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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]

Nonlinear rheology of Pickering emulsions is used to further investigate the nonlinear and unrecoverable transformation of inner structures, which is beyond the linear viscoelastic regime of tiny structural disturbances. Exploring various rheological methods plays a vital role in emulsion applications, such as simulating the macroscopic structural transformation between static and liquidlike flow states, strain overshoot, and regeneration for broken structures. According to our previous studies, cellulose nanofibers (CNFs) Pickering emulsions are a typical system for investigating polymer-based emulsions with the auxiliary surfactant [didodecyldimethylammonium bromide (DDAB)] for enhancing CNF absorption. To further study different rheological properties by varying CNF or DDAB contents, multiple interval thixotropic test, large amplitude oscillatory shear, and concentration-time-dependent superposition are employed to study the linear viscoelasticity and structural transformation of nonlinear range. This research was conducted based on the previous published works [Cui et al., Materials 15, 8285 (2022)] as a further characterization for the same sample series. [ABSTRACT FROM AUTHOR]

We study theoretically the steady viscoelastic flow in confined and symmetric hyperbolic channels considering slip along the walls. Under the lubrication approximation and a variety of constitutive models, a high-order perturbation solution with respect to the Deborah number is calculated. The solution for all the field variables (velocity, pressure, and extra-stress) is found analytically up to eighth order and is used along with proper acceleration techniques to achieve convergence up to order one Deborah number. We reveal that even in the presence of slip, the pressure drop decreases monotonically with increasing the fluid elasticity. We evaluate the influence of slip in terms arising from two different decompositions of the pressure drop obtained with the aid of the total force balance and the mechanical energy balance of the flow system. In contrast to the nonslip Newtonian flow, our analysis also showed that the fluid slip along the walls introduces variations in the strain rate at the midplane with the distance from the inlet. However, these are small, and an effective strain rate can be well-represented using a previously developed formula [Housiadas, K. D., and A. N. Beris, Phys. Fluids 36(2), 021702 (2024)]. We also show that when the solution for the midplane velocity is used in the general formula for the Trouton ratio, instead of the Newtonian lubrication solution, there are no appreciable changes, thus confirming the validity and accuracy of our previously reported results [Housiadas, K. D., and A. N. Beris, J. Rheol. 68(3), 327–339 (2024)]. [ABSTRACT FROM AUTHOR]

We study theoretically the elongational viscosity (or Trouton ratio, in dimensionless form) for steady viscoelastic flows in confined and symmetric hyperbolic tubes considering Navier-type slip along the wall(s). Both the planar and the cylindrical axisymmetric geometrical configurations are addressed. Under the classic lubrication approximation, and for a variety of constitutive models such as Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic with the Peterlin approximation models, the same general analytical formula for the Trouton ratio is derived as for the Oldroyd-B model, in terms of the velocity at the midplane/axis of symmetry and the Deborah number only. Assuming that the velocity field is approximated by the Newtonian lubrication profile, based on our previous study in the absence of slip, we show that a constant extensional strain rate can be achieved in the limits of zero or infinite slip. For finite slip, a slight modification of the geometry is required to achieve a constant strain rate. In these cases, the formula for the steady state Trouton ratio reduces to that for transient homogeneous elongation. We also provide analytical formulae for the modification (decrease) for both the extensional strain rate and the Hencky strain achieved in the confined geometries because of introducing wall slip. [ABSTRACT FROM AUTHOR]

We use nonequilibrium atomistic molecular dynamics simulations of unentangled melts of linear and star oligomer chains ( C 25 H 52 ) to study the steady-state viscoelastic response under confinement within nanoscale hematite (α − F e 2 O 3) channels. We report (i) the negative (positive) first (second) normal stress difference and (ii) the presence of viscoelastic tension at low W i. With the aim of uncovering the molecular mechanism of viscoelasticity, we link these effects to bond alignment such that absorbed chains near the surface can carry the elastic force exerted on the walls, which decays as the chains become more aligned in the flow direction. This alignment is observed to be independent of the film thickness but enhanced as the shear rate increases or the surface attraction weakens. [ABSTRACT FROM AUTHOR]

Thixotropy, antithixotropy, and viscoelasticity are three types of time-dependent dynamics that involve fundamentally different underlying physical processes. Here, we show that the three dynamics exhibit different signatures in hysteresis by examining the fingerprints of the simplest thixotropic kinetic model, a new antithixotropic model that we introduce here, and the Giesekus model. We start by showing that a consistent protocol to generate hysteresis loops is a discrete shear-rate controlled ramp that begins and ends at high shear rates, rather than at low shear rates. Using this protocol, we identify two distinguishing features in the resulting stress versus shear rate loops. The first is the direction of the hysteresis loops: clockwise for thixotropy, but counterclockwise for viscoelasticity and antithixotropy. A second feature is achieved at high ramping rates where all responses lose hysteresis: the viscoelastic response shows a stress plateau at low shear rates due to lack of stress relaxation, whereas the thixotropic and antithixotropic responses are purely viscous with minimal shear thinning or thickening. We establish further evidence for these signatures by experimentally measuring the hysteresis of Laponite suspensions, carbon black suspensions, and poly(ethylene oxide) solutions, each representing a historically accepted example of each class of material behavior. The signatures measured in experiments are consistent with those predicted by the three models. This study reveals different fingerprints in hysteresis loops associated with thixotropy, antithixotropy, and viscoelasticity, which may be helpful in distinguishing the three time-dependent responses. [ABSTRACT FROM AUTHOR]

