Frequency-dependent Viscosity Research Articles

The Effects of Solvent Dynamics on the Back Reaction of Solar-Thermal Energy Storage Systems.

We have investigated dynamic solvent effects on molecular solar-thermal energy storage systems using models describing the effects of frequency dependent viscosities and dielectric constants on chemical reaction rates. We have utilized the generalized Langevin model for understanding how the reactions are affected by the frequency dependent viscosities and dielectric constants. Our results show that the rate constants of the molecular solar-thermal energy storage systems depend strongly on the dielectric electric solvent properties and the frequency dependent viscosities of the solvents.

Frequency-dependent viscosity of salmon ovarian fluid has biophysical implications for sperm-egg interactions.

Gamete-level sexual selection of externally fertilising species is usually achieved by modifying sperm behaviour with mechanisms that alter the chemical environment in which gametes perform. In fish, this can be accomplished through the ovarian fluid, a substance released with the eggs at spawning. While the biochemical effects of ovarian fluid in relation to sperm energetics have been investigated, the influence of the physical environment in which sperm compete remains poorly explored. Our objective was therefore to gain insights on the physical structure of this fluid and potential impacts on reproduction. Using soft-matter physics approaches of steady-state and oscillatory viscosity measurements, we subjected wild Atlantic salmon ovarian fluids to variable shear stresses and frequencies resembling those exerted by sperm swimming through the fluid near eggs. We show that this fluid, which in its relaxed state is a gel-like substance, displays a non-Newtonian viscoelastic and shear-thinning profile, where the viscosity decreases with increasing shear rates. We concurrently find that this fluid obeys the Cox-Merz rule below 7.6 Hz and infringes it above this level, thus indicating a shear-thickening phase where viscosity increases provided it is probed gently enough. This suggests the presence of a unique frequency-dependent structural network with relevant implications for sperm energetics and fertilisation dynamics. This article has an associated ECR Spotlight interview with Marco Graziano.

ECR Spotlight – Marco Graziano

ABSTRACT ECR Spotlight is a series of interviews with early-career authors from a selection of papers published in Journal of Experimental Biology and aims to promote not only the diversity of early-career researchers (ECRs) working in experimental biology during our centenary year, but also the huge variety of animals and physiological systems that are essential for the ‘comparative’ approach. Marco Graziano is first author on ‘ Frequency-dependent viscosity of salmon ovarian fluid has biophysical implications for sperm–egg interactions’, published in JEB. Marco conducted the research described in this article while a PhD candidate in Matthew Gage's lab at University of East Anglia, UK. He is now a senior postdoctoral associate in the lab of Simone Immler at University of East Anglia, investigating how sexual and natural selection shape eco-evolutionary processes at the gametic level: before, during and after the reproductive event.

Bulk Viscosity of Dual Bose and Fermi Gases in One Dimension

One-dimensional Bose and Fermi gases with contact interactions are known to exhibit the weak-strong duality, where the equilibrium thermodynamic properties of one system at weak coupling are identical to those of the other system at strong coupling. Here, we show that such duality extends beyond the thermodynamics to the frequency-dependent complex bulk viscosity, which is provided by the contact-contact response function. In particular, we confirm that the bulk viscosities of the Bose and Fermi gases agree in the high-temperature limit, where the systematic expansion in terms of fugacity is available at arbitrary coupling. We also compute their bulk viscosities perturbatively in the weak-coupling limit at arbitrary temperature, which via the duality serve as those of the Fermi and Bose gases in the strong-coupling limit.

