Oscillatory Relaxation Research Articles

Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined.

Intermediate scattering function for polymer molecules: An approach based on relaxation mode analysis.

The theory of polymer dynamics describes the intermediate scattering function for a polymer molecule in terms of relaxation modes defined by normal coordinates for the corresponding coarse-grained model. However, due to the difficulty of defining the normal coordinates for arbitrary polymer molecules, it is generally challenging to express the intermediate scattering function for a polymer molecule in terms of relaxation modes. To overcome this challenge, we propose a general method to calculate the intermediate scattering function for a polymer molecule on the basis of a relaxation mode analysis approach [Takano and Miyashita, J. Phys. Soc. Jpn. 64, 3688 (1995)]. In the proposed method, relaxation modes defined by eigenfunctions in a Markov process are evaluated on the basis of the simulation results for a polymer molecule and used to calculate the intermediate scattering function for that molecule. To demonstrate the effectiveness of the present method, we simulate the dynamics of a linear polymer molecule in a dilute solution and apply it to the calculation of the intermediate scattering function for the polymer molecule. The evaluation results regarding the relaxation modes reasonably describe the intermediate scattering function on the length scale of the radius of gyration of the polymer molecule. Accordingly, we examine the contributions of the pure relaxation and oscillatory relaxation processes to the entire intermediate scattering function.

Homogenization of Porous Thin Layers With Internal Stratification for the Estimation of Seismic Reflection Coefficients

AbstractStratified thin layers often present a prominent mechanical contrast with regard to the embedding background and, hence, are important targets for seismic reflection studies. An efficient way to study the reflectivity response of these thin layers is to employ their homogenized viscoelastic equivalents. We aim to homogenize a simple, yet realistic, thin‐layer model, which is composed of a finite non‐periodic sequence of homogeneous porous strata embedded in a background deemed impermeable at the seismic frequencies. The overarching objective is to reproduce the reflectivity response of such stratified thin layers. However, the estimation of the equivalent moduli is inherently affected by the boundary conditions (BC) associated with the embedding background. Therefore, classical homogenization procedures, which assume the existence of a periodic structure, are not readily applicable. We, therefore, propose a novel homogenization procedure that incorporates naturally the appropriate BC. To this end, we consider a sample that includes both a part of the background and a section of the thin layer, to which we apply classical oscillatory relaxation tests. However, we estimate the average of stress and strain components only over the thin layer section of interest. To test the accuracy of the method, we consider a sandstone composed of two strata saturated with different fluids embedded in impermeable half‐spaces. After estimating the corresponding equivalent moduli, we compare the resulting P‐wave reflectivities with those obtained using the original model. Our results show that the inferred viscoelastic equivalent closely reproduces the reflectivities of the stratified thin layer in the seismic frequency range.

Nuclear spin diffusion in the central spin system of a GaAs/AlGaAs quantum dot

The spin diffusion concept provides a classical description of a purely quantum-mechanical evolution in inhomogeneously polarized many-body systems such as nuclear spin lattices. The central spin of a localized electron alters nuclear spin diffusion in a way that is still poorly understood. Here, spin diffusion in a single GaAs/AlGaAs quantum dot is witnessed in the most direct manner from oscillatory spin relaxation dynamics. Electron spin is found to accelerate nuclear spin relaxation, from which we conclude that the long-discussed concept of a Knight-field-gradient diffusion barrier does not apply to GaAs epitaxial quantum dots. Our experiments distinguish between non-diffusion relaxation and spin diffusion, allowing us to conclude that diffusion is accelerated by the central electron spin. Such acceleration is observed up to unexpectedly high magnetic fields – we propose electron spin-flip fluctuations as an explanation. Diffusion-limited nuclear spin lifetimes range between 1 and 10 s, which is sufficiently long for quantum information storage and processing.

A Class of Algorithms for Recovery of Continuous Relaxation Spectrum from Stress Relaxation Test Data Using Orthonormal Functions.

