Frequency-dependent Shear Viscosity Research Articles

Measurement of complex shear viscosity up to 3 GHz using an electrodeless AT-cut quartz transducer

An experimental method is proposed to determine the frequency-dependent complex shear viscosity of liquids based on the quartz crystal microbalance with dissipation method. An AT-cut quartz transducer without metal electrodes is immersed in a sample liquid and the transducer is electrically coupled to the circuit through the dielectric response of the sample itself. After correcting for the apparent change in the resonance properties due to the dielectric coupling of the sample, our method is able to determine the viscosity of liquids of high polarity and low viscosity at frequencies as high as 3 GHz. The method was then applied to ethylene glycol and the viscoelastic relaxation in the GHz regime was observed. Furthermore, it was also applied to room-temperature ionic liquids to show that the dielectric correction of the resonance properties is valid for conductive liquids.

Deep learning black hole metrics from shear viscosity

Based on AdS/CFT correspondence, we build a deep neural network to learn black hole metrics from the complex frequency-dependent shear viscosity. The network architecture provides a discretized representation of the holographic renormalization group flow of the shear viscosity and can be applied to a large class of strongly coupled field theories. Given the existence of the horizon and guided by the smoothness of spacetime, we show that Schwarzschild and Reissner-Nordstr\"{o}m metrics can be learned accurately. Moreover, we illustrate that the generalization ability of the deep neural network can be excellent, which indicates that by using the black hole spacetime as a hidden data structure, a wide spectrum of the shear viscosity can be generated from a narrow frequency range. These results are further generalized to an Einstein-Maxwell-dilaton black hole. Our work might not only suggest a data-driven way to study holographic transports but also shed some light on holographic duality and deep learning.

Molecular interpretation of the non-Newtonian viscoelastic behavior of liquid water at high frequencies

Using classical as well as ab-initio molecular dynamics simulations, we calculate the frequency-dependent shear viscosity of pure water and water-glycerol mixtures. In agreement with recent experiments, we find deviations from Newtonian-fluid behavior in the THz regime. Based on an extension of the Maxwell model, we introduce a viscoelastic model to describe the observed viscosity spectrum of pure water. We find four relaxation modes in the spectrum which we attribute to i) hydrogen-bond network topology changes, ii) hydrogen-bond stretch vibrations of water pairs, iii) collective vibrations of water molecule triplets, and iv) librational excitations of individual water molecules. Our model quantitatively describes the viscoelastic response of liquid water on short timescales, where the hydrodynamic description via a Newtonian-fluid model breaks down.

High-temperature expansion of the viscosity in interacting quantum gases

We compute the frequency-dependent shear and bulk viscosity spectral functions of an interacting Fermi gas in a quantum virial expansion up to second quadratic order in the fugacity parameter $z=e^{\beta \mu}$, which is small at high temperatures. Calculations are carried out using a diagrammatic finite-temperature field-theoretic framework, in which the analytic continuation from Matsubara to real frequencies is carried out in closed analytic form. Besides a possible zero-frequency Drude peak, our results for the spectral functions show a broad continuous spectrum at all frequencies with an additional bound-state contribution for frequencies larger than the dimer-breaking energy. Our results are consistent with various sum rules and universal high-frequency tails. In the low-frequency limit, the shear viscosity spectral function is recast as a collision integral, which reproduces known results for the static shear viscosity from kinetic theory. Our findings for the static bulk viscosity of a Fermi gas near unitarity, however, show a nonanalytic dependence on the scattering length, at variance with kinetic theory.

Shear Thinning and Nonlinear Structural Deformation of Ionic Liquids with Long Alkyl Chains Studied by Molecular Dynamics Simulation

Nonequilibrium molecular dynamics (MD) simulation was performed on imidazolium-based ionic liquids of two different alkyl chain lengths, and shear-rate-dependent viscosity was evaluated. Compared with the frequency-dependent linear shear viscosity determined by equilibrium MD simulation, shear thinning occurs at the shear rate several times lower than that predicted by the Cox-Merz rule. The deformation of the structure factor was also evaluated as the function of shear rate. The onset of shear thinning corresponds to that of the nonlinearity in the deformation of the charge-alternation mode in both ionic liquids, which is in harmony with the result of our previous work that the shear relaxation of ionic liquids is mainly coupled to the structural relaxation of the charge-alternation mode. In the presence of the polar-nonpolar domain structure characteristic to ionic liquids with a long alkyl chain, in particular, the nonlinearity in the domain mode begins within the Newtonian regime of shear viscosity.

