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The rheological characterization of complex liquids is of great importance in many applications. Among the properties that can be measured, the relaxation time has great relevance, as it provides a measure of fluid elasticity. In this work, we propose a novel method to estimate the longest relaxation time of viscoelastic fluids by applying machine learning to microfluidics. Specifically, we train a long-short term memory (LSTM) neural network to identify the Weissenberg number that characterizes the dynamics of trains of rigid particles suspended in a viscoelastic liquid flowing in a cylindrical microchannel. We first study the effect of the Weissenberg number on the evolution of the microstructure through numerical simulations. An in silico dataset consisting of the distributions of the interparticle distances at different channel sections is built and used to train the network. The performance of the LSTM model is tested on both classification and regression problems. The proposed method is nonintrusive, requires a simple setup, and can in principle be used to measure other properties of the fluid. [ABSTRACT FROM AUTHOR]

Knowledge of the evolution in the mechanical properties of a curing polymer matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear, is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint, we utilize a combined frequency- and amplitude-modulated chirped strain waveform in conjunction with a homemade sliding plate piezo-operated rheometer (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR, resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and, most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to subsecond scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast-curing resins. The method is validated via calibration tests in both instruments, and the corresponding limitations are discussed. As a proof of concept, the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 s to monitor the rapid evolution in the time and frequency dependence of the complex modulus. Comparison of the chirp implementation, based on parameters such as duration of the experiment, sampling frequency, and frequency range, in a commercial rotational rheometer with the PZR provides further information on the applicability of this technique and its limitations. Finally, FTIR spectroscopy is utilized to gain insights into the evolution of the chemical network, and the gap dependence of the evolving material properties in these heterogeneous systems is also investigated. [ABSTRACT FROM AUTHOR]

Knowledge of the evolution in the mechanical properties of a curing polymer matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear, is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint, we utilize a combined frequency- and amplitude-modulated chirped strain waveform in conjunction with a homemade sliding plate piezo-operated rheometer (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR, resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and, most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to subsecond scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast-curing resins. The method is validated via calibration tests in both instruments, and the corresponding limitations are discussed. As a proof of concept, the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 s to monitor the rapid evolution in the time and frequency dependence of the complex modulus. Comparison of the chirp implementation, based on parameters such as duration of the experiment, sampling frequency, and frequency range, in a commercial rotational rheometer with the PZR provides further information on the applicability of this technique and its limitations. Finally, FTIR spectroscopy is utilized to gain insights into the evolution of the chemical network, and the gap dependence of the evolving material properties in these heterogeneous systems is also investigated. [ABSTRACT FROM AUTHOR]

Rheological characterization of complex fluids subjected to cyclic shear-rate sweep often exhibits hysteresis. Since both viscoelastic and thixotropic materials show hysteresis loops, it is important to understand distinguishing features (if any) in the same shown by either. Lately, there has been substantial work that attempts to relate the area enclosed by the hysteresis loop with the manner in which shear rate is varied in the cycle, in order to infer thixotropic parameters of a material. In this work, we use the nonlinear Giesekus model to study its response to the application of cyclic shear-rate sweep. We find that this model produces each type of qualitatively similar hysteresis loop that has hitherto been ascribed to thixotropic materials. We also show that the area of the hysteresis loop for a viscoelastic material as a function of sweep rate shows bell-shaped/bi-modal curves as has been observed for thixotropic materials. This study illustrates that caution needs to be exercised while attributing hysteresis loops and associated features observed in a material exclusively to thixotropy. Another feature related to the hysteresis loop is the occurrence of shear banding instability. We find that viscoelastic hysteresis may not have any connection to shear banding instability. [ABSTRACT FROM AUTHOR]