The viscoelastic relaxation spectrum provides deep insights into the complex behavior of polymers. The spectrum is not directly measurable and must be recovered from oscillatory shear or relaxation stress data. The paper deals with the problem of recovery of the relaxation spectrum of linear viscoelastic materials from discrete-time noise-corrupted measurements of relaxation modulus obtained in the stress relaxation test. A class of robust algorithms of approximation of the continuous spectrum of relaxation frequencies by finite series of orthonormal functions is proposed. A quadratic identification index, which refers to the measured relaxation modulus, is adopted. Since the problem of relaxation spectrum identification is an ill-posed inverse problem, Tikhonov regularization combined with generalized cross-validation is used to guarantee the stability of the scheme. It is proved that the accuracy of the spectrum approximation depends both on measurement noises and the regularization parameter and on the proper selection of the basis functions. The series expansions using the Laguerre, Legendre, Hermite and Chebyshev functions were studied in this paper as examples. The numerical realization of the scheme by the singular value decomposition technique is discussed and the resulting computer algorithm is outlined. Numerical calculations on model data and relaxation spectrum of polydisperse polymer are presented. Analytical analysis and numerical studies proved that by choosing an appropriate model through selection of orthonormal basis functions from the proposed class of models and using a developed algorithm of least-square regularized identification, it is possible to determine the relaxation spectrum model for a wide class of viscoelastic materials. The model is smoothed and robust on measurement noises; small model approximation errors are obtained. The identification scheme can be easily implemented in available computing environments.

Micronewton shear rheometer performing SAOS using 2 mg of sample

Rheological measurements typically require at least 20–50 mg of sample. We set up a miniaturized sliding-plates shear rheometer (mgRheo) that requires only 2 mg sample or even less. We designed a flexure-based force-sensing device that could measure force ranging from the micronewton to millinewton scale, e.g., 40 μN–400 mN for one particular spring constant. The setup was strain-controlled by a piezostage and could perform standard rheological tests such as small amplitude oscillatory shear, step strain, and stress relaxation. The accuracy and consistencies were evaluated on polydimethylsiloxane viscoelastic standard, entangled poly(hexyl methacrylate), and polystyrene. The obtained phase angles quantitatively agreed with those from commercial rheometers. The exact values of the modulus are prone to the overfilling of the sample. The storage G′ and loss G″ moduli from the mgRheo were systematically higher than those from commercial rheometers (i.e., within 5% with careful trimming or 30% with excessive overfilling). Between 102 and 106 Pa, G′ and G″ were in good agreement with commercial rheometers. Such a setup allowed for general rheometric characterizations, especially obtaining linear viscoelasticity on soft matters that are synthetically difficult to obtain in a large quantity.

Synergistic interactions between konjac glucomannan and welan gum mixtures

This research presents the physicochemical property of the mixtures induced by blending konjac glucomannan (KGM) and welan gum (WL). The effects of the ratio and concentration on the rheological properties of the KGM and WL mixtures, such as shear rate and strain (large-amplitude oscillatory shear, frequency, temperature, time, stress relaxation, and creep), were studied. The combination analysis of Fourier transform infrared spectroscopy, scanning electron microscopy, thermodynamic differential scanning calorimetry, water mobility, and distribution property analyses through low-field nuclear magnetic resonance spectroscopy were used to determine the authenticity of gels. Finally, a model of the interaction force was constructed to elucidate the interaction mechanism when heating. The result showed that the mixtures of KGM and WL were pseudogel. The synergy effect was positively correlated with concentration, which was the strongest when the KGM (g/kg): WL (g/kg) ratio was 2:8. Abnormal temperature sensitivity (sudden drop of modulus around 30 °C) was observed at the ratio, and the mixture owned good temperature reversibility in 3 cycles. This work expanded the application scope of KGM and WL and provides a method for the determination of gels.

