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Journal of Non-Equilibrium Thermodynamics

Founded by Keller, Jürgen U.

Editor-in-Chief: Hoffmann, Karl Heinz

Managing Editor: Prehl, Janett / Schwalbe, Karsten

Ed. by Michaelides, Efstathios E. / Rubi, J. Miguel


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1437-4358
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Volume 43, Issue 1

Issues

Fractional Effects on the Light Scattering Properties of a Simple Binary Mixture

Rosalío F. Rodríguez
  • Corresponding author
  • Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000 CDMX, México
  • Fellow of SNI, México. Also at FENOMEC, UNAM, México
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/ Jorge Fujioka
  • Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000 CDMX, México
  • Fellow of SNI, México. Also at FENOMEC, UNAM, México
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  • Other articles by this author:
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/ Elizabeth Salinas-Rodríguez
  • Departamento I. P. H., Universidad Autónoma Metropolitana, Iztapalapa, Apdo. Postal 55-534, 09340 CDMX, México; Fellow of SNI, México
  • Email
  • Other articles by this author:
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Published Online: 2017-12-14 | DOI: https://doi.org/10.1515/jnet-2017-0036

Abstract

A fractional generalized hydrodynamic (GH) model of the concentration fluctuations correlation function is analyzed. Our analysis is based on a previously proposed irreversible thermodynamics non-fractional model that describes the first GH deviations in a finite frequency and wavelength regime where the local equilibrium assumption is not valid. Our basic purpose is to generalize this theory to investigate the time fractional effects on the intermediate scattering function (ISF) of a model of a binary mixture. We discuss two different forms of introducing the fractional derivatives into the hydrodynamic time evolution equation of the ISF and examine their consistency in the non-fractional limit. We calculate analytically the fractional intermediate scattering function (FISF) and compare it with the non-fractional one. We find that although the FISFs are in general less than ISF, the FISF may be a significant fraction of the ISF (∼36%) and might be measurable by light or neutron scattering techniques. We show that fractional time derivatives provide a consistent description of this correlation function in the GH regime and reduce to its well-known behavior in the Navier–Stokes limit (NS) where local equilibrium is restored. We also suggest an experimental verification of our results for near equilibrium states. Finally, we summarize the main results of our work and make some further physical remarks.

Keywords: fractional derivatives; fluctuations; generalized hydrodynamics; irreversible thermodynamics

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About the article

Received: 2017-07-11

Accepted: 2017-10-27

Revised: 2017-10-20

Published Online: 2017-12-14

Published in Print: 2018-01-26


Citation Information: Journal of Non-Equilibrium Thermodynamics, Volume 43, Issue 1, Pages 43–55, ISSN (Online) 1437-4358, ISSN (Print) 0340-0204, DOI: https://doi.org/10.1515/jnet-2017-0036.

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