Studying the potential of rock magnetism to distinguish combustion structures of different type

Rock magnetism has a significant potential to elucidate archaeological issues related to firing process owing to the strong dependence of clay magnetic properties on firing conditions. The present study is an attempt to characterize some basic fuel installations (hearths, household ovens, pottery kilns, kilns for building ceramics and metallurgical ovens) by the most common magnetic parameters (magnetic remanence, initial magnetic susceptibility, Koenigsberger ratio, frequency-dependent magnetic susceptibility and viscosity coefficient), accumulating a set of relevant magnetic data for exemplary structures. Rasmussen method was used for firing temperature determinations.It is concluded that household ovens, used for cooking/heating activities only, were fired at temperatures below 500 °C. The acquired thermoremanence is in most cases partial TRM, generally less than 800 mA/m, the measured magnetic susceptibility does not exceed 300× 10−8m3/kg, and the corresponding Q ratios are mostly below 10. Experimentally baked clays show that already a firing at temperatures slightly above 500 °C yield much stronger and more stable TRM, and higher χ and Q ratio. Hearth and pottery kilns appear indistinguishable at this research stage, but systematically higher Q ratios were observed for the pottery kilns. Rising the temperature in the kilns for building ceramics and metallurgical ovens causes formation of a higher proportion of coarse-grained hematite and epsilon iron oxide, resulting in thermoremanence increase and magnetic susceptibility decrease.Firing temperatures determined for the household ovens corroborate well the observed magnetic parameters indicating a maximum operating temperature of not more than 460–470 °C. On the other hand, they appear to be underestimated when the highest firing intensity was expected (at T > 900 °C). This is indicative that further studies in this aspect are needed. The slags studied fail to produce any feasible result in terms of their firing temperatures, probably because of their strong inhomogeneity and/or complicated firing history. There is an excellent agreement between the estimated temperatures for clays baked in an experimental dual chamber kiln and the thermocouple readings. Differences in firing atmosphere between archaeological structures (or their experimental analogues) and laboratory furnaces probably have the least effect on low-temperature heated objects (i.e., household ovens) and the strongest on high-temperature ones where reducing conditions dominate that should be taken into account in the data interpretation. An overestimation of Tfiring can happen for low-temperature materials due to possible intense magnetic transformations above 600 °C.

Correlation lengths in nanoconfined water and transport properties.

We report the existence of disparate static and dynamic correlation lengths that could describe the influence of confinement on nanoconfined water (NCW). Various aspects of viscous properties, such as anisotropy and viscoelasticity, of NCW are studied by varying the separation distance "d" between two confining hydrophobic plates. The transverse component of the mean square stress exhibits slow spatial decay (measured from the surface) beyond ∼1.8nm, which was not reported before. The static correlation length obtained from fitting the exponential decay of the transverse mean-square stress with d is 0.75nm, while the decay time of the stress-stress time correlation function gives a dynamic correlation length of only 0.35nm. The shortness of the dynamic correlation length seems to arise from the low sensitivity of orientational relaxation to confinement. In the frequency-dependent viscosity, we observe a new peak at about 50cm-1 that is not present in the bulk. This new peak is prominent even at 3nm separations. The peak is absent in the bulk, although it is close to the intermolecular -O-O-O- bending mode well known in liquid water. We further explore the relationship between diffusion and viscosity in NCW by varying d.

A New High‐Speed Biaxial Testing System for Rodent Myocardium Viscoelastic Measurement under Dynamic Loadings