Anisotropic Effective Elastic Properties for Multi-Dimensional Fractured Models

The size, distribution, and orientation of fractures are generally multiscale and multi-dimensional in nature, leading to complex anisotropic characteristics. Theoretical or semi-analytical methods to determine the effective elastic properties depend on several assumptions, including the absence of the stress interaction and idealized fractures. On the basis of finite-element models, we conduct numerical oscillatory relaxation tests for determining the effective elastic properties of fractured rocks. The numerical approach for calculating equivalent stiffness tensors in two-dimensions is compared to the theoretical models for different fracture densities. Due to fracture interactions at high fracture densities, the suggested model makes a physical prediction. The effective elastic properties obtained from the application to a real fractured model, established from an outcrop, obviously disperse at different frequencies, which can be used to investigate fracture interactions and dynamic stress disturbances. The algorithm is extended to three-dimensional cases and also validated by using conventional effective medium theories. It is found that the fracture density obviously impacts the effective anisotropy properties, and the proposed method gives a reasonable prediction for high-fracture density. This work is significant because it enables the calculation of effective elastic properties of multi-dimensional fractured models and the fracture interaction mechanism.

Oscillatory Microrheology, Creep Compliance and Stress Relaxation of Biological Cells Reveal Strong Correlations as Probed by Atomic Force Microscopy

The mechanical properties of cells are important for many biological processes, including wound healing, cancers, and embryogenesis. Currently, our understanding of cell mechanical properties remains incomplete. Different techniques have been used to probe different aspects of the mechanical properties of cells, among them microplate rheology, optical tweezers, micropipette aspiration, and magnetic twisting cytometry. These techniques have given rise to different theoretical descriptions, reaching from simple Kelvin-Voigt or Maxwell models to fractional such as power law models, and their combinations. Atomic force microscopy (AFM) is a flexible technique that enables global and local probing of adherent cells. Here, using an AFM, we indented single retinal pigmented epithelium cells adhering to the bottom of a culture dish. The indentation was performed at two locations: above the nucleus, and towards the periphery of the cell. We applied creep compliance, stress relaxation, and oscillatory rheological tests to wild type and drug modified cells. Considering known fractional and semi-fractional descriptions, we found the extracted parameters to correlate. Moreover, the Young’s modulus as obtained from the initial indentation strongly correlated with all of the parameters from the applied power-law descriptions. Our study shows that the results from different rheological tests are directly comparable. This can be used in the future, for example, to reduce the number of measurements in planned experiments. Apparently, under these experimental conditions, the cells possess a limited number of degrees of freedom as their rheological properties change.

Effects of the surface wettability of nanoparticles on the impact dynamics of droplets

Herein, we report an experimental investigation on droplet impact dynamics with a particular interest in the effects of hydrophilicity and hydrophobicity of particles on the impact dynamics. Remarkable contact line pinning and receding breakup were observed when hydrophobic particles were present in the droplets, while hydrophilic particles showed little effect on the dynamics. Furthermore, the maximum retraction height and vertical oscillatory relaxation time for the droplet were restrained by hydrophobic particles. Scanning electron microscopy and rheological analyses revealed that these phenomena may be related to the adsorption and deposition of hydrophobic particles near the three-phase contact line, which leads to an increase in local viscosity and friction near the edge of the drop. In addition, the contact line pinning is positively associated with the Weber number and particle concentration. Our work provides a novel approach for droplet impact dynamics control, particularly for suppressing the oscillation and contraction of droplets.