The inference of the spectral function representing the relaxation process of a material is an ill-posed problem and regularization is key to solving such problems. Significant information about molecular structure can be found from the relaxation time spectra of materials, such as polymers and soft materials. Various deterministic data-driven methods including L-curve and generalized cross-validation in Tikhonov regularization have been employed in the literature to find the optimal regularization parameter. The application of Bayesian techniques for solving such ill-posed inverse problems has gained significant interest in recent years due to the increasing availability of computational resources. In this work, we formulate the inverse problem in a hierarchical Bayesian framework and consider the degree of regularization as a stochastic quantity and the relaxation spectra as the high-dimensional model parameters. Using synthetic and real data (frequency-dependent storage and loss moduli), this novel approach is employed to characterize the linear viscoelastic response of materials and obtain sparse probabilistic solutions to regression. The computations are carried out using Metropolis–Hastings-within-Gibbs sampling. Numerical results demonstrating the performance of the hierarchical Bayesian approach and comparisons with the deterministic L-curve approach are presented. [ABSTRACT FROM AUTHOR]

Owing to nonlinear viscoelasticity, materials often show characteristic features that resemble those of thixotropy. This issue has been debated in the literature over the past several decades, and several experimental protocols have been proposed to distinguish thixotropy from viscoelasticity. In this work, we assess these protocols by carrying out experiments using polymer solutions, thixotropic clay dispersions, and modeling their behavior, respectively, using the finitely extensible nonlinear elastic—Peterlin (FENE-P) constitutive equation and a viscoelastic aging model. We find that the criteria proposed in the literature, such as a step-down jump in the shear rate and shear start-up at different waiting times elapsed since preshear, are inadequate to distinguish thixotropy from viscoelasticity. In marked contrast, we show that the application of step-strain or step-stress after cessation of the preshear serves as a useful discriminant between thixotropy and viscoelasticity. In thixotropic materials, we observe that the application of step strain (or step stress) after cessation of the preshear eventually leads to slowing down of relaxation dynamics as a function of waiting time. However, for viscoelastic materials, the relaxation modulus (creep compliance) curve shifts to lower modulus (higher compliance) values as a function of waiting time until equilibrium is reached. While the proposed criterion offers a robust distinction between viscoelasticity and thixotropy for the systems studied here, further experimental investigations based on other systems are needed to establish its versatility and will lead to a greater insight into this long-standing issue in rheological categorization. [ABSTRACT FROM AUTHOR]

A new mathematical representation for nonlinear viscoelasticity is presented based on the application of the Volterra series expansion to the general nonlinear relationship between shear stress and shear strain history. This theoretical and experimental framework, which we call medium amplitude parallel superposition (MAPS) rheology, reveals a new material property, the third-order complex modulus, which describes completely the weakly nonlinear response of a viscoelastic material in an arbitrary simple shear flow. In this first part, we discuss several theoretical aspects of this mathematical formulation and new material property. For example, we show how MAPS measurements can be performed in strain- or stress-controlled contexts and provide relationships between the weakly nonlinear response functions measured in each case. We show that the MAPS response function is a superset of the response functions that have been previously reported in medium amplitude oscillatory shear and parallel superposition rheology experiments. We also show how to exploit inherent symmetries of the MAPS response function to reduce it to a minimal domain for straightforward measurement and visualization. We compute this material property for a few constitutive models to illustrate the potential richness of the datasets generated by MAPS experiments. Finally, we discuss the MAPS framework in the context of some other nonlinear, time-dependent rheological probes and explain how the MAPS methodology has a distinct advantage over these others because it generates data embedded in a very high-dimensional space without driving fluid mechanical instabilities, and is agnostic to the flow protocol. [ABSTRACT FROM AUTHOR]

We characterize the yield behavior and flow curve of a commercially available, molten, tempered milk chocolate with a fat content of 30%, from rheological measurements performed with a rotational rheometer fitted with a four-bladed vane spindle in a large-gap setup. We show that the yield behavior can be captured by the viscoelastic White–Metzner model, which indicates that elastic deformation precedes flow as the shear stress is increased. Following an initial fluidization cycle, the shear modulus of the tempered chocolate increases by a factor of 60 to G = 4.4 × 10 4 Pa. We find that the Bingham model provides the best fit to our extensive flow curve data, where the yield stress is τ yield = 36.1 ± 0.6 Pa and the Newtonian plateau viscosity is μ B = 8.7 ± 0.02 Pa s. [ABSTRACT FROM AUTHOR]

