-n -hexane, at 0.9-49.55-49.55% mass fraction. Time decays of the non-equilibrium fluctuations have been obtained revealing the accurate detectability of three modes. The slowest mode has been attributed to the mass diffusion of the polymer into the binary solvent; the intermediate one to mass diffusion of the two molecular components of the solvent; finally, the fastest one has been attributed to the thermal diffusivity of the overall mixture. The two eigenvalues of the mass diffusion matrix have been evaluated with accuracy in the order of 1%. Neglecting cross-diffusion effects we obtain a simplified expression for the relative amplitude of the two mass diffusion modes, allowing a parameterized determination of polystyrene and toluene Soret coefficients in the ternary mixture. We suggest that a two wavelength shadowgraph experiment is needed for a complete determination of all the coefficients.
Collapse
Affiliation(s)
- Henri Bataller
- Univ Pau & Pays Adour, CNRS, TOTAL, LFCR-IPRA, UMR5150, 1 Allée du Parc Montaury, 64600, Anglet, France.
| | - Thomas Triller
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - Bastian Pur
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - Werner Köhler
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | | | - Fabrizio Croccolo
- Univ Pau & Pays Adour, CNRS, TOTAL, LFCR-IPRA, UMR5150, 1 Allée du Parc Montaury, 64600, Anglet, France
- Centre National d'Etudes Spatiales (CNES), 2, Place Maurice Quentin, 75001, Paris, France
| |
Collapse
|
19
|
Lizarraga I, Croccolo F, Bataller H, Mounir Bou-Ali M. Soret coefficient of the n-dodecane-n-hexane binary mixture under high pressure. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:36. [PMID: 28361186 DOI: 10.1140/epje/i2017-11520-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2016] [Accepted: 02/27/2017] [Indexed: 06/07/2023]
Abstract
In the present work, the Soret coefficient has been determined at high pressure for a binary hydrocarbon mixture by combining the thermogravitational column and the dynamic near-field imaging techniques. The analyzed mixture is an iso-massic n -dodecane-n -hexane mixture at 298.15K. The molecular diffusion coefficient has been measured up to 20MPa by means of the dynamic analysis of the light scattered by non-equilibrium concentration fluctuations. With a cylindrical thermogravitational column the thermodiffusion coefficient was determined from 0.1MPa to 10MPa. Density, as well as, mass expansion and thermal expansion have been measured with a high pressure densimeter. Dynamic viscosity at up to 20MPa has been determined with a high pressure viscometer. This work shows the decreasing tendency of both the molecular diffusion and the thermodiffusion coefficient with increasing pressure.
Collapse
Affiliation(s)
- Ion Lizarraga
- MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Loramendi 4, Apartado 23, 20500, Mondragon, Spain
| | - Fabrizio Croccolo
- Univ. Pau & Pays Adour, CNRS, TOTAL, LFCR-IPRA, UMR5150, 1 allée du Parc Montaury, 64600, Anglet, France
- CNES Centre National d'Études Spatiales, 2 place Maurice Quentin, 75 039, Paris Cedex 01, France
| | - Henri Bataller
- Univ. Pau & Pays Adour, CNRS, TOTAL, LFCR-IPRA, UMR5150, 1 allée du Parc Montaury, 64600, Anglet, France
| | - M Mounir Bou-Ali
- MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Loramendi 4, Apartado 23, 20500, Mondragon, Spain.
| |
Collapse
|
20
|
Oprisan A, Rice A, Oprisan SA, Giraudet C, Croccolo F. Non-equilibrium concentration fluctuations in superparamagnetic nanocolloids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:14. [PMID: 28181056 DOI: 10.1140/epje/i2017-11503-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2016] [Accepted: 01/11/2017] [Indexed: 06/06/2023]
Abstract
We investigate non-equilibrium concentration fluctuations during the free diffusion of a colloidal suspension against pure water. We investigate Fe2O3 superparamagnetic nanocolloids with sizes between 1 and 10 nm by means of a shadowgraph apparatus to determine the mixture mass diffusion coefficient and kinematic viscosity. The experiments were performed in three distinct conditions: Experiment 1 is without any magnetic field; Experiment 2 with a vertical magnetic field; Experiment 3 after turning off the magnetic field. We found no correlation between the kinematic viscosity coefficient and the external magnetic field. Conversely, we found that the mass diffusion coefficient decreases in the presence of the external magnetic field and slowly rebounds after the magnetic field was turned off.