IntroductionMyocardium stiffening is well known in heart failure (HF) development, and it contributes to cardiac dysfunction. Myocardium is viscoelastic, which means that both elastic and viscous resistance exist under dynamic loading. There are limited studies of myocardium viscoelasticity, particularly for the right ventricle (RV). Because viscoelasticity is a time‐ and strain‐dependent mechanical behavior, the measurement at physiological rates & non‐linear deformation is critical. This study aims to develop a high‐speed biaxial tester that induces physiological deformation to characterize RV viscoelasticity in rats.MethodsTo enable the viscoelasticity measurement at physiological conditions, we built a biaxial tester that induces non‐linear, cyclic stretch of myocardium at rodent heart rates. Biaxial sinusoidal stretches were induced by actuators (1400mm/s) (Zaber), forces were recorded by load cells (Honeywell) at 1 kHz, and strains were obtained by a high‐speed camera (Baumer) at up to 200 fps. The LabVIEW and MATLAB codes were developed for performing biaxial tests at various frequencies with synchronized force and image data acquisition. To validate the biaxial tester, isotropic polydimethylsiloxane (PDMS) was used due to its similar viscoelasticity to cardiovascular tissues. PDMS sheets were prepared (Sylgard 184) for equibiaxial tests. Then, consistency between different axes’ measurements, synchronization of the axes’ movement, and accurate viscoelastic measurement were evaluated. Next, we performed equibiaxial cyclic sinusoidal tests on healthy rat RVs. After euthanasia, RV free wall was dissected and mounted. The outflow track direction was defined as the longitudinal direction. The RV was placed in a relaxant solution prior to testing, then preloaded by ~0.1 N and preconditioned by 15 cycles. Stress‐strain loops were derived for viscoelastic analysis.ResultsFirst, we examined if the biaxial tester could achieve planar biaxial tests at desired frequencies. The equibiaxial data obtained from PDMS sheets showed that the tester induced cyclic sinusoidal stretch at various frequencies up to 8 Hz (Fig. 1a), and the viscoelastic behavior measured at two axes were very close (Fig. 1b), thus confirming the tester’s accurate biaxial measurement of the isotropic material. The PDMS clearly showed frequency‐dependent changes in the hysteresis loops (Fig. 1c), with trends of increasing elasticity (slope of loop) and viscosity (area of loop) at higher frequencies. We further derived the viscosity by measuring Tan(δ) (Fig. 1d). The frequency‐dependent elasticity and viscosity of the PDMS sheet were consistent with literature data. Next, we obtained preliminary viscoelasticity data of healthy rat RVs (at 0.1‐2 Hz). Our data showed strain‐rate dependent changes in the hysteresis loops (Fig. 2). The dissipated energy (loop area) as well as the stiffness (loop slope) of the RV tended to increase with increasing frequency. The RV tissue showed similar viscoelastic behavior in both directions at all frequencies.ConclusionOur data showed that this novel testing system enables biaxial viscoelastic measurement of myocardium under physiological conditions (0.1‐8Hz) across small and large animal species. The establishment of this system allows further exploration of RV tissues at higher frequencies (5‐8 Hz) and in diseased states, which will improve the understanding of cardiac biomechanics in HF progression.

Tidal Dissipation Due to Inertial Waves Can Explain the Circularization Periods of Solar-type Binaries

Abstract Tidal dissipation is responsible for circularizing the orbits and synchronizing the spins of solar-type close binary stars, but the mechanisms responsible are not fully understood. Previous work has indicated that significant enhancements to the theoretically predicted tidal dissipation rates are required to explain the observed circularization periods (P circ) in various stellar populations and their evolution with age. This was based partly on the common belief that the dominant mechanism of tidal dissipation in solar-type stars is turbulent viscosity acting on equilibrium tides in convective envelopes. In this paper, we study tidal dissipation in both convection and radiation zones of rotating solar-type stars following their evolution. We study equilibrium tide dissipation, incorporating a frequency-dependent effective viscosity motivated by the latest hydrodynamical simulations, and inertial wave (dynamical tide) dissipation, adopting a frequency-averaged formalism that accounts for the realistic structure of the star. We demonstrate that the observed binary circularization periods can be explained by inertial wave (dynamical tide) dissipation in convective envelopes. This mechanism is particularly efficient during pre-main-sequence phases, but it also operates on the main sequence if the spin is close to synchronism. The predicted P circ due to this mechanism increases with the main-sequence age in accordance with observations. We also demonstrate that both equilibrium tide and internal gravity-wave dissipation are unlikely to explain the observed P circ, even during the pre-main sequence, based on our best current understanding of these mechanisms. Finally, we advocate more realistic dynamical studies of stellar populations that employ tidal dissipation due to inertial waves.

Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment.