High-frequency shear viscosity and ionic mobility of solutions of polyethylene glycol in ionic liquids

The frequency-dependent complex shear viscosity of the solutions of polyethylene glycol (PEG) in various ionic liquids is measured in the frequency range of 5–205 MHz, and the ionic mobility of the corresponding solutions was also determined. The plateau viscosity in the MHz regime increases on the addition of PEG, and the relaxation in the 100 MHz regime is retarded simultaneously. The amount of the increase in the plateau viscosity correlates with that in the relaxation time, suggesting that the retardation of the relaxation is a reason for the increase in the plateau viscosity. Although the increase in the plateau viscosity is far smaller than that in the zero-frequency viscosity, these two values are correlated with each other, which can be explained as the consequence of the strength of the same kind of the solute-solvent attractive interaction. The decrease in the molar ionic conductivity also correlates with the increase in the plateau viscosity, suggesting that the plateau viscosity can be regarded as the local viscosity of ionic liquids related to the ion conduction. Based on the correlation with the Kamlet-Taft α parameter, the hydrogen bond between the ionic liquid and the oxygen atoms of PEG is suggested to be a possible origin of the increase in the plateau viscosity.

Translation-orientation coupling and Cox-Merz rule of liquid hexane.

Equilibrium and non-equilibrium molecular dynamics simulations are performed on liquid hexane in order to clarify the origin of the Cox-Merz rule of liquids composed of chain-like molecules. The relation between the frequency-dependent complex shear viscosity and the shear-rate dependent nonlinear viscosity follows the Cox-Merz rule as expected. The slowest viscoelastic relaxation mode is explained by the translation-orientation coupling mechanism, and the saturation of the shear-induced orientational order is observed in the non-equilibrium simulation at the onset of the shear thinning. The origin of the Cox-Merz rule is discussed in terms of the translation-orientation coupling.

Re-investigation of translational–orientational coupling behavior of nematogen in isotropic phase with non-nematogenic additives

We investigated the effects of additives on the translational–orientational coupling constant R using polarized (VV) and depolarized (VH) heterodyne dynamic light scattering, and frequency-dependent shear viscosity measurements of nematogen with two additives mixtures, in order to resolve the inconsistency between previous works using the heterodyne dynamic light scattering and high-frequency strain-optical coefficient measurements. R did not show a significant decrease owing to additives in the concentration range investigated in this work. The significant decrease in R in mixtures reported in previous works is ascribed to the insufficiency of light scattering equipment in the low frequency range.

Viscoelastic relaxations of high alcohols and alkanes: Effects of heterogeneous structure and translation-orientation coupling

The frequency-dependent shear viscosity of high alcohols and linear alkanes, including 1-butanol, 1-octanol, 1-dodecanol, n-hexane, n-decane, and n-tetradecane, was calculated using molecular dynamics simulation. The relaxation of all the liquids was bimodal. The correlation functions of the collective orientation were also evaluated. The analysis of these functions showed that the slower relaxation mode of alkanes is assigned to the translation-orientation coupling, while that of high alcohols is not. The X-ray structure factors of all the alcohols showed prepeaks, as have been reported in the literature, and the intermediate scattering functions were calculated at the prepeak. Comparing the intermediate scattering function with the frequency-dependent shear viscosity based on the mode-coupling theory, it was demonstrated that the slower viscoelastic relaxation of the alcohols is assigned to the relaxation of the heterogeneous structure described by the prepeak.

Experimental study on the relationship between the frequency-dependent shear viscosity and the intermediate scattering function of representative viscous liquids.

The frequency-dependent shear viscosity of two representative viscous liquids, o-terphenyl and glycerin, was experimentally determined at several temperatures and compared with the intermediate scattering functions reported in the literature. A comparison based on mode-coupling theory succeeded in relating the frequency-dependent shear viscosity with the intermediate scattering function at the main peak of the static structure factor. It suggests that the slow relaxation mode of the shear viscosity of both liquids is governed by the density fluctuation at the main peak of the static structure factor, in spite of the differences in the details of their intermolecular interactions.

Relationship between Structural Relaxation, Shear Viscosity, and Ionic Conduction of LiPF6/Propylene Carbonate Solutions.