Collapse
Affiliation(s)
- Ana Oprisan
- College of Charleston, Department of Physics and Astronomy, Charleston, SC, USA.
| | - Ashley Rice
- College of Charleston, Department of Physics and Astronomy, Charleston, SC, USA
| | - Sorinel A Oprisan
- College of Charleston, Department of Physics and Astronomy, Charleston, SC, USA
| | - Cédric Giraudet
- Erlangen Graduate School in Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Erlangen, Germany
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, Anglet, France
- Centre Nationale d'Etudes Spatiales (CNES), Paris, France
| |
Collapse
|
21
|
Martínez Pancorbo P, Ortiz de Zárate JM, Bataller H, Croccolo F. Gravity effects on Soret-induced non-equilibrium fluctuations in ternary mixtures. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:22. [PMID: 28236112 DOI: 10.1140/epje/i2017-11513-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Accepted: 02/06/2017] [Indexed: 06/06/2023]
Abstract
We discuss the gravity effects on the dynamics of composition fluctuations in a ternary mixture around the non-equilibrium quiescent state induced by thermodiffusion when subjected to a stationary temperature gradient. We found that the autocorrelation matrix of concentration fluctuations can be expressed as the sum of two exponentially decaying concentration modes. Without accounting for confinement, we obtained exact analytical expressions for the two decay rates which, as a consequence of gravity, display a wave-number-dependent mixing. The stability of the quiescent solution is also examined, as a function of the two solutal Rayleigh numbers used to express the decay rates. After having discussed the dynamics of the two concentration modes, we calculate the corresponding amplitudes. Consequences for optical experiments are discussed.
Collapse
Affiliation(s)
- Pablo Martínez Pancorbo
- Departamento de Física Aplicada I, Universidad Complutense, Plaza de las Ciencias 1, 28040, Madrid, Spain.
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 64600, Anglet, France.
| | - José M Ortiz de Zárate
- Departamento de Física Aplicada I, Universidad Complutense, Plaza de las Ciencias 1, 28040, Madrid, Spain
| | - Henri Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 64600, Anglet, France
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 64600, Anglet, France
- Centre National d'Etudes Spatiales (CNES), 2 Place Maurice Quentin, 75001, Paris, France
| |
Collapse
|
22
|
Mialdun A, Shevtsova V. Analysis of multi-wavelength measurements of diffusive properties via dispersion dependence of optical properties. APPLIED OPTICS 2017; 56:572-581. [PMID: 28157913 DOI: 10.1364/ao.56.000572] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We suggest a novel approach to analyze the diffusive properties of mixtures using their optical dispersion relations. Two diagnostics are required to determine the thermodiffusion coefficients in a ternary mixture, e.g., two different wavelengths. The literature results on thermodiffusion experiments indicate that the choice of a pair of wavelengths affects the result of the sought-after thermodiffusion (Soret) coefficients somewhat, because the numerical values of the refractive index variation with the concentration (optical contrast factor ∂n/∂C) depend on the wavelength. The present study offers three main contributions. First, we show that the available measurements for the optical contrast factors and component separation caused by the Soret effect for the mixture tetralin-isobutylbenzene-n-dodecane can be described by the same type of Cauchy dispersion relation as the refractive index n=f(λ). Then, we discuss an algorithm for eliminating the two types of systematic errors from the reported measurements of contrast factors in order to elaborate new synthetic dispersion curves of the Cauchy type. Lastly, we create a general dispersion curve for the stationary component separation which merges the results obtained at different pairs of wavelengths and provides consistent Soret coefficients.
