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Paul T. Callaghan - One of the best experts on this subject based on the ideXlab platform.
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NMR measurement of nonlocal dispersion in complex flows.
Physical review letters, 2007Co-Authors: M.w. Hunter, Paul T. CallaghanAbstract:The flow and diffusion driven separation of initially adjacent liquid molecules is known as dispersion. The primary physical quantity describing this process, the nonlocal dispersion tensor, provides insight regarding both the spatial and temporal correlations of Molecular Velocity fluctuations in complex flows. We here propose and demonstrate a nuclear magnetic resonance method for the measurement of this tensor, validating its implementation for the case of cylindrical Couette flow, and demonstrating its application to the study of fluid dispersion in a random bead pack.
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Low-frequency Velocity correlation spectrum of fluid in a porous media by modulated gradient spin echo.
Magnetic resonance imaging, 2001Co-Authors: Janez Stepišnik, Paul T. CallaghanAbstract:In addition to the fast correlation for local stochastic motion, the Molecular Velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. Here we present its study by the NMR modulated gradient spin-echo method (MGSE) [1] on a system of water trapped in the space between the closely packed polystyrene beads. With MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin phase. It gives the spin echo attenuation proportional to a value of the Molecular Velocity correlation spectrum at the modulation frequency. Covering the frequency range between Hz and MHz, it is a complement to the quasi-elastic neutron scattering, and so a suitable technique for the investigation of low frequency Molecular dynamics in fluids. In our experiment, it enables to extract the low frequency correlation spectrum of water molecules confined in porous media. The function exhibits a negative long time-tail characteristic (a low frequency decay of the spectrum), which can be interpreted as a Molecular back scattering on boundaries. The results can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) [2] as well as with the spectrum obtained when simulating the hydrodynamics of Molecular motion constrained by capillary walls (which gives an algebraic decay) [3]. Despite much work on theories and simulation, which predict slow negative long time tail of Molecular Velocity correlation dynamics in confined fluids, the obtained Velocity correlation spectrum is the first experimental evidence to confirm these effects. The obtained dependence of spin echo attenuation on time, gradient strength and modulation frequency is also the first experimental verification of the recently developed approach to the spin echo in porous media, that uses the spin phase average with the cumulant expansion to get the attenuation as a discord of spin spatial coherence [4].
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The long time tail of Molecular Velocity correlation in a confined fluid: observation by modulated gradient spin-echo NMR
Physica B-condensed Matter, 2000Co-Authors: Janez Stepišnik, Paul T. CallaghanAbstract:Abstract In addition to the fast correlation for local stochastic motion the Molecular Velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time tail decay [1] , [2] . This article presents a study by the NMR modulated gradient spin-echo method (MGSE) [3] on a system of water trapped in the space between the closely packed polystyrene beads. The results prove that the obtained dependence of spin-echo attenuation on time, gradient strength and modulation frequency nicely corresponds to the recently developed NMR approach, which is able to describe the effects of arbitrarily shaped gradient pulse sequence on the spin-echo attenuation [4] , [5] . With an MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin-phase, giving the spin-echo attenuation proportional to a value of the Velocity correlation spectrum at the modulation frequency. It enables to extract the low-frequency correlation spectrum of confined water molecules. The function exhibits a negative long time tail characteristic (a low-frequency decay of the spectrum), that can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) as well as with the spectrum obtained when simulating the hydrodynamics of Molecular motion constrained by capillary walls (which gives an algebraic decay).
Janez Stepišnik - One of the best experts on this subject based on the ideXlab platform.
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Hydrodynamic Fluctuations in Liquids Observed by NMR-Modulated Gradient Spin-Echo Method
Applied Magnetic Resonance, 2020Co-Authors: Janez StepišnikAbstract: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.
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Molecular Velocity auto-correlations in glycerol/water mixtures studied by NMR MGSE method
Physica A: Statistical Mechanics and its Applications, 2020Co-Authors: Janez Stepišnik, Carlos Mattea, Siegfried Stapf, Aleš MohoričAbstract:Abstract Molecular dynamics in binary mixtures of water and glycerol was studied by measuring the spectrum of water Velocity auto-correlation in the frequency range from 0 . 05 − 10 kHz by using the NMR method of modulated gradient spin echo. The method shows that the diversity of diffusion signature in the short spin trajectories provides information about heterogeneity of Molecular motion due to the motion in the micro-vortexes of hydrodynamic fluctuation, which is especially pronounced for the mixtures with low glycerol content. As concentration of glycerol increases above 10vol % , a new feature of spectrum appears due to interaction of water molecules with the clusters formed around hydrophilic glycerol molecules. New spectrum exposes a rate thickening of Molecular friction, according to Einstein–Smoluchowski–Kubo formula, which inhibits rapid Molecular motions and creates the conditions for a slow process of spontaneously folding of disordered poly-peptides into biologically active protein molecules when immersed in such a mixture.
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Molecular Velocity auto-correlation of simple liquids observed by NMR MGSE method
The European Physical Journal B, 2018Co-Authors: Janez Stepišnik, Carlos Mattea, Siegfried Stapf, Aleš MohoričAbstract:The Velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a t −3∕2 long-time tail decay only for non-polar liquid toluene, while the spectra of polar liquids, such as ethanol, water and glycerol, are more congruent with the model of diffusion of particles temporarily trapped in potential wells created by their neighbors. As the method provides the spectrum averaged over ensemble of particle trajectories, the initial non-exponential decay of spin echoes is attributed to a spatial heterogeneity of Molecular motion in a bulk of liquid, reflected in distribution of the echo decays for short spin trajectories. While at longer time intervals, and thus with longer trajectories, heterogeneity is averaged out, giving rise to a spectrum which is explained as a combination of Molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic fluctuations.