Strongly coupled plasmas in a liquid phase can be characterized by a complex viscosity η(ω), which is a function of frequency. Data from a single experiment with dusty plasma were analyzed to compare η(ω) obtained by two fundamentally distinct methods. In a nonequilibrium method, a pair of counterpropagating laser beams, separated by a gap, applied a sinusoidal shear to a two-dimensional liquid, and η(ω) was determined using the constitutive relation. In an equilibrium method, there was no externally applied shear, so η(ω) could be calculated with a generalized Green-Kubo relation. The results for these two methods are compared for the real and imaginary parts of η(ω). For both parts, it is confirmed that the two methods yield results that agree qualitatively in their trends with frequency, with the real part diminishing with ω and the imaginary part increasing with ω, as expected for viscoelastic liquids. Quantitatively, the values of η(ω) obtained by the two methods differ slightly. For the experiment that we analyze, values for the real and imaginary parts of η(ω) are substantially greater than those reported in an earlier experiment, which we attribute to shear thinning effects in the earlier experiment. The experiment we analyze was designed to minimize shear thinning, unlike the earlier experiment.

Anomalous viscosity of a chiral two-orbital superconductor in tight-binding model

We study the linear response of the deformation potential of a chiral two-orbital superconductor Sr $$_2$$ RuO $$_4$$ to the applied strain. This response rises due to the strain-induced modified interatomic distances. In the linear response theory, the deformation potential–deformation potential correlation function defines the full complex frequency-dependent viscosity tensor. We calculate the anti-symmetric part of this tensor, the phonon Hall viscosity, to consider the static and dynamical Hall responses. The static phonon Hall static enables us to distinguish the different topological phases of Sr $$_2$$ RuO $$_4$$ . We focus on two regimes: (a) the phonon Hall viscosity due to the changes in the hopping energies of the tight-binding Hamiltonian and is termed the normal phonon Hall viscosity and (b) the phonon Hall viscosity due to the variation in the amplitudes of the order parameter of the superconducting state that causes an anomalous momentum transport coefficient and is analogous to the one-dimensional odd isotropic part of the viscosity tensor of an incompressible fluid in two dimension space. In both cases, the tetragonal crystal symmetry which corresponds to the isotropy in the system plays an important role. We also investigate the effect of the crystal symmetry on the stability of the nontrivial topological phase.

Bayesian inference of the viscoelastic properties of a Jeffrey\u2019s fluid using optical tweezers

Bayesian inference is a conscientious statistical method which is successfully used in many branches of physics and engineering. Compared to conventional approaches, it makes highly efficient use of information hidden in a measured quantity by predicting the distribution of future data points based on posterior information. Here we apply this method to determine the stress-relaxation time and the solvent and polymer contributions to the frequency dependent viscosity of a viscoelastic Jeffrey’s fluid by the analysis of the measured trajectory of an optically trapped Brownian particle. When comparing the results to those obtained from the auto-correlation function, mean-squared displacement or the power spectrum, we find Bayesian inference to be much more accurate and less affected by systematic errors.

Tidal dissipation in evolving low-mass and solar-type stars with predictions for planetary orbital decay

ABSTRACT We study tidal dissipation in stars with masses in the range 0.1–1.6 M⊙ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves (IWs) in convection zones, and internal gravity waves in radiation zones. We consider a range of stellar evolutionary models and incorporate the frequency-dependent effective viscosity acting on equilibrium tides based on the latest simulations. We compare the tidal flow and dissipation obtained with the conventional equilibrium tide, which is strictly invalid in convection zones, finding that the latter typically overpredicts the dissipation by a factor of 2–3. Dissipation of IWs is computed using a frequency-averaged formalism accounting for realistic stellar structure for the first time, and is the dominant mechanism for binary circularization and synchronization on the main sequence. Dissipation of gravity waves in the radiation zone assumes these waves to be fully damped (e.g. by wave breaking), and is the dominant mechanism for planetary orbital decay. We calculate the critical planetary mass required for wave breaking as a function of stellar mass and age, and show that this mechanism predicts destruction of many hot Jupiters but probably not Earth-mass planets on the main sequence. We apply our results to compute tidal quality factors following stellar evolution, and tidal evolutionary time-scales, for the orbital decay of hot Jupiters, and the spin synchronization and circularization of binary stars. We also provide predictions for shifts in transit arrival times due to tidally driven orbital decay of hot Jupiters that may be detected with NGTS, TESS, or PLATO.