Collapse
|
23
|
Croccolo F, Ortiz de Zárate JM, Sengers JV. Non-local fluctuation phenomena in liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:125. [PMID: 27987100 DOI: 10.1140/epje/i2016-16125-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Accepted: 11/18/2016] [Indexed: 06/06/2023]
Abstract
Fluids in non-equilibrium steady states exhibit long-range fluctuations which extend over the entire system. They can be described by non-equilibrium thermodynamics and fluctuating hydrodynamics that assume local equilibrium for the thermophysical properties as a function of space and time. The experimental evidence for the consistency between this assumption of local equilibrium in the equations and the non-local fluctuation phenomena observed is reviewed.
Collapse
Affiliation(s)
- F Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs, UMR 5150, Université de Pau et des Pays de l'Adour, 64600, Anglet, France.
- Centre National d'Etudes Spatiales (CNES), 2 Place Maurice Quentin, 75001, Paris, France.
| | - J M Ortiz de Zárate
- Departamento de Física Aplicada I, Facultad de Física, Universidad Complutense, 28040, Madrid, Spain
| | - J V Sengers
- Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA
| |
Collapse
|
24
|
Giraudet C, Bataller H, Sun Y, Donev A, Ortiz de Zárate JM, Croccolo F. Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:120. [PMID: 28012142 DOI: 10.1140/epje/i2016-16120-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2016] [Accepted: 11/18/2016] [Indexed: 06/06/2023]
Abstract
In a recent letter (C. Giraudet et al., EPL 111, 60013 (2015)) we reported preliminary data showing evidence of a slowing-down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing-down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing-down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results.
Collapse
Affiliation(s)
- Cédric Giraudet
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 1 Allée du Parc Montaury, 64600, Anglet, France
- Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität, 91052, Erlangen, Germany
| | - Henri Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 1 Allée du Parc Montaury, 64600, Anglet, France
| | - Yifei Sun
- Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA
| | - José M Ortiz de Zárate
- Departamento de Fısica Aplicada I, Facultad de Fısica, Universidad Complutense, 28040, Madrid, Spain
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 1 Allée du Parc Montaury, 64600, Anglet, France.
- Centre National d'Études Spatiales (CNES) 2, Place Maurice Quentin, 75001, Paris, France.
| |
Collapse
|
25
|
Croccolo F, Bataller H. Microgravity in a thin film: How confinement kills gravity. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:132. [PMID: 28012145 DOI: 10.1140/epje/i2016-16132-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Accepted: 11/30/2016] [Indexed: 06/06/2023]
Abstract
Fluctuations in the presence of concentration gradients are long-ranged and decay diffusively for small spatial scales. At larger scales fluctuations are influenced by gravity and confinement. The confinement in the direction of the concentration gradient couples to gravity generating a slowing down that ends up in a diffusion-like behavior of fluctuations of size comparable to the vertical extension of the sample. The resulting enhanced diffusion coefficient depends on the solutal Rayleigh number of the system. For small (in modulus) values of the solutal Rayleigh number the apparent diffusion coefficient tends towards the normal one and a simple diffusive behavior is obtained. This is quite similar to what happens in microgravity conditions when the solutal Rayleigh number is drastically reduced because of the reduction of g by about 6 orders of magnitude. Experiments are shown for positive and negative solutal Rayleigh numbers smaller (in modulus) than 1000. The effect of the confinement on the statics is also investigated. Comparison with microgravity data obtained through the GRADFLEX project is performed.
Collapse
Affiliation(s)
- Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 1 Allée du Parc Montaury, 64600, Anglet, France.
- Centre National d'Études Spatiales (CNES) 2, Place Maurice Quentin, 75001, Paris, France.
| | - Henri Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 1 Allée du Parc Montaury, 64600, Anglet, France
| |
Collapse
|
26
|
Baaske P, Bataller H, Braibanti M, Carpineti M, Cerbino R, Croccolo F, Donev A, Köhler W, Ortiz de Zárate JM, Vailati A. The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:119. [PMID: 28012143 DOI: 10.1140/epje/i2016-16119-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2016] [Accepted: 11/07/2016] [Indexed: 06/06/2023]
Abstract
Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean-square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q-4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation in micro-gravity conditions of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the development of fluctuations during transient diffusion. We envision to parallel these experiments with state-of-the-art multi-scale simulations.