The structure and dynamics of the solutions of LiPF6 in propylene carbonate over a concentration range of 0-3 mol/kg are studied with neutron spin echo spectroscopy, alternating-current (AC) conductometry, and shear impedance spectroscopy. The neutron diffraction shows a prepeak at ≈10 nm(-1) in addition to the main peak at ≈14 nm(-1) when the concentration of the salt is no less than 2 mol/kg. Compared with the frequency-dependent shear viscosity and AC conductivity, the relaxation of the shear stress agrees with that expected from the structural relaxation of the main peak. On the other hand, the relaxation of the conductivity is slower than the shear relaxation at all the concentrations, and the former approximately matches with the relaxation of the prepeak at the highest concentration, 3 mol/kg, which is several times slower than that of the main peak. The possible contribution of the prepeak structure to the ionic conduction is discussed.

Dielectric and shear relaxations of ionic liquid composed of symmetric ions.

The frequency-dependent conductivity and shear viscosity of an ionic liquid composed of symmetric ions were determined experimentally in the MHz region. The ionic liquid studied was tetraoctylphosphonium bromide. An isomer with an asymmetric cation, trihexyltetradecylphosphonium bromide, was also investigated to clarify the possible role of the reorientational motion of the cations in the two relaxation spectra. Both the conductivity and the shear viscosity show relaxation in the MHz region, and these relaxation spectra scarcely depend on the asymmetry of the cations. It is, therefore, concluded that the coupling of the reorientational mode of cations with these relaxation spectra is marginal, and that these spectra reflect mainly the frequency-dependent translational motion of ions.

Does shear viscosity relaxation control the dynamics of critical fluctuations in polystyrene-cyclohexane?

Between 20 and 90 MHz frequency-dependent shear viscosities of the polystyrene-cyclohexane mixture of critical composition have been measured at polymer molar weight Mw = 30,000. The viscosity data reveal dispersion, in conformity with relaxation characteristics in the non-critical background contributions to the ultrasonic attenuation, i.e., in the longitudinal viscosity of the critical system. The dispersion behavior is discussed with a view to its effect on the critical dynamics of the liquid near its consolute point. Attention is especially given to the relaxation rates of fluctuations of that system. The data as resulting from ultrasonic attenuation spectroscopy on the one hand and from quasi-elastic light scattering and viscosity measurements on the other hand differ near the critical temperature. It is concluded that likely an additional dispersion exists in the shear viscosity at frequencies below the presently available frequency range of measurement.

Temperature evolution of the shear viscosity in a unitary Fermi gas

We present an ab initio determination of the shear viscosity for the unitary Fermi gas based on finite temperature quantum Monte Carlo (QMC) calculations and the Kubo linear-response formalism. The results are confronted with the bound for the shear viscosity originating from hydrodynamic fluctuations. Assuming smoothness of the frequency dependent shear viscosity $\ensuremath{\eta}(\ensuremath{\omega})$, we show that the bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper pairing in the system. In order to preserve the hydrodynamic bound in QMC $\ensuremath{\eta}(\ensuremath{\omega})$ has to possess a sharp structure located in the vicinity of zero frequency which is not resolved by an analytic continuation procedure.

Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma

The viscoelasticity of a two-dimensional (2D) liquid stronglycoupled dusty plasma is studied experimentally, without macroscopic shear. Positions and velocities of the dust particles, measured by video microscopy, are used as the inputs to the generalized Green-Kubo relation to obtain the complex viscosity η(ω). The real part of η(ω) (which corresponds to dissipation) diminishes gradually with frequency, while the imaginary part (which corresponds to elasticity) is peaked at a frequency below the 2D dusty plasma frequency. The viscoelastic approximation is found to accurately describe the 2D experimental results for η(ω), yielding the Maxwell relaxation time τ(M)=0.10 s. Results for η(ω) are compared to 2D molecular dynamics Yukawa simulations and to a previous experiment that was performed using an oscillating macroscopic shear.

Shear and conductivity relaxations of lithium ion electrolytes in polyethyleneglycol dimethyl ethers

The frequency-dependent shear viscosity and electric conductivity of the solution of lithium perchlorate in tetraglyme (TEG) and polyethyleneglycol dimethyl ether (P10, average molecular weight is 500) are measured and compared with each other. The shear viscosity of neat P10 shows a relaxation around 100MHz, and its relaxation amplitude increases with the concentration of the salt, which can be ascribed to the large-scale intramolecular mode of a solvent molecule. In addition, another relaxation appears at 10MHz after the addition of the salt. No relaxation is found in the shear viscosity of TEG solution below 200MHz. The conductivity of P10 solution does not show any dispersion around 10MHz, which indicates that the ionic mobility is decoupled from the relaxation process at 10MHz. Although a relaxation of conductivity is found around 100MHz in P10 solution, the relaxation frequency increases with concentration, while the relaxation frequency of the shear viscosity little depends on the concentration. These two relaxations are therefore assigned to different mechanisms, indicating that the ionic mobility is decoupled also from the large-scale intramolecular mode of a chain. The comparison between the conductivity spectra of P10 and TEG solution shows that the mobility of the local mode of solvent is the determining factor of the ionic mobility.