This study discusses the feasibility of using a combined torsional-axial rheometer to indirectly measure the complex Poisson's ratio based on shear and Young's modulus. For this purpose, isothermal frequency sweeps in torsion and extension are performed sequentially on the same cylindrical specimen and under the same environmental conditions. The method is tested on two amorphous polymers, a semicrystalline polymer, a polymer blend, and a copolymer. The article includes an extensive literature review and an uncertainty assessment of the method to provide a basis for subsequent data comparison with existing research. The experimental data show a monotonic increase in the complex Poisson's ratio up to 0.5 as the temperature approaches α-relaxation for all samples, except for the amorphous polymer. The latter shows a local minimum in the complex Poisson's ratio observed near α-relaxation, which disappears after thermal annealing of the sample above the α-relaxation temperature. The real and imaginary parts of the complex Poisson's ratio are additionally determined by evaluating both phase shift angles from torsional and extensional measurements. All polymers show a certain offset between the torsional and extensional phase shift angles in the glassy state, which gradually decreases as the temperature approaches α-relaxation. The complex Poisson's ratio results are in good agreement with the literature data obtained by existing methods. This confirms that the method is applicable to polymers up to α-relaxation temperatures with significant time savings due to the nondestructive approach. This is of particular interest, given the limited availability of data in the literature. [ABSTRACT FROM AUTHOR]

In a recent paper [Hassager, J. Rheol. 64, 545–550 (2020)], Hassager performed an analysis of the start up of stress-controlled oscillatory flow based on the general theory of linear viscoelasticity. The analysis provided a theoretical basis for exploring the establishment of a steady strain offset that is inherent to stress controlled oscillatory rheometric protocols. However, the analysis neglected the impact of instrument inertia on the establishment of the steady periodic response. The inclusion of the inertia term in the framework is important since it (i) gives rise to inertio-elastic ringing and (ii) introduces an additional phase shift in the periodic part of the response. Herein, we modify the expressions to include an appropriate inertial contribution and demonstrate that the presence of the additional terms can have a substantial impact on the time scale required to attain the steady state periodic response. The analysis is then applied to an aqueous solution of wormlike micelles. [ABSTRACT FROM AUTHOR]

The trade-off between hardness and stretchability is a cornerstone of materials science. Balancing this trade-off is important in the molecular design of both chemical and physical networks. In this study, we report the quantitative trade-off at the molecular level for physical networks. Namely, we analyze, based on the reversible gelation model, a scaling relationship between the characteristic terminal relaxation modulus Gc in linear viscoelasticity and the stretch ratio λmax at the stress overshoot during the nonlinear elongation flow for unentangled randomly associative polymers, i.e., λmax ∼ Gc−0.17 and λmax ∼ Gc−0.33 in the mean-field and critical-percolation regimes, respectively. We use sulfonated polystyrene having different alkali counterions as a model system to test the relationship. The exponent of λmax ∼ Gc−0.25 seen in the experiment is in between the two theoretical values. We also discuss the quantitative deviation with respect to the size distribution of the network strands. [ABSTRACT FROM AUTHOR]

Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is "ultradilute", the extensional viscosity is well described by Peterlin's finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement. [ABSTRACT FROM AUTHOR]

Programmable hydrogels, such as thiolated hydrogels, are frequently used for tissue engineering and drug delivery applications, because they offer the ability to control gelation, degradation, and adhesion. Understanding how the mechanical properties of these materials change during these processes is essential as they directly impact cell fate and delivery efficacy. The rheology of hydrogels has been quantified primarily via bulk rheological methods. While such methods are effective, they require large sample volumes and result in the destruction of the sample; therefore, responses to multiple stimuli must be recorded across many different samples. We have developed a magnetic microwire rheometer that can characterize the rheology of small sample volumes while maintaining the integrity of the sample, such that the material response to a range of stimuli can be recorded for a single sample. This capability enables insights into time-dependent rheological changes, such as gelation and degradation, and can be applied to characterize dynamic in situ systems that are the basis for tissue scaffolding, drug delivery vehicles, and other important biological applications. [ABSTRACT FROM AUTHOR]