Collapse
Affiliation(s)
| | - Henri Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, F-64600, Anglet, France
| | | | - Marina Carpineti
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| | - Roberto Cerbino
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, 20090, Segrate (MI), Italy
| | - Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, F-64600, Anglet, France
- Centre Nationale d'Etudes Spatiales, Paris, France
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA
| | - Werner Köhler
- Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | | | - Alberto Vailati
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy.
| |
Collapse
|
27
|
Mialdun A, Shevtsova V. Temperature dependence of Soret and diffusion coefficients for toluene-cyclohexane mixture measured in convection-free environment. J Chem Phys 2016; 143:224902. [PMID: 26671399 DOI: 10.1063/1.4936778] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report on the measurement of diffusion (D), Soret (S(T)), and thermodiffusion (D(T)) coefficients in toluene-cyclohexane mixture with mass fraction of toluene 0.40 onboard of the International Space Station. The coefficients were measured in the range of the mean temperatures between 20 °C and 34 °C. The Soret coefficient is negative within the investigated temperature range and its absolute value |S(T)| decreases with increasing temperature. The diffusion coefficient for this system increases with temperature rising. For comparison, the temperature dependence of diffusion coefficient was measured in ground laboratory using counter-flow cell technique and revealed a good agreement with microgravity results. A non-direct comparison of the measured onboard Soret coefficients with different systems indicated a similar trend for the temperature dependent behavior. Unexpected experimental finding is that for this system the thermodiffusion coefficient D(T) does not depend on temperature.
Collapse
Affiliation(s)
- A Mialdun
- MRC, CP165/62, Université Libre de Bruxelles, Av. F.D. Roosevelt, 50, B-1050 Brussels, Belgium
| | - V Shevtsova
- MRC, CP165/62, Université Libre de Bruxelles, Av. F.D. Roosevelt, 50, B-1050 Brussels, Belgium
| |
Collapse
|
28
|
Giraudet C, Marlin L, Bégué D, Croccolo F, Bataller H. Concentration dependent refractive index of CO2/CH4 mixture in gaseous and supercritical phase. J Chem Phys 2016; 144:134304. [PMID: 27059567 DOI: 10.1063/1.4944984] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Carbon dioxide (CO2)/methane (CH4) binary mixtures are investigated at pressure values up to 20 MPa at 303 K in order to investigate the pressure dependence of the optical concentration contrast factor, ∂n/∂c(P,T), through gaseous and supercritical phase. Refractive index is measured by means of a Michelson interferometer. Refractivities of the mixtures are found in good agreement with Lorentz-Lorenz predictions after density calculations by means of the AGA8-DC92 equation of state. Experimental polarizabilities of pure fluids are compared to quantum calculations of monomers and dimers for each pressure; it results that the quantity of dimers is small in the investigated thermodynamic conditions. Finally, by extending our experimental database with numerical simulations, we evidence that ∂n/∂cP,T presents a critical enhancement similar to heat capacity.