A well-known Phan-Thien and Tanner differential viscoelastic constitutive equation has been employed to analyze the nonlinear stability and dynamics of nonisothermal film casting. A finite element method combined with stabilization techniques including discrete elastic viscous stress splitting and the streamline upwind Petrov-Galerkin method was first performed for the numerical calculation of transient film casting. Therefore, the stability analysis of film casting was carried out based on a wider parameter space of processing and the rheological properties of the polymer melt, during which the critical draw ratio for the occurrence of draw resonance (Drc) was taken as an indicator for flow stability. Unlike the results predicted by the upper-convected Maxwell model, the stabilizing region upon an upper critical draw ratio is nonexistent, while more than one peak of Drc was observed with varying aspect ratios, which was dominated by two deformation types named planar and transitional deformations, respectively. Our simulation results show that elongational rheological behavior plays a dominant role in the stability of flow for both extensional-thickening and extensional-thinning fluids, while the effects of processing parameters such as extrusion rate and cooling and rheological parameters such as relaxation time on Drc all can be attributed to elongational viscosity. [ABSTRACT FROM AUTHOR]

Oscillatory and steady shear of cellulose in 1-ethyl-3-methylimidazolium methylphosphonate {[EMIm][P(OCH3)(H)O2]} were studied for cellulose concentrations from 0.017 to 10 wt. %, spanning the dilute, semidilute unentangled and entangled regimes. The overlap concentration of our cellulose in [EMIm][P(OCH3)(H)O2] is 0.065 wt. % and the entanglement concentration is 8× larger (0.5 wt. %). The concentration dependences of specific viscosity, relaxation time, and terminal modulus suggest that [EMIm][P(OCH3)(H)O2] is a good solvent for cellulose. Compared with the cellulose/1-butyl-3-methyl imidazolium chloride ([BMIm]Cl) system, this native cellulose in [EMIm][P(OCH3)(H)O2] has lower c* and ce, and much higher extent of entanglement. A significantly wider than expected rubbery plateau for the entangled solutions and failure of the Cox–Merz rule suggest that cellulose in [EMIm][P(OCH3)(H)O2] is not simply a flexible polymer in a good solvent. The relaxation mode distribution in the terminal regime is much broader for cellulose in [EMIm][P(OCH3)(H)O2] compared with the same cellulose in [BMIm]Cl. The delocalized phosphonate anion likely binds to hydroxyl groups on multiple cellulose chains, acting as temporary crosslinks. [ABSTRACT FROM AUTHOR]

Elastoviscoplastic materials present a transition from a gel-like to a liquidlike state induced by shearing: While the first is primarily elastic, the second is predominantly viscous. The point that characterizes this transition is usually known as the yield point, which is associated to critical quantities such as yield stress and/or yield strain. Another characteristic of elastoviscoplastic materials is the transition from linear to nonlinear viscoelasticity. In the current work, a commercial hair gel, which is an elastoviscoplastic material, was tested in two rotational rheometers in order to evaluate these two transition points. Stress oscillatory amplitude sweeps at different frequencies were performed and a Fourier-Transform analysis was applied to the results in order to determine the linear viscoelastic limit. The linear viscoelastic limit stresses and strains at different frequencies were then compared to quantities that are usually associated to the yield point: The extrapolated zeroshear-rate stress obtained from the equilibrium flow curve, the minimum stress required to start up flows in creep experiments, the stress overshoot reached in constant shear rate experiments and the G0-and-G00 crossover stress determined through oscillatory amplitude sweeps. The results showed that the stresses and strains obtained as the linear viscoelastic limits were smaller than the critical quantities associated to the yield point for all evaluated cases. Although the critical quantities depend on the experimental condition, the linear viscoelastic limit strain was remarkably constant. Additionally, the linear viscoelastic limit strain was found to be in the same order of magnitude of the strain that characterizes the onset of plastic behavior in recovery experiments. This suggests that the beginning of the transition from a completely structured state of elastoviscoplastic materials to an unstructured state might be associated to the threshold of nonlinear viscoelasticity. [ABSTRACT FROM AUTHOR]