Mud is a suspension of fine-grained particles (sand, silt, and clay) in water. The interaction of clay minerals in mud gives rise to complex rheological behaviors, such as yield stress, thixotropy, and viscoelasticity. Here, we experimentally examine the flow behaviors of kaolinite clay suspensions, a model mud, using steady shear rheometry. The flow curves exhibit both yield stress and rheological hysteresis behaviors for various kaolinite volume fractions (ϕ k). Further understanding of these behaviors requires fitting to existing constitutive models, which is challenging due to numerous fitting parameters. To this end, we employ a Bayesian inference method, Markov chain Monte Carlo, to fit the experimental flow curves to a microstructural viscoelastic model. The method allows us to estimate the rheological properties of the clay suspensions, such as viscosity, yield stress, and relaxation time scales. The comparison of the inherent relaxation time scales suggests that kaolinite clay suspensions are strongly viscoelastic and weakly thixotropic at relatively low ϕ k , while being almost inelastic and purely thixotropic at high ϕ k. Overall, our results provide a framework for predictive model fitting to elucidate the rheological behaviors of natural materials and other structured fluids. [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]

Mixtures of polymers of varying topologies and stiffnesses display complex emergent rheological properties that often cannot be predicted from their single-component counterparts. For example, entangled blends of ring and linear polymers have been shown to exhibit enhanced shear thinning and viscosity, as well as prolonged relaxation timescales, compared to pure solutions of rings or linear chains. These emergent properties arise in part from the synergistic threading of rings by linear polymers. Topology has also been shown to play an important role in composites of flexible (e.g., DNA) and stiff (e.g., microtubules) polymers, whereby rings promote mixing while linear polymers induce demixing and flocculation of stiff polymers, with these topology-dependent interactions giving rise to highly distinct rheological signatures. To shed light on these intriguing phenomena, we use optical tweezers microrheology to measure the linear and nonlinear rheological properties of entangled ring-linear DNA blends and their composites with rigid microtubules. We show that linear viscoelasticity is primarily dictated by microtubules at lower frequencies, but their contributions become frozen out at frequencies above the DNA entanglement rate. In the nonlinear regime, we reveal that mechanical response features, such as shear thinning and stress softening, are mediated by entropic stretching, threading, and flow alignment of entangled DNA, as well as forced dethreading, disentanglement, and clustering. The contributions of each of these mechanisms depend on the strain rate as well as the entanglement density and stiffness of the polymers, leading to nonmonotonic rate dependences of mechanical properties that are most pronounced for highly concentrated ring-linear blends rather than DNA-microtubule composites. [ABSTRACT FROM AUTHOR]

We provide a canonical introduction to dual-junction-functionality associative polymer networks, which combine high and low functionality (f) dynamic cross-link junctions to impart load-bearing, dissipation, and self-repairing ability to the network. This unique type of network configuration offers an alternative to traditional dual-junction networks consisting of covalent and reversible cross-links. The high-f junctions can provide load-bearing abilities similar to a covalent cross-link while retaining the ability to self-repair and concurrently confer stimuli-responsive properties arising from the high-f junction species. We demonstrate the mechanical properties of this design motif using metal-coordinating polymer hydrogel networks, which are dynamically cross-linked by different ratios of metal nanoparticle (high-f) and metal ion (low-f) cross-link junctions. We also demonstrate the spontaneous self-assembly of nanoparticle-cross-linked polymers into anisotropic sheets, which may be generalizable for designing dual-junction-functionality associative networks with low volume fraction percolated high-f networks. [ABSTRACT FROM AUTHOR]

Existing single-chain models for unentangled associating polymers account for the association by assigning the sticky junctions a large value of the monomeric friction coefficient, which prevents them from moving in space unless stickers effectively dissociate. With such an assumption, comparison of model predictions with linear viscoelastic data is not fully successful in the intermediate range of frequency. In this work, we improve agreement with data by developing a single-chain model where sticky junctions are allowed to quickly move in space without dissociating. We also account for a random distribution of the stickers but differently from the recent model by Jiang et al. [Macromolecules 53, 3438–3451 (2020)]. Predictions of the model are successfully compared with unentangled melt data for two different copolymer chemistries and different sticker concentrations. Particularly significant are the data by Cui et al. [J. Rheol., 62, 1155–1174 (2018)] of melts of polymers with only two stickers per chain, revealing that sticky junctions are in fact also endowed with fast mobility. [ABSTRACT FROM AUTHOR]

This study examines the linear viscoelasticity of double-associative ionomers based on poly(hexyl methacrylate). The ionomer samples are unentangled and contain a fixed number of ionic stickers per chain, f ion ≅ 4 , but a varied number of hydrogen-bonding stickers per chain, fH = 5.5–27. Increasing fH has distinct effects on the glassy and rubbery dynamics. On the one hand, the glassy relaxation mode distribution broadens, and the glassy-to-rubbery transition region delays significantly with increasing fH. On the other hand, the delay of the ionic dissociation and, accordingly, the terminal relaxation (activated by continuous ionic dissociations) are much weaker. This contrast suggests that the ionic dissociation is not only activated by the segmental motion of the main backbone but is also partly activated by the motion of the side chains that is less dependent on fH. [ABSTRACT FROM AUTHOR]