Collapse
Affiliation(s)
- C Giraudet
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR 5150, CNRS, Université de Pau et des Pays de l'Adour, 64600 Anglet, France
| | - L Marlin
- Atelier de Physique Générale, Université de Pau et des Pays de l'Adour, BP 1155, 64013 Pau Cedex, France
| | - D Bégué
- Institut Pluridisciplinaire de Recherche sur l'Environnement et les Matériaux - UMR 5254, CNRS, Université de Pau et des Pays de l'Adour, BP 1155, 64013 Pau Cedex, France
| | - F Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR 5150, CNRS, Université de Pau et des Pays de l'Adour, 64600 Anglet, France
| | - H Bataller
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR 5150, CNRS, Université de Pau et des Pays de l'Adour, 64600 Anglet, France
| |
Collapse
|
29
|
Bou-Ali MM, Ahadi A, Alonso de Mezquia D, Galand Q, Gebhardt M, Khlybov O, Köhler W, Larrañaga M, Legros JC, Lyubimova T, Mialdun A, Ryzhkov I, Saghir MZ, Shevtsova V, Van Vaerenbergh S. Benchmark values for the Soret, thermodiffusion and molecular diffusion coefficients of the ternary mixture tetralin+isobutylbenzene+n-dodecane with 0.8-0.1-0.1 mass fraction. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:30. [PMID: 25916233 DOI: 10.1140/epje/i2015-15030-7] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2014] [Revised: 11/06/2014] [Accepted: 02/17/2015] [Indexed: 06/04/2023]
Abstract
With the aim of providing reliable benchmark values, we have measured the Soret, thermodiffusion and molecular diffusion coefficients for the ternary mixture formed by 1,2,3,4-tetrahydronaphthalene, isobutylbenzene and n-dodecane for a mass fraction of 0.8-0.1-0.1 and at a temperature of 25°C. The experimental techniques used by the six participating laboratories are Optical Digital Interferometry, Taylor Dispersion technique, Open Ended Capillary, Optical Beam Deflection, Thermogravitational technique and Sliding Symmetric Tubes technique in ground conditions and Selectable Optical Diagnostic Instrument (SODI) in microgravity conditions. The measurements obtained in the SODI installation have been analyzed independently by four laboratories. Benchmark values are proposed for the thermodiffusion and Soret coefficients and for the eigenvalues of the diffusion matrix in ground conditions, and for Soret coefficients in microgravity conditions.
Collapse
Affiliation(s)
- M M Bou-Ali
- Mechanical and Industrial Manufacturing Department, MGEP Mondragon Goi Eskola Politeknikoa, Loramendi 4 Apdo 23, 20500, Mondragon, Spain,
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
30
|
Oprisan A, Oprisan SA, Hegseth JJ, Garrabos Y, Lecoutre C, Beysens D. Direct imaging of long-range concentration fluctuations in a ternary mixture. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:17. [PMID: 25788436 DOI: 10.1140/epje/i2015-15017-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2014] [Revised: 11/10/2014] [Accepted: 02/04/2015] [Indexed: 06/04/2023]
Abstract
We used a direct imaging technique to investigate concentration fluctuations enhanced by thermal fluctuations in a ternary mixture of methanol (Me), cyclohexane (C), and partially deuterated cyclohexane (C*) within 1mK above its consolute critical point. The experimental setup used a low-coherence white-light source and a red filter to visualize fluctuation images. The red-filtered images were analyzed off-line using a differential dynamic microscopy algorithm that allowed us to determine the correlation time, τ, of concentration fluctuations. From τ, we determined the mutual mass diffusion coefficient, D, very near and above the critical point of Me-CC* mixtures. We also numerically estimated both the background and critical contributions to D and compared the results against our experimental values determined from τ. We found that the experimental value of D is close to the prediction based on Stokes-Einstein diffusion law with Kawasaki's correction.