Tidal evolution of eccentric binaries driven by convective turbulent viscosity

ABSTRACT Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main-sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency ωtide; when ωtide is larger than the turnover frequency of convective eddies, the viscosity is reduced. Previous works have focused on binaries in nearly circular orbits. However, for eccentric orbits, the tidal potential has many forcing frequencies. In this paper, we develop a formalism for computing tidal dissipation that captures the effect of frequency-dependent turbulent viscosity and is valid for arbitrary binary eccentricities. We also present an alternative simpler formulation that is suitable for very high eccentricities. We apply our formalisms to a giant branch (GB) star model and a solar-type star model. We find that a range of pseudo-synchronous rotation rates are possible for both stellar models, and the pseudo-synchronous rate can differ from the prediction of the commonly used weak tidal friction theory by up to a factor of a few. We also find that tidal decay and circularization due to turbulent viscosity can be a few orders of magnitude faster than predicted by weak tidal friction in GB stars on eccentric, small pericentre orbits, but is suppressed by a few orders of magnitude in solar-type stars due to viscosity reduction.

Anomalous viscoelastic response of water-dimethyl sulfoxide solution and a molecular explanation of non-monotonic composition dependence of viscosity.

Amphiphilic molecules such as dimethyl sulfoxide (DMSO) and its aqueous binary mixtures exhibit pronounced nonideality in composition dependence of several static and dynamic properties. We carry out detailed molecular dynamics simulations to calculate various properties including viscosity of the mixture and combine the results with a mode coupling theory analysis to show that this nonideality can be attributed to local structures that are stable on a short time scale but transient on a long time scale to maintain the large scale homogeneity of the solution. Although the existence of such quasistable structures has been deciphered from spectroscopy, a detailed characterization does not exist. We calculate stress-stress autocorrelation functions (SACFs) of water-DMSO binary mixtures. We employ two different models of water, SPC/E and TIP4P/2005, to check the consistency of our results. Viscosity shows a pronounced nonmonotonic composition dependence. The calculated values are in good agreement with the experimental results. Fourier transform of SACF provides frequency-dependent viscosity. The frequency-dependent viscosity (that is, viscoelasticity) is also found to be strongly dependent on composition. Viscoelasticity exhibits sharp peaks due to intramolecular vibrational modes of DMSO, which are also seen in the density of states. We evaluate the wavenumber dependent dynamic structure factor and wavenumber dependent relaxation time. The latter also exhibits a sharp nonmonotonic composition dependence. The calculated dynamic structure factor is used in mode coupling theory expression of viscosity to obtain a semiquantitative understanding of anomalous composition dependence of viscosity. Both the self-diffusion coefficients and rotational correlation times of water and DMSO molecules exhibit nonmonotonic composition dependence.

On the frequency-dependent effective viscosity of laminar and turbulent flows

The efficiency of tidal dissipation in convective zones of stars and giant planets depends, in part, on the response of a three-dimensional fluid flow to the periodic deformation due to the equilibrium tide — a problem considered by Jean-Paul Zahn in his PhD thesis. We review recent results on this problem and present novel calculations based on some idealized models.

Free and confined Brownian motion in viscoelastic Stokes–Oldroyd B fluids

We linearize the Stokes–Oldroyd B model for small perturbations and instantaneous hydrodynamic friction to simulate the environment for a free and confined Brownian particle. We use the standard Green’s function approach to determine the viscoelasticity, and show that the expression obtained for the frequency dependent viscosity is similar to that given by the Jeffrey’s model, though the latter describes viscoelasticity by the bulk storage and loss moduli that is represented by a complex elastic modulus of the fluid concerned. In contrast, we consider the characteristics of the polymer chains and the Newtonian solvent of the complex fluid individually, and determine an expression for frequency-dependent viscosity that would be useful for microrheology performed from Brownian trajectories measured in experiments. Finally, we evaluate the trajectory of a free Brownian particle in a viscoelastic environment using our formalism, and calculate various important parameters quantifying Brownian dynamics, which we then extend to the particle confined in a harmonic potential as provided by optical tweezers.

