Nonequilibrium fractional correlation functions and fluctuation–dissipation in linear viscoelasticity

A simple model for time retarded fractional density and velocity hydrodynamic fluctuations correlations of a linear viscoelastic fluid under an external gradient is proposed. A fractional generalized Langevin equation with a Caputo’s fractional time derivative is formulated for a power-law memory ke...

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Bibliographic Details
Published in:Physica A 2021-12, Vol.583, p.126352, Article 126352
Main Authors: Rodríguez, R.F., Fujioka, J., Salinas-Rodríguez, E.
Format: Article
Language:English
Subjects:
Fractional fluctuations
Fractional fluctuation–dissipation
Fractional transport equations
Linear viscoelasticity
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Summary:A simple model for time retarded fractional density and velocity hydrodynamic fluctuations correlations of a linear viscoelastic fluid under an external gradient is proposed. A fractional generalized Langevin equation with a Caputo’s fractional time derivative is formulated for a power-law memory kernel with long correlation noise. The fractional density and velocity fluctuations correlation functions, as well as the fractional light scattering spectra, and the fractional intermediate scattering function (FISF) are calculated analytically for power-law viscoelasticity. Their relation to the longitudinal modulus of the viscoelastic fluid is also obtained. We find that for different frequency intervals appropriate to perform isothermal light scattering experiments using Fabry–Perot interferometry and photon correlation, the non-equilibrium fractional structure factor may be smaller or larger than its fractional equilibrium values. We also discuss the validity of a fractional fluctuation–dissipation theorem for this model in terms of the asymptotic behavior of the equilibrium fractional correlation functions of the model. •Fractional time derivatives are incorporated into fluctuating transport equations of a viscoelastic liquid.•An analytical relation between the longitudinal modulus and the fractional light scattering spectrum is derived.•The intermediate fractional nonequilibrium scattering function is enhanced with respect to its fractional equilibrium values.•The asymptotic behavior of fractional density and velocity correlation functions complies with fluctuation–dissipation.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2021.126352