Collapse
Affiliation(s)
- Ana Oprisan
- Department of Physics and Astronomy, College of Charleston, 29424, Charleston, SC, USA,
| | | | | | | | | | | |
Collapse
|
31
|
Croccolo F, Bataller H, Scheffold F. Erratum: “A light scattering study of non equilibrium fluctuations in liquid mixtures to measure the Soret and mass diffusion coefficient” [J. Chem. Phys. 137, 234202 (2012)]. J Chem Phys 2014. [DOI: 10.1063/1.4903189] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
32
|
Delong S, Sun Y, Griffith BE, Vanden-Eijnden E, Donev A. Multiscale temporal integrators for fluctuating hydrodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:063312. [PMID: 25615227 DOI: 10.1103/physreve.90.063312] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2014] [Indexed: 06/04/2023]
Abstract
Following on our previous work [S. Delong, B. E. Griffith, E. Vanden-Eijnden, and A. Donev, Phys. Rev. E 87, 033302 (2013)], we develop temporal integrators for solving Langevin stochastic differential equations that arise in fluctuating hydrodynamics. Our simple predictor-corrector schemes add fluctuations to standard second-order deterministic solvers in a way that maintains second-order weak accuracy for linearized fluctuating hydrodynamics. We construct a general class of schemes and recommend two specific schemes: an explicit midpoint method and an implicit trapezoidal method. We also construct predictor-corrector methods for integrating the overdamped limit of systems of equations with a fast and slow variable in the limit of infinite separation of the fast and slow time scales. We propose using random finite differences to approximate some of the stochastic drift terms that arise because of the kinetic multiplicative noise in the limiting dynamics. We illustrate our integrators on two applications involving the development of giant nonequilibrium concentration fluctuations in diffusively mixing fluids. We first study the development of giant fluctuations in recent experiments performed in microgravity using an overdamped integrator. We then include the effects of gravity and find that we also need to include the effects of fluid inertia, which affects the dynamics of the concentration fluctuations greatly at small wave numbers.
Collapse
Affiliation(s)
- Steven Delong
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Yifei Sun
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Boyce E Griffith
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA
| | - Eric Vanden-Eijnden
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| |
Collapse
|
33
|
Croccolo F, Bataller H, Scheffold F. Static versus dynamic analysis of the influence of gravity on concentration non-equilibrium fluctuations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:105. [PMID: 25374309 DOI: 10.1140/epje/i2014-14105-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Revised: 09/02/2014] [Accepted: 10/14/2014] [Indexed: 06/04/2023]
Abstract
In a binary fluid mixture subject to gravity and a stabilizing concentration gradient, concentration non-equilibrium fluctuations are long-ranged. While the gradient leads to an enhancement of the respective equilibrium fluctuations, the effect of gravity is a damping of fluctuations larger than a "characteristic" size. This damping is visible both in the fluctuation power spectrum probed by static and the temporal correlation function probed by dynamic light scattering. One aspect of the "characteristic" size can be appreciated by the dynamic analysis; in fact at the corresponding "characteristic" wave vector q* one can observe a maximum of the fluctuation time constant indicating the more persistent fluctuation of the system. Also in the static analysis a "characteristic" size can be extracted from the crossover wave vector. According to common theoretical concepts, the result should be the same in both cases. In the present work we provide evidence for a systematic difference in the experimentally observed "characteristic" size as obtained by static and dynamic measurements. Our observation thus points out the need for a more refined theory of non-equilibrium concentration fluctuations.
Collapse
Affiliation(s)
- Fabrizio Croccolo
- Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150, Université de Pau et des Pays de l'Adour, 64600, Anglet, France,
| | | | | |
Collapse
|
34
|
Giraudet C, Bataller H, Croccolo F. High-pressure mass transport properties measured by dynamic near-field scattering of non-equilibrium fluctuations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:107. [PMID: 25403832 DOI: 10.1140/epje/i2014-14107-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2014] [Revised: 10/21/2014] [Accepted: 10/22/2014] [Indexed: 06/04/2023]
Abstract
High-pressure mass diffusion and Soret coefficients of the equimassic 1,2,3,4-tetrahydronaphthalene and n-dodecane binary mixture are obtained from dynamic light scattering analysis of concentration non-equilibrium fluctuations at the steady state of Soret-driven separation. A high-pressure shadowgraph set-up has been developed to investigate thermodiffusion in free medium from atmospheric pressure up to 20 MPa. Results at atmospheric pressure show excellent agreement with benchmark values. High-pressure results for the mass diffusion coefficient confirm theoretical predictions by Leffler-Cullinan relation. Further calculation of the thermodiffusion coefficient allows also comparison with previous experimental results with, again, very good agreement.