This work investigates the effect a fractional derivative may have on the spectrum of relaxation modes of a viscoelastic material. It is shown that the order of the fractional derivative results in a modification to the constitutive relationships that exist within the Rouse model for viscoelasticity. These relationships that are used in engineering analyses have been previously developed from an empirical standpoint. The resulting modification to these constitutive relationships further supports the inclusion of fractional calculus in models of viscoelastic materials and hence increase their level of confidence associated with their usage. [ABSTRACT FROM AUTHOR]

Failure of polymer liquids under flow has been the subject of a relatively strong computational, theoretical, and experimental effort over the years, despite which a clear picture of the phenomenon is still nonexistent. For example, there are still arguments in the literature whether the maximum in engineering stress, also known as the Considère limit for failure, is a point of true yielding of the polymer network or simply a purely elastic mechanical instability and if this onset of yielding also corresponds to the true onset of non-homogeneous deformation, as expressed for example by necking. The main objective of the present work is to contribute to the ongoing discussion on this matter by studying a linear polyisobutylene melt in terms of its failure and rupture behavior in both the viscoelastic and purely elastic deformation regimes of deformation showing that homogeneous flow still occurs after the maximum in engineering stress and quantifying this deviation. This is ultimately connected with the observation of a limiting stress at rupture in the rubbery (elastic) regime. From the results, it is apparent that, for this particular polydisperse melt and in the viscoelastic regime, the Considère criterion underestimates by approximately 60% the point of onset of non-homogeneous deformation, i.e., necking. The calculated true onset of failure, on the other hand, agrees almost exactly with the visually determined onset. However, it is clear that a general working criterion for failure of entangled polymer melts, especially in the all-important viscoelastic deformation regime, is still lacking. [ABSTRACT FROM AUTHOR]

In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference. [ABSTRACT FROM AUTHOR]

The inertialess three-dimensional (3D) flow of viscoelastic shear-thinning fluids in a 4:1 sudden square-square contraction was investigated experimentally and numerically and compared with the flow of inelastic fluids. Whereas for a Newtonian fluid the vortex length remains unchanged at low Reynolds numbers, with the non-Newtonian fluid there is a large increase in vortex length with fluid elasticity leading to unstable periodic flow at higher flow rates. In the steady flow regime the vortices are 3D and fluid particles enter the vortex at the middle plane, rotate towards its eye, drift sideways to the corner-plane vortex, rotate to its periphery, and exit to the downstream duct. Such dynamic process is reverse of that observed and predicted with Newtonian fluids. Numerical predictions using a multimode Phan-Thien–Tanner viscoelastic model are found to match the visualizations accurately and in particular are able to replicate the observed flow reversal. The effect of fluid rheology on flow reversal, vortex enhancement, and entry pressure drop is investigated in detail. [ABSTRACT FROM AUTHOR]

The transient and steady-state elongational viscosity data of three bidisperse polystyrene blends were investigated recently by Nielsen et al. [J. Rheol. 50, 453–476 (2006)]. The blends contain a monodisperse high molar mass component (ML=390 kg/mol) in a matrix of a monodisperse small molar mass component (either MS=103 kg/mol or MS=52 kg/mol at two different weight fractions). The experimental data are analyzed in the framework of the molecular stress function model of Wagner et al. [J. Rheol. 49, 1317–1327 (2005)], which is based on the assumption of a strain-dependent tube diameter and the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37, 3934–3942 (2004)]. The dilution of the long chains in the matrix of the short chains is identified as the origin of a drastic increase in the tube-diameter relaxation time of the long chains, leading to a large stretching potential of the long-chain component and an increasing steady-state elongational viscosity with increasing strain rate. In addition, in the dilution regime, a transition from affine chain stretch to nonaffine tube squeeze with decreasing strain rate is identified. The dilution regime ends at a critical strain rate, when the tube diameter of the supertubes created by the interaction of the long chains among themselves, is reduced by deformation to the tube diameter of the bulk. A nonlinear extension of the basic double reptation concept is developed comprising all of these different phenomena, and allowing (albeit by use of empirical linear-viscoelastic shift factors to correct the linear-viscoelastic predictions) for a quantitative description of the transient and steady-state elongational viscosities of the bidisperse polystyrene blends. [ABSTRACT FROM AUTHOR]