The Nature's Superviscous Nano-channel: Insight from Big Data-Driven Biophysical Modeling

The nuclear pore complex (NPC) is the unique gateway to the cell nucleus and is primarily filled with intrinsically disordered proteins (IDPs) rich in Phe-Gly (FG) repeat domains. While the microdynamics of these IDPs is still under debate, there is no information and/or consensus about their microrheological properties. Here, we use state-of-the-art computational methods to explore, for the first time, the microrheology of IDPs confined inside the nuclear pore. Our results indicate that the IDPs rich in FG repeat domains show an intriguing rheological behavior, which uniquely stems from the interplay of biophysical factors including hydrophobicity, charge, the ratios of positive and negative charge content to hydrophobicity content, geometrical confinement, chains’ lengths, channel wall permeability, and the chains’ end-tethering. Performing several long-run biophysical simulations of tens of milliseconds, we developed detailed mechanical spectrums of the polymeric meshwork inside the NPC under these physical conditions over a wide range of frequencies. It appears that among these factors, the chains’ end-tethering plays the dominant role in shaping the mechanical spectrum of FG-meshwork, particularly in the low-frequency regime. The frequency-dependent viscosity of the FG-meshwork is reminiscent of pseudo-plasticity, and thus, the FG-repeats form a shear-thinning polymeric meshwork. The meshwork poses a ‘super-viscous’ environment to the inert (non-specific) cargos while behaving as a less viscous liquid for nuclear-transport-factor-bound cargos.

Implementation of viscoelastic mud-induced energy attenuation in the third-generation wave model, SWAN

The interaction of waves with fluid mud can dissipate the wave energy significantly over few wavelengths. In this study, the third-generation wave model, SWAN, was advanced to include attenuation of wave energy due to interaction with a viscoelastic fluid mud layer. The performances of implemented viscoelastic models were verified against an analytical solution and viscous formulations for simple one-dimensional propagation cases. Stationary and non-stationary test cases in the Surinam coast and the Atchafalaya Shelf showed that the inclusion of the mud-wave interaction term in the third-generation wave model enhances the model performance in real applications. A high value of mud viscosity (of the order of 0.1 m2/s) was required in both field cases to remedy model overestimation at high frequency ranges of the wave spectrum. The use of frequency-dependent mud viscosity value improved the performance of model, especially in the frequency range of 0.2–0.35 Hz in the wave spectrum. In addition, the mud-wave interaction might affect the high frequency part of the spectrum, and this part of the wave spectrum is also affected by energy transfer from wind to waves, even for the fetch lengths of the order of 10 km. It is shown that exclusion of the wind input term in such cases might result in different values for parameters of mud layer when inverse modeling procedure was employed. Unlike viscous models for wave-mud interaction, the inverse modeling results to a set of mud parameters with the same performance when the viscoelastic model is used. It provides an opportunity to select realistic mud parameters which are in more agreement with in situ measurements.

Swimmer-Microrheology

We discuss a locomotion of a three-sphere microswimmer in a viscoelastic medium and propose a new type of active microrheology. We derive a relation which connects average swimming velocity and frequency-dependent viscosity of the surrounding medium. In this relation, the viscous contribution can exist only when the time-reversal symmetry is broken, whereas the elastic contribution is present only when the structural symmetry of the swimmer is broken. The Purcell's scallop theorem breaks down for a three-sphere swimmer in a viscoelastic medium.

Viscoelastic nematodynamics.

Nematic liquid crystals exhibit both crystallike and fluidlike features. In particular, the propagation of an acoustic wave shows an interesting occurrence of some of the solidlike features at the hydrodynamic level, namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation. The non-Newtonian behavior of nematics also emerges from the frequency-dependent viscosity coefficients. To account for these phenomena, we put forward a viscoelastic model of nematic liquid crystals, and we extend our previous theory to fully include the combined effects of compressibility, anisotropic elasticity, and dynamic relaxation, at any shear rate. The low-frequency limit agrees with the compressible Ericksen-Leslie theory, while at intermediate frequencies the model correctly captures the relaxation mechanisms underlying finite shear and bulk elastic moduli. We show that there are only four relaxation times allowed by the uniaxial symmetry.