Retarded hydrodynamic fluctuations effects on the light scattering spectrum and elastic moduli of a linear viscoelastic liquid
DOI:
https://doi.org/10.31349/SuplRevMexFis.1.4.7Keywords:
viscoelasticity, light scattering, correlation functions, stochastic equationsAbstract
Fluctuating hydrodynamics (FH) is one of the theories that describes the dynamics of the fluctuations for fluids at mesoscopic scales. However, it is only valid for Markovian processes. Here we extend this approach for a viscoelastic liquid by using a generalized Langevin equation (GLE). We obyain general analytic expressions for the density fluctuations correlation function, the dynamic structure factor and the light scattering spectrum. In particular, we calculate the intermediate scattering function when the time memory and the noise correlation function are power-laws. We find that the difference in values of this quantity as functions of the viscoelasticity may be ∼62% and might be measurable.References
R. M. Chritensen. Theory of Viscoelasticity: An Introduction. Academic, New York, (1971)
J. C. Simo and T. J. R. Hughes. Computational Viscoelasticity. Springer-Verlag, Berlin, (1998)
G. Guigas, C. Kalla and M. Weiss. Probing the nanoscale viscoelasticity of intracellular fluids in living cells. Biophysical Journal 93: 313-323, (2007)
F. J. Sevilla, R. F. Rodríguez and J. R. Gómez-Solano. Generalized Ornstein-Uhlenbeck model for active motion. Physical Review E 100: 032123, (1931)
J. P. Boon and S. Yip, Molecular Hydrodynamics. McGraw-Hill, New York, (1980)
T. A. Mason and D. Weitz. Optical measurements of frequency dependent linear viscoelastic moduli of complex fluids. Physical Review Letters 74: 1250-1253, (1995)
J. C. Ferry. Viscoelastic Properties of Polymers. Wiley, New York, (1980) Chapter 1, 3rd ed.
C. H. Wang and E. W. Fischer. Density fluctuations, dynamic light scattering, longitudinal compliance, and stress modulus in a viscoelastic medium. Journal of Chemical Physics 82: 632-639, (1985)
K.F. Herzfeld and T.A. Litovitz. Absorption and Dispersion of Ultrasonic Waves. Academic, New York, (1959)
L. D. Landau and E. M. Lifshitz. Fluid Mechanics. Addison-Wesley, Reading, (1959) Chapter XVII
R. F. Fox, The generalized Langevin equation with Gaussian fluctuations. Journal of Mathematical Physics 18: 2331-2336, (1977)
L. Onsager. Reciprocal relations in irreversible processes. I. Physical Review 37: 405-426, (1931)
R. F. Fox, Gaussian stochastic processes in physics. Physics Reports 48: 179-283 (1978)
K.G. Wang and M. Tokuyama. Nonequilibrium statistical description of anomalous diffusion. Physica A 265: 341-351, (1999)
J. M. Porrá, K. G. Wang, J. Masoliver, Generalized Langevin equations: Anomalous diffusion and probability distributions. Physical Review E 53: 5872-5881, (1996)
K. C. Leptos, J. S. Guasto, J. P. Gollub, A. I. Pesei and R. E. Goldstein. Dynamics of enhanced tracer diffusion in suspension of swimming eukaryotic microorganisms. Physical Review Letters 103: 198103-4, (2009)
B. Eckardt and S. Zammert. Non-normal tracer diffusion from stirring by swimming microorganisms. The European Physical Journal E 35: 96 , (2012)
M.Toda, R. Kubo and N Saito. Statistical Physics II (Equilibrium Statistical Mechanics). Springer-Verlag, Berlin, (1983)
R. F. Rodríguez, J. Fujioka and E. Salinas-Rodríguez. Fractional correlation functions in simple viscoelastic fluids. Physica A 427: 326-340, (2015)
R. F. Rodríguez, J. Fujioka and E. Salinas-Rodríguez. Fractional fluctuations effects on the light scattered by a viscoelastic suspension. Physical Review E 88: 022154-13, (2013)
K. S. Fa. Generalized Langevin equation with fractional derivative and long-time correlation function. Physical Review E 73: 061104, (2006)
C. H. Wang. Depolarized Raleigh-Brillouin scattering of shear waves and molecular reorientation in a viscoelastic liquid. Molecular Physics 41: 541-565, (1980)
B. J. Berne and R. Pecora, Dynamic Light Scattering. Wiley, New York, (1976) Chapter 10
G. N. Greaves, A. L. Greer, R. S. Lakes and T. Rouxel. Poisson's ratio and modern materials. Nature Materials 10: 823--837, (2011)
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Copyright (c) 2020 Rosalío Fernando Rodríguez, Rosalío Fernando Rodríguez, Elizabeth Salinas Rodríguez, Jorge Fernando Camacho
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