Several internal parameters are studied for a 3D simple shear flow of soft polydispersed granular materials consisting of viscoelastic spheres. These internal parameters include the contact time, the multiple collision group size, and the coordination number. It is found that the contour plots of the contact time and the coordination number in the plane defined by the concentration (solid fraction) and dimensionless stiffness are similar. These contours are qualitatively the same as the regime chart/flowmap proposed in earlier studies. The resulting constitutive relation shows different rate dependency at different concentrations and shear rates. Based on a simple dimensional analysis and a power law formulation, the rate dependency may be expressed by an index. The two extreme values of this index, 0 and 1, correspond to solidlike and gaslike granular materials, respectively. The contour map of this rate index (the power of the dimensionless shear rate in the constitutive relation) resembles those of the λ-shaped curve typical of a phase diagram for ordinary materials. [ABSTRACT FROM AUTHOR]

The breakdown of finite element (FEM) computations for the steady symmetric two-dimensional flow of dilute and ultradilute Oldroyd-B fluids around a cylinder in a channel, at Weissenberg numbers Wi=O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules in the wake of the cylinder in the vicinity of the location of the stress maximum on the centerline. In dilute Oldroyd-B fluids, due to the modification of the flow caused by the presence of the polymer, the coil-stretch transition leads to the stress maximum diverging toward infinity at a finite value of Wi≈0.7. On the other hand, in ultradilute solutions, the stress maximum approaches infinity only as Wi→∞. In FENE-P fluids, the coil-stretch transition leads to the mean extension of the molecules saturating to a value close to the fully-extended length, with the maximum stress remaining bounded with increasing Wi. An estimation of the number of finite elements required to achieve convergence for ultradilute Oldroyd-B fluids reveals that obtaining solutions at Wi>1 is not feasible. [ABSTRACT FROM AUTHOR]

When coal is heated in the absence of oxygen it softens at approximately 400 °C, becomes viscoelastic, and volatiles are driven off. With further heating, the viscous mass reaches a minimum viscosity in the range of 103–105 Pa s and then begins to resolidify. A high-torque, high-temperature, controlled-strain rheometer with parallel plates has been used to study the rheology during this process. Under shear, the viscosity of the softening mass decreases with increasing shear rate. During resolidification, the viscosity increases as C-C bond formation and physical interactions gives rise to an aromatic network, but, under shear, the network breaks apart and flows. This is viewed as a yielding of the structure. The higher the shear rate, the earlier the yielding occurs, such that if the shear rate is low enough, the structure is able to build. Also, further into resolidification lower shear rates are able to break the structure. It is proposed that resolidification occurs through the formation of aromatic clusters that grow and become cross-linked by non-covalent interactions. As the clusters grow, the amount of liquid surrounding them decreases and it is thought that the non-covalent interactions between clusters and liquid could decrease and the ability of growing clusters to move past each other increases, which would explain the weakening of the structure under shear. This work is part of a program of work aimed at attaining a greater understanding of microstructural changes taking place during carbonization for different coals, in order to understand the mechanisms that give rise to good quality cokes and coke oven problems such as excessive wall pressure. [ABSTRACT FROM AUTHOR]

Viscoelastic properties are followed during the formation of gels by moderately concentrated solutions of atactic polystyrene (aPS) in a mixed solvent of carbon disulfide and tri-m-tolyl phosphate (TCP). This mixture is a thermodynamically “good” solvent for aPS and with solution glass transition temperatures far below the temperatures used in the study. Gel formation is driven by the CS2 component, at temperatures and polymer concentrations similar to those observed in solutions of aPS in pure CS2. The TCP adjusts the viscoelastic response to a convenient range. The results show appreciable hysteresis in the melting and formation temperatures of gels, with the gel formation being a slow process, permitting dynamic mechanical or creep and creep recovery studies as a function of ageing during gel formation, as well as on the solutions prior to permit gel formation. These data reveal systematic behavior analyzed using the linear viscoelastic constitutive relation to obtain the viscosity and a measure of the steady-state recoverable compliance prior to gel formation and the equilibrium compliance after gel formation. This behavior is discussed in terms of models in which segments of the backbone possess a helical conformation stabilized by interactions with CS2 and gel crosslink loci formed via these sequences. [ABSTRACT FROM AUTHOR]