Collapse
Affiliation(s)
- C Giraudet
- Laboratoire des Fluides Complexes et leurs Réservoirs, UMR 5150, Université de Pau et des Pays de l'Adour, 64600, Anglet, France
| | | | | |
Collapse
|
35
|
Maeda K, Shinyashiki N, Yagihara S, Wiegand S, Kita R. How does thermodiffusion of aqueous solutions depend on concentration and hydrophobicity? THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:94. [PMID: 25339283 DOI: 10.1140/epje/i2014-14094-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Revised: 09/15/2014] [Accepted: 09/29/2014] [Indexed: 06/04/2023]
Abstract
The thermal diffusion of aqueous solutions of mono-, di-ethylene glycols, poly(ethylene glycol), methanol, and glycerol is investigated systematically as a function of concentration using the Thermal Diffusion Forced Rayleigh Scattering (TDFRS). For all investigated binary mixtures, the Soret coefficient, S(T), decays with increasing concentration of the non-aqueous component showing two regions. For aqueous solution of ethylene glycol, at a very low solute content the decay is steep, while it becomes less steep for higher solute concentration. All mixtures show a sign change of S(T) with concentration. The sign change concentration is discussed with respect to chemical structures of solute molecules and the partition coefficient, log p. It turns out that the number of hydroxyl groups plays an important role. For the investigated aqueous mixtures, we find empirical linear relations between the sign change concentration and the ratio of the number of hydroxyl groups to the number of carbon atoms as well as the partition coefficient, log p.
Collapse
Affiliation(s)
- Kousaku Maeda
- Graduate School of Science and Technology, Tokai University, Hiratsuka, 259-1292, Kanagawa, Japan,
| | | | | | | | | |
Collapse
|
36
|
Italia M, Croccolo F, Scheffold F, Vailati A. Inclined layer convection in a colloidal suspension with negative Soret coefficient at large solutal Rayleigh numbers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:101. [PMID: 25348665 DOI: 10.1140/epje/i2014-14101-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2014] [Revised: 10/02/2014] [Accepted: 10/08/2014] [Indexed: 06/04/2023]
Abstract
Convection in an inclined layer of fluid is affected by the presence of a component of the acceleration of gravity perpendicular to the density gradient that drives the convective motion. In this work we investigate the solutal convection of a colloidal suspension characterized by a negative Soret coefficient. Convection is induced by heating the suspension from above, and at large solutal Rayleigh numbers (of the order of 10(7)-10(8)) convective spoke patterns form. We show that in the presence of a marginal inclination of the cell as small as 19 mrad the isotropy of the spoke pattern is broken and the convective patterns tend to align in the direction of the inclination. At intermediate inclinations of the order of 33 mrad ordered square patterns are obtained, while at inclination of the order of 67 mrad the strong shear flow determined by the inclination gives rise to ascending and descending sheets of fluid aligned parallel to the direction of inclination.
Collapse
Affiliation(s)
- Matteo Italia
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
| | | | | | | |
Collapse
|
37
|
Ortiz de Zárate JM, Giraudet C, Bataller H, Croccolo F. Non-equilibrium fluctuations induced by the Soret effect in a ternary mixture. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:34. [PMID: 25160490 DOI: 10.1140/epje/i2014-14077-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2014] [Accepted: 07/10/2014] [Indexed: 06/03/2023]
Abstract
We present, based on fluctuating hydrodynamics, the theory of concentration fluctuations in a ternary mixture subjected to a stationary temperature gradient, so that composition gradients are present due to thermal diffusion (Soret effect). We neglect gravity and confinement (boundary conditions) but consider a completely generic diffusion matrix, including cross-diffusion effects. We find, as in the case of binary mixtures, an important non-equilibrium enhancement of the concentration fluctuations, which is proportional to the square of the gradient and inversely proportional to the fourth power of the fluctuations wave number, q(-4). The results of this paper are expected to be asymptotically correct for fluctuations of large q, while for shorter q gravity and confinement effects need to be incorporated. Comparison with previous work in the topic is included.