We report the linear rheology for dense suspensions of sterically stabilized smooth and mesoscopically rough colloids interacting as hard particles. Small amplitude oscillatory measurements reveal that rough colloids at high volume fractions exhibit storage and loss moduli that are orders of magnitude greater than smooth colloids. Frequency-concentration superposition is used to collapse the viscoelasticity data onto a master curve, where shift factors suggest a more elastic microstructure and reduced cage volume for rough particles. A combination of the mode-coupling theory, hydrodynamic modeling, and the activated hopping theory shows that these rough particles with significantly reduced localization lengths tend to become trapped in their glassy cages for extended periods of time. High-frequency data show that rough colloids, but not smooth colloids, display a transition from a free-draining to a fully lubricated state above the crossover volume fraction and, furthermore, exhibit solidlike behavior. Scaling analyses support the idea that lubrication forces between interlocking asperities are enhanced, leading to rotational constraints and stress-bearing structures that significantly elevate the viscoelasticity of dense suspensions. The results provide a framework for how particle surface topology affects the linear rheology in applications such as coatings, cement, consumer products, and shock-absorbing materials. [ABSTRACT FROM AUTHOR]

We report a detailed experimental study of peculiar thixotropic dynamics of carbon black (CB, Vulcan XC-72) suspensions in mineral oil, specifically the observation of sequential stress increase then decrease at a fixed shear rate in a step-down test. We verify that such dynamics, though peculiar, come from a true material response rather than experimental artifacts. We also reveal how this long-time stress decay is associated with antithixotropic structural change rather than viscoelastic stress relaxation by using orthogonal superposition (OSP) rheometry to probe viscoelastic moduli during the step-down tests. The orthogonal storage and loss moduli are present, showing this two-timescale recovery then decay response, which demonstrates that this response is antithixotropic, and it involves shear-induced structuring. We further show a mechanical anisotropy in the CB suspension under shear using OSP. Based on the rheological results, a microstructural schematic is proposed, considering qualitatively thixotropic structure build-up, antithixotropic densification, and anisotropic structure evolution. Our observation for these CB suspensions is outside the standard paradigm of thixotropic structure-parameter models, and the elastic response provides us with new insight into the transient dynamics of CB suspensions. [ABSTRACT FROM AUTHOR]

We use molecular dynamics (MD) simulations in conjunction with the probe rheology technique to investigate the linear viscoelasticity of nanocolloidal suspensions. A particulate model of the solvent is used in which the hydrodynamics is governed by interparticle interactions. Active and passive probe rheology molecular simulations are performed on the colloidal suspensions of different volume fractions ranging from 0.30 to 0.45 to determine the linear viscoelastic properties of these systems. The viscoelastic modulus of the suspensions is obtained by analyzing the probe motion using continuum mechanics. In active rheology, the distribution of colloid particles around the probe is observed to be symmetric indicating that the system is in the linear regime at all conditions investigated. In passive rheology, the mean-squared displacement of the probe covers the range of motion from ballistic to diffusive regimes. The dynamic modulus and the reduced complex viscosity values obtained from probe rheology simulations are in good agreement with the results from the oscillatory nonequilibrium MD (NEMD) simulations and the literature theoretical predictions. At low frequency values, accounting for artificial hydrodynamic interactions between the probe and its periodic images improves the quantitative accuracy of the modulus values obtained from simulations. Simulations carried out using probes of different sizes indicate that only the probes that are larger than the colloids yield viscoelastic modulus values that are in good agreement with the NEMD values at all volume fractions investigated. [ABSTRACT FROM AUTHOR]

A thorough study is made of the dependences on salt concentration and polymer chain lengths of the low-frequency plateau of coacervates of poly (diallyl dimethyl ammonium chloride), PDADMAC, and poly (sodium 4-styrenesulfonate), PSS. The reliability and reproducibility of these measurements are carefully checked by determining the frequency-dependent stress limits of the rheometer through the use of reference fluids and by repeat experiments with coacervates. Long-time frequency sweeps show that coacervates with less salt are more repeatable than those with higher salt. A low-frequency plateau reliably appears only below a critical salt concentration, and the magnitude of the plateau depends strongly on salt concentration and chain lengths of both polycation and polyanion. It is only present for the molecular weight of the polycation, PDADMAC, higher than 100 kDa, but the magnitude of the plateau is more strongly influenced by the chain length of the polyanion, PSS. Possible causes of the low-frequency plateau are discussed. [ABSTRACT FROM AUTHOR]

In this work, a study of the linear viscoelastic properties of co-continuous polypropylene/polystyrene blends filled with multiwall carbon nanotubes (MWCNTs) is presented. The YZZ rheological model [W. Yu et al., Polymer 51, 2091–2098 (2010)] is employed to correlate the rheological behavior of the blends with their microstructure and electrical properties. A test design involving a sequence of small amplitude oscillatory shear and a time sweep (simulating thermal annealing) is used to evaluate the morphology and evolution of electrical properties. It was shown that the YZZ rheological model could be successfully modified to be able to quantify a co-continuous morphology of filled composites. The calculated characteristic domain size was found to be in good agreement with the experimental data obtained via scanning electron microscopy. Furthermore, it is shown that the characteristic domain size slightly decreased after 30 min of thermal annealing. It was shown, as well, that thermal annealing promoted a reduction in the electrical percolation threshold (wt. % MWCNT) from 0.28 to 0.06. [ABSTRACT FROM AUTHOR]

