Hydrodynamic Fluctuations in Liquids Observed by NMR-Modulated Gradient Spin-Echo Method
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Applied Magnetic Resonance
ORIGINAL PAPER
Hydrodynamic Fluctuations in Liquids Observed by NMR‑Modulated Gradient Spin‑Echo Method Janez Stepišnik1 Received: 16 May 2020 / Revised: 4 August 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The modulated gradient spin echo is an NMR method that provides direct insight into the low-frequency part of the molecular velocity auto-correlation spectra in fluids. Because the method gives a spectrum that is time-averaged over the trajectory elapsed, the spins are able to observe local inhomogeneities in the initial interval after spin excitation. In fluid measurements, it manifests as an initial non-exponential decay of the spin-echo signals, which we attribute to the spatial heterogeneity of molecular self-diffusion due to the molecular motion in microvortices of hydrodynamic oscillations. The hydrodynamic fluctuations occur in water, ethanol, toluene, and a mixture of water with lower glycerol content, while they disappeared with increasing glycerol content.
1 Introduction One of the significant discoveries in the field of molecular dynamic in fluids is the existence of hydrodynamic fluctuations [11, 13, 14, 30] that results in a non-exponential long-time tail of the molecular velocity auto-correlation function (VAF), with the power law decay ≈ t−3∕2 for 3D systems. The hydrodynamic fluctuation phenomena were first predicted on the ground of Landau–Lifshitz theory, but the discovery gained momentum after the confirmation of phenomena by the simulations of hard-sphere fluid dynamics [2], which shows that a diffusing hard spheres develop a vortex backflow effect responsible for the persistence of the VAF at long times [3]. The hydrodynamic fluctuations cause the dispersion of the viscosity coefficient or thermal conductivity [14], and can also affect the molecular self-diffusion in liquids [26, 27]. Studies of hydrodynamic fluctuations in non-equilibrium systems are known, where their intensities can cover the whole system and which are strongly influenced by gravity and
* Janez Stepišnik [email protected]‑lj.si 1
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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confinement [6]. However, we deal here with hydrodynamic fluctuations in fluids that are in thermodynamic equilibrium. The VAF is a key quantity of the molecular translation dynamics containing information about the underlying processes of molecular interaction in fluids, but its measurement by neutron [4, 15, 20] and light scattering [17] method does not provide very conclusive results on the asymptotic long-time behavior of VAF due to the short-time scale limits of methods [5]. Thus, the measurement of the VAF asymptotic behavior in dense systems remains a challenge, which complete understanding cannot be revealed by using the traditional experimental techniques. Scientific efforts are, therefore, focused on finding methods that are not related to these main research tools to be able
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