Collapse
Affiliation(s)
- José M Ortiz de Zárate
- Departamento de Física Aplicada I, Universidad Complutense, Plaza de las Ciencias, 1, 28040, Madrid, Spain,
| | | | | | | |
Collapse
|
38
|
Ahadi A, Varenbergh SV, Saghir MZ. Measurement of the Soret coefficients for a ternary hydrocarbon mixture in low gravity environment. J Chem Phys 2014; 138:204201. [PMID: 23742467 DOI: 10.1063/1.4802984] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
While the Soret coefficients of binary mixtures have been widely measured in the past, here we report the first measurement of the Soret coefficient of a ternary mixture in a low gravity environment on board the International Space Station. The sample was contained in a 10 mm × 10 mm × 5 mm (w, l, h) cell and was monitored by means of a Mach-Zehnder interferometer at two wavelengths. The analyzed sample was a mixture of tetrahydronaphthalene, isobutylbenzene, and dodecane at the weight fraction of 0.1∕0.8∕0.1. While the lateral walls of the cell did not possess complete thermal isolation, the separation of the components in the central region of the cavity was comparable to purely diffusive behavior. The same experimental parameters have been monitored in Run7 and Run12 of the Selectable Optical Diagnostics Instrument-Diffusion and Soret Coefficient experiment in order to verify the accuracy of the setup. The similarity of the results demonstrates the repeatability of thermodiffusion experiments in a microgravity environment. There was nearly equal separation of the tetrahydronaphthalene and isobutylbenzene components in opposite directions, while dodecane experienced a weak separation in the same direction as isobutylbenzene. Finally, Fourier image processing and calculations of the transient separation of the components were used to analyze the heat transfer in the system and to measure the Soret coefficients for this ternary mixture. The successful measurements shown in this work can serve as the standard for ground experiments and for numerical modeling of hydrocarbon mixtures.
Collapse
Affiliation(s)
- Amirhossein Ahadi
- Microgravity Laboratory, Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario M5B 2K3, Canada
| | | | | |
Collapse
|
39
|
Balakrishnan K, Garcia AL, Donev A, Bell JB. Fluctuating hydrodynamics of multispecies nonreactive mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:013017. [PMID: 24580330 DOI: 10.1103/physreve.89.013017] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2013] [Indexed: 06/03/2023]
Abstract
In this paper we discuss the formulation of the fluctuating Navier-Stokes equations for multispecies, nonreactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of nonequilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multispecies fluids.
Collapse
Affiliation(s)
- Kaushik Balakrishnan
- Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - Alejandro L Garcia
- Department of Physics and Astronomy, San Jose State University, 1 Washington Square, San Jose, California 95192, USA
| | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA
| | - John B Bell
- Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| |
Collapse
|
40
|
Croccolo F, Scheffold F, Vailati A. Effect of a marginal inclination on pattern formation in a binary liquid mixture under thermal stress. PHYSICAL REVIEW LETTERS 2013; 111:014502. [PMID: 23863004 DOI: 10.1103/physrevlett.111.014502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2013] [Indexed: 06/02/2023]
Abstract
Convective motions in a fluid layer are affected by its orientation with respect to the gravitational field. We investigate the long-term stability of a thermally stressed layer of a binary liquid mixture and show that pattern formation is strongly affected by marginal inclinations as small as a few milliradians. At small Rayleigh numbers, the mass transfer is dominated by the induced large scale shear flow, while at larger Rayleigh numbers, it is dominated by solutal convection. At the transition, the balance between the solutal and shear flows gives rise to drifting columnar flows moving in opposite directions along parallel lanes in a superhighway configuration.
Collapse
Affiliation(s)
- Fabrizio Croccolo
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland.
| | | | | |
Collapse
|
41
|
Gebhardt M, Köhler W, Mialdun A, Yasnou V, Shevtsova V. Diffusion, thermal diffusion, and Soret coefficients and optical contrast factors of the binary mixtures of dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene. J Chem Phys 2013; 138:114503. [DOI: 10.1063/1.4795432] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|