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Low-frequency Velocity correlation spectrum of fluid in a porous media by modulated gradient spin echo.
Magnetic resonance imaging, 2001Co-Authors: Janez Stepišnik, Paul T. CallaghanAbstract:In addition to the fast correlation for local stochastic motion, the Molecular Velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. Here we present its study by the NMR modulated gradient spin-echo method (MGSE) [1] on a system of water trapped in the space between the closely packed polystyrene beads. With MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin phase. It gives the spin echo attenuation proportional to a value of the Molecular Velocity correlation spectrum at the modulation frequency. Covering the frequency range between Hz and MHz, it is a complement to the quasi-elastic neutron scattering, and so a suitable technique for the investigation of low frequency Molecular dynamics in fluids. In our experiment, it enables to extract the low frequency correlation spectrum of water molecules confined in porous media. The function exhibits a negative long time-tail characteristic (a low frequency decay of the spectrum), which can be interpreted as a Molecular back scattering on boundaries. The results can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) [2] as well as with the spectrum obtained when simulating the hydrodynamics of Molecular motion constrained by capillary walls (which gives an algebraic decay) [3]. Despite much work on theories and simulation, which predict slow negative long time tail of Molecular Velocity correlation dynamics in confined fluids, the obtained Velocity correlation spectrum is the first experimental evidence to confirm these effects. The obtained dependence of spin echo attenuation on time, gradient strength and modulation frequency is also the first experimental verification of the recently developed approach to the spin echo in porous media, that uses the spin phase average with the cumulant expansion to get the attenuation as a discord of spin spatial coherence [4].
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The long time tail of Molecular Velocity correlation in a confined fluid: observation by modulated gradient spin-echo NMR
Physica B-condensed Matter, 2000Co-Authors: Janez Stepišnik, Paul T. CallaghanAbstract:Abstract In addition to the fast correlation for local stochastic motion the Molecular Velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time tail decay [1] , [2] . This article presents a study by the NMR modulated gradient spin-echo method (MGSE) [3] on a system of water trapped in the space between the closely packed polystyrene beads. The results prove that the obtained dependence of spin-echo attenuation on time, gradient strength and modulation frequency nicely corresponds to the recently developed NMR approach, which is able to describe the effects of arbitrarily shaped gradient pulse sequence on the spin-echo attenuation [4] , [5] . With an MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin-phase, giving the spin-echo attenuation proportional to a value of the Velocity correlation spectrum at the modulation frequency. It enables to extract the low-frequency correlation spectrum of confined water molecules. The function exhibits a negative long time tail characteristic (a low-frequency decay of the spectrum), that can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) as well as with the spectrum obtained when simulating the hydrodynamics of Molecular motion constrained by capillary walls (which gives an algebraic decay).
Shigeru Takata - One of the best experts on this subject based on the ideXlab platform.
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singularity of the Velocity distribution function in Molecular Velocity space
Communications in Mathematical Physics, 2016Co-Authors: Ikun Chen, Hitoshi Funagane, Shigeru TakataAbstract:We study the boundary singularity of the solutions to the Boltzmann equation in the kinetic theory. The solution has a jump discontinuity in the microscopic Velocity \({\zeta}\) on the boundary and a secondary singularity of logarithmic type around the Velocity tangential to the boundary, \({\zeta_{n} \sim 0_{-}}\), where \({\zeta_{n}}\) is the component of Molecular Velocity normal to the boundary, pointing to the gas. We demonstrate this secondary singularity by obtaining an asymptotic formula for the derivative of the solution on the boundary with respect to \({\zeta_{n}}\) that diverges logarithmically when \({\zeta_{n} \sim 0_{-}}\). Our study is for the thermal transpiration problem between two plates for the hard sphere gases with sufficiently large Knudsen number and with the diffuse reflection boundary condition. The solution is constructed and its singularity is studied by an iteration procedure.
J. A. Padró - One of the best experts on this subject based on the ideXlab platform.
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Diffusion in multicomponent liquids: A new set of collective Velocity correlation functions and diffusion coefficients
The Journal of Chemical Physics, 1993Co-Authors: J. Trullàs, J. A. PadróAbstract:A new set of time correlation functions for the description of the microscopic collective dynamic behavior in multicomponent liquids is introduced. These functions, the relative mean Molecular Velocity correlations, are independent of the considered reference frame and the related diffusion coefficients may be defined. The advantages of this kind of description are discussed and relations between the proposed diffusion coefficients and both phenomenological and empirical transport coefficients are derived. Special attention is devoted to the binary liquids.
Ikun Chen - One of the best experts on this subject based on the ideXlab platform.
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singularity of the Velocity distribution function in Molecular Velocity space
Communications in Mathematical Physics, 2016Co-Authors: Ikun Chen, Hitoshi Funagane, Shigeru TakataAbstract:We study the boundary singularity of the solutions to the Boltzmann equation in the kinetic theory. The solution has a jump discontinuity in the microscopic Velocity \({\zeta}\) on the boundary and a secondary singularity of logarithmic type around the Velocity tangential to the boundary, \({\zeta_{n} \sim 0_{-}}\), where \({\zeta_{n}}\) is the component of Molecular Velocity normal to the boundary, pointing to the gas. We demonstrate this secondary singularity by obtaining an asymptotic formula for the derivative of the solution on the boundary with respect to \({\zeta_{n}}\) that diverges logarithmically when \({\zeta_{n} \sim 0_{-}}\). Our study is for the thermal transpiration problem between two plates for the hard sphere gases with sufficiently large Knudsen number and with the diffuse reflection boundary condition. The solution is constructed and its singularity is studied by an iteration procedure.