Shear-induced pair interactions between viscous drops suspended in a viscoelastic matrix are numerically investigated examining the effects of elasticity and drop deformability on their post-collision trajectory. Two different trajectory types are identified depending on the Weissenberg number Wi and capillary number Ca. Drops suspended in a Newtonian matrix (Wi = 0.0) show a passing trajectory where drops slide past each other and separate in the stream-wise direction. However, when increasing the Weissenberg number above a critical value, a tumbling/doublet trajectory is observed where two drops rotate around the midpoint of the line joining their centers, as was also seen previously for rigid particles. The tumbling trajectory is explained by investigating the flow around a single drop in shear. Elasticity generates a larger region of spiraling streamlines around a drop, which, during a pair interaction, traps the second drop giving rise to the tumbling pair. Decreasing deformability (lower Ca) and increasing viscoelasticity (higher Wi) favor a tumbling trajectory. With simulations sweeping the parameter space, we obtain a phase plot of the two different trajectories as functions of Ca and Wi. Treating the tension along the curved streamlines due to the non-zero first normal stress difference in the viscoelastic medium as an enhancement to the interfacial tension, we have developed an approximate force balance model for the zone of spiraling streamlines. It qualitatively captures the observed scaling of the critical Ca and Wi values at the phase boundary. The effects of unequal size, initial configuration, and non-unity viscosity ratio are briefly investigated. [ABSTRACT FROM AUTHOR]

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, yield stress, and thixotropy. There is renewed interest in the modeling of human blood with thixo-elasto-visco-plastic rheological models. Previous work [Armstrong and Tussing, Phys. Fluids 32, 094111 (2020)] has led to the development of the enhanced thixotropic viscoelastic model for blood (ethixo-mHAWB; called here, after a minor modification, ETV) that incorporates viscoelasticity to a thixotropic model for the stress contributed by the rouleaux aggregates, in addition to describing using a nonlinear viscoelastic model the stress contributed by the individual red blood cells deforming under the action of the flow. This model has shown superior performance in fitting human blood steady state and transient rheological data from a strain-controlled rheometer [Horner et al., J. Rheol. 62, 577–591 (2018); 63, 799–813 (2019)] as compared to other alternate models. In the present work, we first develop another variant of the ETV model, the enhanced structural stress thixotropic-viscoelastic (ESSTV) model, and the modification patterned following an elastoviscoplastic model developed recently [Varchanis et al., J. Rheol. 63, 609–639 (2019)]. We develop full tensorial stress formulations of the rouleaux stresses for both the above-mentioned models, resulting in the t-ETV and t-ESSTV models. We use steady state and step-ups, and step-downs in shear rate data to independently fit the parameters of all before-mentioned models. We compare predictions against experimental data obtained on small, large, and unidirectional large amplitude oscillatory shear conditions. We find that the full tensor stress formulations t-ETV and t-ESSTV significantly improved the predictive capability of the earlier ETV model. [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]

In the present work, we focus on the large deformation of a viscoelastic droplet suspended in a Newtonian matrix. We use the constrained volume model as a basic theoretical framework for the description of droplet shape evolution, and we account for the viscoelasticity of the droplet phase using the single-mode Giesekus model. The velocity gradient term describing flow inside the droplet is modified by the viscoelastic stresses, and the resulting model—we herein call the non-Newtonian constrained volume model—is calibrated by matching its predictions to those of the model of Yu et al. [J. Rheol. 48, 417–438 (2004)] at small deformation and slow flow conditions. The non-Newtonian constrained volume model is then examined under conditions of large deformation and/or fast flow, and its predictions are compared against experimental results. The new model shows the growth of the droplet's width in the vorticity direction at conditions of large capillary number, moderate-to-large viscosity ratio, and small elastocapillary number. [ABSTRACT FROM AUTHOR]

In rheological experiments, the relationship between stress and strain is determined. In the transient regime, this relationship may depend on which of these properties is applied and which is measured. In general, data collected using one or the other as the control parameter are not necessarily equivalent. Moreover, the assumed steady state and the relaxation following this state might depend on whether stress or strain has been applied. We examined colloidal suspensions with concentrations around the glass transition and compared their response to stress and strain, in particular, their transient response after the start-up of shear, their steady state, and their relaxation after cessation of shear. After the start-up of shear, the transient behavior was found to significantly depend on whether the sample is exposed to a constant shear rate or a constant stress. Nevertheless, the transients lead to a rheological steady state that is independent of how it is reached, as long as yielding occurred and the corresponding shear rate or stress is applied. After cessation of shear, the relaxation under strain and stress control shows both similarities and differences. This is quantified based on, e.g., the hydrodynamic, Brownian, and residual stress as well as the recovered strain. In addition, the responses of the rheometers to the abrupt changes have been characterized. The corresponding technical data are presented and taken into account in the data interpretation. [ABSTRACT FROM AUTHOR]