Extensional Effects during Viscoelastic Polymer Flooding: Understanding Unresolved Challenges

Summary Several studies have tried to relate polymers’ enhanced oil recovery (EOR) potential to their viscoelastic characteristics such as onset, rheo thickening, extensional viscosity, and Deborah number (De). Contradictions prevail when it comes to reduction in residual oil saturation (Sor) during polymer flooding and the role of extensional properties. De calculated using the oscillatory relaxation time fails to explain the different pressure profiles exhibited by the viscous and viscoelastic polymers. Extensional viscosity has been ignored in many studies as the reason for additional Sor reduction based on the core-scale apparent viscosity and core-scale capillary number (Nc). In recent studies, a significant oil mobilization was shown by the viscoelastic polymers even before the critical Nc, which indicates that the capillary theory breaks out under specific conditions during polymer flooding. Moreover, the additional residual oil recovery caused by the high-salinity polymer solutions cannot be explained by the oscillatory De. In this paper, we compile and examine many such unresolved challenges from various literature with rheological and petrophysical insights. The uniaxial bulk extensional rheology is performed on the relevant polymers using a capillary breakup extensional rheometer to measure the extensional relaxation time, maximum extensional viscosity at the critical De, and strain hardening index. A detailed analysis signifies the role of extensional rheology on the viscoelastic onset, rheo thickening, and Sor reduction even under varying salinity conditions. The results also highlight the advantages of extensional rheology over oscillatory rheology and validate the capillary theory using modified capillary number.

Squirt Flow in Cracks with Rough Walls

AbstractWe explore the impact of roughness in crack walls on the P wave modulus dispersion and attenuation caused by squirt flow. For that, we numerically simulate oscillatory relaxation tests on models having interconnected cracks with both simple and intricate aperture distributions. Their viscoelastic responses are compared with those of models containing planar cracks but having the same hydraulic aperture as the rough wall cracks. In the absence of contact areas between crack walls, we found that three apertures affect the P wave modulus dispersion and attenuation: the arithmetic mean, minimum aperture, and hydraulic aperture. We show that the arithmetic mean of the crack apertures controls the effective P wave modulus at the low‐ and high‐frequency limits, thus representing the mechanical aperture. The minimum aperture of the cracks tends to dominate the energy dissipation process and, consequently, the characteristic frequency. An increase in the confining pressure is emulated by uniformly reducing the crack apertures, which allows for the occurrence of contact areas. The contact area density and distribution play a dominant role in the stiffness of the model, and in this scenario, the arithmetic mean is not representative of the mechanical aperture. On the other hand, for a low percentage of minimum aperture or in the presence of contact areas, the hydraulic aperture tends to control the characteristic frequency. Analyzing the local energy dissipation, we can more specifically visualize that a different aperture controls the energy dissipation process at each frequency, which means that a frequency‐dependent hydraulic aperture might describe the squirt flow process in cracks with rough walls.

Preparation and evaluation of microfluidic magnetic alginate microparticles for magnetically templated hydrogels

Our aim is to develop a hydrogel-based scaffold containing porous microchannels that mimic complex tissue microarchitecture and provide physical cues to guide cell growth for scalable, cost-effective tissue repair. These hydrogels are patterned through the novel process of magnetic templating where magnetic alginate microparticles (MAMs) are dispersed in a hydrogel precursor and aligned in a magnetic field before hydrogel crosslinking and subsequent MAM degradation, leaving behind an aligned, porous architecture. Here, a protocol for fabricating uniform MAMs using microfluidics was developed for improved reproducibility and tunability of templated microarchitecture. Through iron quantification, we find that this approach allows control over magnetic iron oxide loading of the MAMs. Using Brownian dynamics simulations and nano-computed tomography of templated hydrogels to examine MAM chain length and alignment, we find agreement between simulated and measured areal densities of MAM chains. Oscillatory rheology and stress relaxation experiments demonstrate that magnetically templated microchannels alter bulk hydrogel mechanical properties. Finally, in vitro studies where rat Schwann cells were cultured on templated hydrogels to model peripheral nerve injury repair demonstrate their propensity for providing cell guidance along the length of the channels. Our results show promise for a micro-structured biomaterial that could aid in tissue repair applications.