Shear Relaxation of Water–Ionic Liquid Mixtures

Abstract The frequency-dependent shear viscosity of the mixtures of water with two ionic liquids, 1-butyl-3-methylimidazolium tetrafluoroborate and 1-hexyl-3-methylimidazolium tetrafluoroborate, is measured at frequencies between 5 and 205 MHz. In the cases of both mixtures, the normalized spectra at different water contents reduce to single curves when they are plotted against frequency multiplied with zero-frequency shear viscosity. It indicates that the addition of water into ionic liquids reduces their shear viscosity through the promotion of structural relaxation.

Shear Modulus and Viscosity of Deionized Suspensions of Charged Liposomes

The frequency-dependent shear modulus and viscosity of suspensions of charged liposomes were measured by use of an oscillating optical trap. Deionized suspensions of extruded 100 nm unilamellar liposomes composed of PG:PC mixtures form electrostatically-stabilized gels. A 1.5 μm polystyrene probe particle is suspended in the gel, trapped by optical tweezers, and the trap is oscillated over a frequency range ω = 1-1000 Hz. The relative displacement and phase of the probe in the trap yield the complex response function G(ω), whose real and imaginary parts G′(ω) and G″(ω) are the storage and loss moduli, respectively, which are related to the shear modulus and viscosity of the gel. The dependence of shear modulus on liposome charge can thus be measured. For PG:PC 1:5 (mol:mol) liposomes at 12% volume fraction, we find G′(ω) ∼ 1000 dyne/cm2 over the entire frequency range. This result is consistent with earlier measurements on similar liposome suspensions by an oscillating bobbin technique and is comparable to the shear moduli of colloidal crystals composed of polystyrene spheres of similar size at similar volume fractions. Given the polydispersity of the liposomes (Δr/r ∼ 0.3) compared to that of the polystyrene spheres (Δr/r ∼ 0.02), the liposome suspension is surprisingly rigid. We use the analysis of Joanny (1979) with Poisson-Boltzmann potentials to relate the shear modulus of the liposome gel to the average liposome charge. Such measurements offer a new way to determine the charge of liposomes, biological vesicles, and other nanoparticles.

Shear relaxation of ammonium- and phosphonium-based ionic liquids with oxyethylene chain

Frequency-dependent shear viscosities of ammonium- and phosphonium-based ionic liquids with an oxyethylene chain were determined between 5 and 205MHz, and compared with those of corresponding ionic liquids with an alkyl chain. The shear relaxation spectra show that the substitution of the alkyl chain with the oxyethylene one lowers shear viscosity through the reduction of relaxation time, which is attributed to the higher flexibility of the latter. Comparing the relaxation spectra of ionic liquids with those of non-ionic ones, higher shear viscosities of ionic liquids are ascribed to the larger high-frequency shear modulus due to the interionic Coulombic interaction.

Hydrogen Network Fluctuations of Alcohols. Evidence from Ultrasonic, Dielectric, and Shear Impedance Spectrometry

Broadband dielectric spectra (1 MHz to 40 GHz) and ultrasonic attenuation spectra (300 kHz to 3 GHz) as well as frequency-dependent complex shear viscosities (6 MHz to 120 MHz) are reported for alcohols and for their mixtures with other alcohols, with alkanes, and with water. The spectra are discussed with a view to features controlling the molecular dynamics of associating liquids. Special attention is given to (i) the rotation of terminal single-hydrogen-bonded hydroxy groups of associated structures, (ii) the dominating relaxation process of the structures, involving multiply-hydrogen-bonded hydroxy groups, (iii) the alkyl chain rotational isomerization, (iv) effects of clustering in alcohol–alkane mixtures, and (v) indications of non-critical concentration fluctuations of alcohol–water mixtures. The hydrogen network fluctuations of the alcohol systems can be consistently described in terms of a wait-and-switch model of relaxation. The concentration fluctuations are well represented by a recent “unifying” theoretical model, indicating a predominant impact of hydrophobic groups in the promotion of a micro-heterogeneous structure of mixtures with water.