We perform immersed-boundary-method numerical simulations of small amplitude oscillatory shear flow of suspensions of monodisperse noncolloidal rigid spherical particles in non-Newtonian liquids from the dilute to the concentrated regime. We study the influence of suspending liquid inertia and rheology and particle concentration on the computationally measured storage and loss moduli of the suspensions. In particular, the rheology of the suspending liquid is modeled through the inelastic shear-thinning Carreau–Yasuda constitutive equation and the viscoelastic Giesekus and Oldroyd-B constitutive equations. The role of inertia is quantified by the Stokes number, St, whereas the relevance of the non-Newtonian effects of the suspension matrix is measured through the Carreau number, Cu, for the Carreau–Yasuda liquid and the Deborah number, De, for the viscoelastic liquids. In suspensions with a Carreau–Yasuda matrix, both the storage and the loss modulus increase with St and decrease with Cu, yet the order of magnitude of Cu has to be greater than unity for these effects to be visible. In suspensions with a viscoelastic matrix, both the moduli increase with St and have a nonmonotonic trend with De, showing a maximum with no quantitative differences between the results pertaining suspensions with Giesekus and Oldroyd-B constitutive equations. [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]

Although bead microrheology experiments are routinely used to characterize the viscoelasticity of complex matter, their simulation analog—probe rheology molecular simulations—has been scarcely used since the system characteristics required for its robust implementation are not established in the literature. We address this issue by analyzing an active probe rheology simulation setup consisting of a probe particle that is subjected to an external oscillatory force and a harmonic trapping force. We identify a set of eight conditions of the system properties that must be satisfied for the successful implementation of the probe rheology technique in molecular simulations. Among these criteria, the two most important are as follows: (1) The spring force constant for the trapping force should be sufficiently large such that the peak in the Fourier transform of the probe displacement occurs at the same frequency as that of the applied force. (2) System parameters should be chosen such that the magnitude of the external force used to drive the probe motion should be comparable to the magnitude of the hydrodynamic friction force experienced by the probe particle in the viscoelastic medium. Furthermore, a scaling relation that can be used to determine the frequency at which inertial effects set in for a given probe size is also established. The validity of our procedure is demonstrated by applying it to determine the viscoelastic properties of a weakly entangled polymer melt system. [ABSTRACT FROM AUTHOR]

Polymers bearing associative groups (APs) are characterized by their fantastic viscoelastic behaviors. In a work recently published by our group [Jiang et al., Macromolecules53, 3438–3451 (2020)], a single chain sticky Rouse model (SRM) is proposed to describe the linear viscoelasticity of APs without the entanglement effect. In this work, equilibrium molecular dynamics simulation of an unentangled melt of an AP with uniformly distributed stickers is carried out, and the dynamic properties are simultaneously analyzed from the SRM. A chain model with capped stickers is proposed so that a well-defined association chemistry is promised in the simulation system. The relative effective frictional coefficient of stickers, which is the key parameter in the SRM, is extracted from the chain center-of-mass diffusion, and it is found to be consistent with the dynamics of associative reaction in the fully gelated network. Based on this, a linear relaxation modulus and segmental diffusion functions are predicted from the SRM without fitting parameters, and these are found to quantitatively agree with the simulation results, showing the effectiveness of the SRM in connecting the dynamic properties at different molecular levels. The change in relaxation modes and the definition of the effective chain center are found to be crucial in the scenario of the SRM. Finally, the above analysis from the SRM is successfully extended to the simulation system with asymmetric chains. All these simulation results strongly support the SRM as a molecular model for the linear rheology of AP. [ABSTRACT FROM AUTHOR]

Until the advent of the novel Enders catalysts, the nonlinear rheological characterization of polyethylene (PE) blends, containing up to 50 wt. % of ultra-high molecular weight PE (UHMWPE, with weight average molecular weight Mw > 106 g/mol) was unattainable. In this study, by melt blending of a commercially available high-density PE (polymer matrix) and PE-reactor-blends (RBs), multimodal PE blends were prepared, and their nonlinear viscoelastic properties were investigated. The experiments revealed how extraordinarily high amount of UHMWPE content and ultra-broad molecular weight distribution characterized by well separated molecular weight modes influence the nonlinear viscoelasticity. Furthermore, in order to evaluate the strain hardening ability of the multimodal PE, an approach was proposed allowing to objectively analyze and quantify the nonlinear response of the investigated samples. Analyzing the "state diagram" of the extended specimens, which captures the melt behavior and flow instabilities during uniaxial extensional measurements, unveiled that the observed SH of multimodal PE blends, at temperatures notably higher than their melting temperature, is controlled by the stretched chains of the 2nd well separated UHMWPE molecular weight mode. Moreover, it was found that, in order to highly stretch the PE chains, a characteristic strain must be applied. [ABSTRACT FROM AUTHOR]

