Difference in the behavior of the limiting elastic moduli in high-viscosity fluids with different molecular anisotropies
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AL, NONLINEAR, AND SOFT MATTER PHYSICS
Difference in the Behavior of the Limiting Elastic Moduli in HighViscosity Fluids with Different Molecular Anisotropies K. V. Kovalenkoa*, S. V. Krivokhizhaa**, and I. A. Chaban†b a
Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia *email: [email protected] **email: [email protected] b Andreev Acoustic Institute, Moscow, 117036 Russia Received June 26, 2008
Abstract—The experimentally detected difference in the behavior of the high and lowfrequency limiting elastic moduli in highviscosity fluids that have almost spherical (isotropic) and elongated (anisotropic) mol ecules and can easily be supercooled and vitrified is discussed. This difference is shown to be related to anisot ropytensor fluctuations. The observed characteristic temperature dependence of the relaxation time of the anisotropy tensor is explained, and the cause of the linear temperature dependence of the limiting elastic moduli in such fluids is revealed. PACS numbers: 43.35.+d, 61.20.Gy, 62.10.+s, 43.35.Fj DOI: 10.1134/S106377610905015X †
1. INTRODUCTION Highviscosity fluids (which can easily be under cooled and vitrified) cover a wide range of substances interest in which does not wane from year to year. This is related to both the tendency to perfectly understand the physics of liquid and glassy states and to the rapid development of cluster concepts, which are directly associated with these states, in the last few years. The range of practical application of this class of sub stances is very wide, from various building materials to storage devices, which also stimulates their investiga tion. One of the most informative methods is the study of the propagation of waves of various types in them. The propagation of longitudinal and shear waves of various frequencies and electromagnetic waves in highviscosity fluids has the following main specific features [1, 2]: (i) Sound velocity v and sound absorption coeffi cient δ divided by frequency have almost the same dependence on sound frequency ω and viscosity η for various viscous fluids, so that these characteristics are considered to be dependent on ωη or dimensionless parameter ωτ, where τ is the characteristic relaxation time (which is proportional to viscosity). (ii) For every temperature, there exist the limiting lowfrequency (v0) and limiting highfrequency (v∞) sound velocities and, correspondingly, the limiting 2 2 elastic moduli K0 = ρv 0 and K∞ = ρv ∞ , where ρ is the density. As follows from experiments, the dependences K0(T) and K∞(T) represent straight lines. The differ † Deceased.
ence between v∞ and sound velocity v at frequency ω decreases asymptotically as (ωτ)–1/2 with increasing ωτ, in contrast to the result of the relaxation theory in [3], which yields the decreasing law (ωτ)–2 and well describes the propagation of sound in lowviscosity benzenetype fluids. (iii) At low frequencies, the absorption coefficient divided by frequency (δ/ω) is proportional to ωτ, as in the case of the relaxat
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