Quantification of the Viscoelastic Effects During Polymer Flooding: A Critical Review

SummarySince the late 1960s, several enhanced–oil–recovery (EOR) researchers have developed various continuum and pore–scale viscoelastic models for quantifying the altered injectivity and incremental oil recovery because of the polymer's viscoelastic effects. In this paper, limitations in each of the continuum and pore–scale models are discussed. The critiques are made on the basis of the contradicting literature.Most of the earlier models rely on the exclusive use of the Deborah number to quantify the viscoelastic effects. The Deborah number overlooks mechanical–degradation effects. There exists a large difference in the magnitudes of the reported Deborah number in the literature because of the inconsistency in using different relaxation time and residential time. Oscillatory relaxation time used by most of the EOR researchers to calculate the Deborah number failed to distinguish the different porous–media behavior of the viscous and viscoelastic polymer. Therefore, the accuracy of relaxation time obtained from the weak oscillatory field for EOR applications in porous media is questionable. The main limitation with all the existing continuum viscoelastic models is the empirical reliance on coreflood data to predict the shear–thickening effects in porous media. The strain hardening index, needed for quantifying the thickening regime, cannot be obtained by the conventional shear rheological techniques. The conventional capillary number (Nc) failed to explain the reduction in residual oil saturation (Sor) during viscoelastic polymer flooding. Pore–scale viscoelastic models use the conventional oscillatory Deborah number for quantifying the polymer's viscoelastic effects on Sor reduction. However, this approach has many drawbacks.Discussions on the shortcomings of the existing viscoelastic models caution the current chemical EOR (cEOR) researchers about their applications and potential consequences. Also, this research provides a path forward for future research to address the limitations associated with the quantification of viscoelastic flow through porous media.

Brownian dynamics investigation of the Boltzmann superposition principle for orthogonal superposition rheology

The most general linear equation describing the stress response at time t to a time-dependent shearing perturbation may be written as the integral over the past history t' of a time dependent relaxation modulus, depending on t - t', multiplied by the perturbing shear rate at time t'. This is in agreement with the Boltzmann superposition principle, which says that the stress response of a system to a time dependent shearing deformation may be written as the sum of responses to a sequence of step-strain perturbations in the past. In equilibrium rheology, the Boltzmann superposition principle gives rise to the equality of the shear relaxation modulus, obtained from oscillatory experiments, and the stress relaxation modulus measured after a step-strain perturbation. In this paper, we describe the results of Brownian dynamics simulations of a simple soft matter system showing that the same conclusion does not hold when the system is steadily sheared in a direction perpendicular to the probing flows, and with a gradient parallel to that of the probing deformations, as in orthogonal superposition rheology. In fact, we find that the oscillatory relaxation modulus differs from the step-strain modulus even for the smallest orthogonal shear flows that we could simulate. We do find, however, that the initial or plateau levels of both methods agree and provide an equation relating the plateau value to the perturbation of the pair-function.

Oscillatory relaxation of zonal flows in a multi-species stellarator plasma

The low frequency oscillatory relaxation of zonal potential perturbations is studied numerically in the TJ-II stellarator (where it was experimentally detected recently for the first time in Alonso et al 2017 Phys. Rev. Lett. 118 185002). It is studied in full global gyrokinetic simulations of multi-species plasmas. The oscillation frequency obtained is compared with predictions based on single-species simulations using simplified analytical relations. It is shown that the frequency of this oscillation for a multi-species plasma can be accurately obtained from single-species calculations using extrapolation formulas. The damping of the oscillation and the influence of the different inter-species collisions is studied in detail. It is concluded that taking into account multiple kinetic ions and electrons with impurity concentrations realistic for TJ-II plasmas allows to account for the values of frequency and damping rate in zonal flows relaxations observed experimentally.