The paraffin molecules in crude oil crystalize and precipitate out as the oil cools, resulting in a sharp increase in oil viscosity and further the gelation of the oil. The waxy crude oil gel exhibits complex rheological behaviors, such as viscoelasticity, yield stress, and thixotropy, posing challenges to the flow assurance of pipelines. Previous studies have verified that applying a high-voltage electric field to a flowing liquid oil can significantly reduce its viscosity. In this work, the electrorheological behaviors of waxy crude oil gel are explored by a stress-controlled rheometer equipped with in situ DC electric field manipulation. It is reported for the first time that the gel structure can be significantly weakened upon the application of an electric field for a duration of not less than 10 s, with the yield stress, storage modulus, loss modulus, and apparent viscosity reduced by up to 90%. In addition, the gel structure fracture is observed to transit from brittle-like to ductile-like. A stronger structure weakening effect can be obtained at a higher field strength and lower temperature. The structure weakening effect induced by the electric field can be maintained for a certain period of time after the removal of the electric field, with a recovery of yield stress and moduli less than 10% in 48 h. We hold the view that the electrorheological behaviors of waxy oil should be attributed to the weakened attraction between wax particles induced by the electric field. [ABSTRACT FROM AUTHOR]

The linear viscoelasticity of coacervates formed by oppositely charged polyelectrolytes in the salt solution is reviewed, with a focus on time-temperature, time-salt, time-pH, and time-hydration superpositions, and on fundamental relaxation mechanisms. A variety of polyelectrolyte pairs are covered, showing the frequent, but not universal, success of the time-salt superposition. Master curves in many cases are similar to those for neutral polymers, including Rouse and reptation theories. However, in some cases, solidlike, as opposed to fluidlike, response is observed at low frequencies, especially at low salt concentrations. Some coacervates seem to fit "sticky diffusion" theory reasonably well, wherein relaxation is controlled by the breakage rate of ion pairs; the dependence of the "sticker" lifetime on salt concentration has been explored but is not well understood as yet. It is also possible that local relaxation is not controlled by breakage of ion pairs but by cooperative, "glassy," relaxation of monomers, salt ions, and water molecules. Compilation and comparison of different datasets and suggested formulas for rheological time constants are presented, and some suggestions are given for future directions. [ABSTRACT FROM AUTHOR]

We found an anomalous nonlinear behavior under large amplitude oscillatory shears, where the amplitude stress deviates strongly from the linear dependence of strain, while the time dependence of stress remains sinusoidal. This phenomenon is usually accompanied with the Payne effect of filled rubbers. In order to understand the molecular details regarding this unusual behavior, we examined a series of polybutadiene/tetradecane solutions filled with carbon black. Our results show that there is a previously unrecognized transition in the system as the matrix polymer concentration ϕ approaches and passes through a characteristic polymer concentration ϕc. Below ϕc, the system typically shows the classic nonlinearity, where the storage modulus G′ decreases as the strain amplitude γ0 increases and the resulting stress waveforms are distorted from sinusoidal waves. Above ϕc, the system displays an anomalous nonlinearity, where the stress responses at any given strain remain surprisingly sinusoidal regardless of the drop in the storage modulus G′. The critical concentration ϕc is about an order of magnitude greater than the entanglement polymer concentration ϕe. The degree of entanglement in the matrix apparently determines the occurrence of this unusual rheological event and plays a key role here. Increasing the polymer molecular weight enhances this transition. [ABSTRACT FROM AUTHOR]

Rheological models based on fractional order derivatives have been applied to characterize the linear viscoelasticity of asphalt cements for a long time. Such models provide continuous spectra which are fundamentally related to the molecular characteristics and facilitate analytical investigations as compared to discrete representations. With the increasing complexity in asphalt composition to satisfy various purposes, however, the inadequacy of existing fractional models has been noted. This paper proposed a generalized fractional Maxwell-dashpot (GFMD) model as a general framework for describing the modulus behaviors of asphalt cements. The generalized fractional Voigt (GFV) model was considered the counterpart for the compliances. The material functions given by each model are primarily the superposition of its constituent fractional Maxwell-dashpot or fractional Voigt (FV) elements. Geometric features of these elements were investigated such that a proper initial guess of model parameters can be obtained graphically with relative ease. For computational efficiency, the continuous spectra were discretized to provide the Prony representations of the material functions. To demonstrate the model capability, the dynamic mechanical data of a neat asphalt showing the typical behavior and a heavily polymer-modified asphalt exhibiting strong cross-linking were utilized. For the typical behavior, the GFMD and GFV models containing two fractional elements yielded excellent descriptions. A third fractional unit was necessitated in both models to account for the cross-linking mechanism for the modified asphalt. A relaxation/retardation mode density of two points equidistantly per decade produced material functions with negligible waviness and almost the same accuracy as compared to the use of the continuous spectra. [ABSTRACT FROM AUTHOR]