1/f electrophysiological spectra in resting and drug-induced states can be explained by the dynamics of multiple oscillatory relaxation processes

Neurophysiological recordings are dominated by arhythmical activity whose spectra can be characterised by power-law functions, and on this basis are often referred to as reflecting scale-free brain dynamics (1/fβ). Relatively little is known regarding the neural generators and temporal dynamics of this arhythmical behaviour compared to rhythmical behaviour. Here we used Irregularly Resampled AutoSpectral Analysis (IRASA) to quantify β, in both the high (5–100 Hz, βhf) and low frequency bands (0.1–2.5 Hz, βlf) in MEG/EEG/ECoG recordings and to separate arhythmical from rhythmical modes of activity, such as, alpha rhythms. In MEG/EEG/ECoG data, we demonstrate that oscillatory alpha power dynamically correlates over time with βhf and similarly, participants with higher rhythmical alpha power have higher βhf. In a series of pharmaco-MEG investigations using the GABA reuptake inhibitor tiagabine, the glutamatergic AMPA receptor antagonist perampanel, the NMDA receptor antagonist ketamine and the mixed partial serotonergic agonist LSD, a variety of effects on both βhf and βlf were observed. Additionally, strong modulations of βhf were seen in monkey ECoG data during general anaesthesia using propofol and ketamine. We develop and test a unifying model which can explain, the 1/f nature of electrophysiological spectra, their dynamic interaction with oscillatory rhythms as well as the sensitivity of 1/f activity to drug interventions by considering electrophysiological spectra as being generated by a collection of stochastically perturbed damped oscillators having a distribution of relaxation rates.

An insight into the interaction between functionalized thermoplastic elastomer and layered double hydroxides through rheological investigations

Abstract Nanocomposites based on maleated poly(styrene-(ethylene-co-butylene)-styrene) copolymer (SEBSgMA) and organo-modified layered double hydroxide (OLDH) have been formulated with the aim to investigate the effects of interfacial interactions between the grafted maleic anhydride groups of the copolymer and the OLDH nanolayers on the rheological properties of nanocomposites. The spectroscopic analysis indicates the establishment of specific polymer/nanofiller interactions, whose extent has been highlighted through morphological and rheological investigations. Specifically, oscillatory melt rheology and shear relaxation tests have been considered in order to deeply investigate the interfacial bridging interactions. Obtained results highlight that SEBSgMA-based nanocomposites containing a high amount of OLDH show solid-like rheological behavior, quite similar to that of crosslinked polymers, attributable to the formation of a gel-like structure.

Simulation of the linear rheological behavior of silica-filled, star-shaped SBR compounds

The rheological behavior of star-shaped SSBR/silica 60 phr compounds with different filler surface areas was experimentally studied and simulated using constitutive modeling. Rheological behavior was characterized in small amplitude oscillatory shear (SAOS) and stress relaxation after a small step shear. Unfilled SBR and SBR filled with four different silica grades with BET surface areas of 55, 135, 160, and 195 m2/g were used. A clear trend in rheological behavior was observed with surface area. A frequency sweep in the SAOS regime indicated an increase in dynamic properties with surface area. Additionally, linear stress relaxation tests at a strain level of 0.05 showed an increase in relaxation modulus with surface area and the presence of a plateau in the relaxation modulus at large times in compounds containing silica with high surface areas. The Leonov and Simhambhatla-Leonov models, modified to incorporate multimode particle network relaxation, were successfully used to simulate the frequency dependence of the storage modulus and the time evolution of the linear relaxation modulus for all samples. However, simulations of the frequency dependence of the loss modulus showed poor results in comparison with experimental data for the filled compounds.

Observation of Oscillatory Radial Electric Field Relaxation in a Helical Plasma

Measurements of the relaxation of a zonal electrostatic potential perturbation in a nonaxisymmetric magnetically confined plasma are presented. A sudden perturbation of the plasma equilibrium is induced by the injection of a cryogenic hydrogen pellet in the TJ-II stellarator, which is observed to be followed by a damped oscillation in the electrostatic potential. The waveform of the relaxation is consistent with theoretical calculations of zonal potential relaxation in a nonaxisymmetric magnetic geometry. The turbulent transport properties of a magnetic confinement configuration are expected to depend on the features of the collisionless damping of zonal flows, of which the present Letter is the first direct observation.