We derive new analytical solutions for the nonaffine Johnson–Segalman/Gordon–Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS [Martinetti and Ewoldt, Phys. Fluids 31, 021213 (2019)]. The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the nonaffine deformation field that acts on stress-generating elements to reinforce the physical interpretation of the JS/GS class of models. Finally, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be reinterpreted based on the concept of nonaffine motion of the JS/GS framework. [ABSTRACT FROM AUTHOR]

Aging soft glassy materials do not follow time-translational invariance and violate the principles of linear viscoelasticity, such as the relation between the dynamic moduli in the frequency domain and the stress relaxation modulus in the time domain. Using an aqueous suspension of hectorite clay, a model aging soft glassy material, we account for time-dependent behavior by transforming the experimentally obtained stress relaxation and dynamic moduli from the real-time domain to the effective-time domain by normalizing the real-time by a time-dependent relaxation time. We find that the two sets of experiments probe different aging and deformation timescales, and simultaneous analysis provides insights into material behavior over a wide range of timescales. Careful analysis of the dynamic moduli reveals contamination of (slow) aging α modes by (fast) nonaging β modes, which is not clearly evident in the stress relaxation modulus. On the other hand, the stress relaxation measurements probe timescales long enough to characterize the terminal relaxation of the suspension. A toy Maxwell model is used to elucidate the interaction of the slow aging and fast nonaging modes, and their effect of measurements. The synergistic relationship between the two sets of experiments offers guidelines for characterizing time-dependent materials by generalizing the principles of linear viscoelasticity. [ABSTRACT FROM AUTHOR]

We explore theoretically the interplay between shear banding and edge fracture in complex fluids by performing a detailed simulation study within two constitutive models: the Johnson–Segalman model and the Giesekus model. We consider separately parameter regimes in which the underlying constitutive curve is monotonic and nonmonotonic, such that the bulk flow (in the absence of any edge effects) is, respectively, homogeneous and shear banded. Phase diagrams of the levels of edge disturbance and of bulk (or quasibulk) shear banding are mapped as a function of the surface tension of the fluid–air interface, the wetting angle where this interface meets the walls of the flow cell, and the imposed shear rate. In particular, we explore in more detail the basic result recently announced by Hemingway and Fielding [Phys. Rev. Lett. 120, 138002 (2018)]: that precursors to edge fracture can induce quasibulk shear banding. We also appraise analytical predictions that shear banding can induce edge fracture [S. Skorski and P. D. Olmsted, J. Rheol., 55, 1219 (2011)]. Although a study of remarkable early insight, Skorski and Olmsted [J. Rheol., 55, 1219 (2011)] made some strong assumptions about the nature of the "base state," which we examine using direct numerical simulation. The basic prediction that shear banding can cause edge fracture remains valid but with qualitatively modified phase boundaries. [ABSTRACT FROM AUTHOR]

Blood-derived products, particularly platelet-rich plasma (PRP), have received increased attention in the past several years due to their great potential as a therapy for osteoarthritis and tendon injuries. Therefore, characterizing the mechanical properties of PRP becomes important to better understand its therapeutic efficacy. This paper aims to investigate the rheological properties of PRP in order to provide further insight into its mechanism of action. The PRP samples in our study may have higher erythrocyte count than the average PRP reported in the literature. Flow-sweep, small amplitude oscillatory shear (SAOS), large amplitude oscillatory shear (LAOS), and thixotropy tests have been performed at room and physiological temperatures to characterize the non-Newtonian properties of PRP samples. Flow-sweep tests reveal shear-thinning behavior, with higher apparent viscosity observed at a lower temperature. Rheological models such as Carreau, Casson, power-law, and Herschel–Bulkley have been fitted to flow-sweep data with the latter showing the closest agreement. Over the acceptable narrow range of frequency in SAOS tests, the loss modulus appears to be slightly larger than the storage modulus with both moduli decreasing at higher temperature. The nonlinear viscoelastic properties are furthermore quantified through the static and dynamic LAOS analyses. For a given strain and angular frequency, the former identifies strain-softening and shear-thinning, while the latter discloses a range of other transient behavior within an oscillation cycle. Lastly, peak-hold tests have revealed consistent thixotropy in PRP solutions. [ABSTRACT FROM AUTHOR]

In this paper, I present a simple and self-consistent framework based on microrheology that allows one to obtain the mechanical response of viscoelastic fluids and gels from the motion of probe particles immersed on it. By considering a non-Markovian Langevin equation, I obtain general expressions for the mean-squared displacement and the time-dependent diffusion coefficient that are directly related to the memory kernels and the response function, and which allow one to obtain estimates for the complex shear modulus and the complex viscosity of the material. The usefulness of such an approach is demonstrated by applying it to describe experimental data on chemically cross-linked polyacrylamide through its solgel transition. [ABSTRACT FROM AUTHOR]

Here, we report for the first time that resonance in dynamic-mode cantilever sensors persists in hydrogels and enables the real-time characterization of hydrogel viscoelastic properties and the continuous monitoring of sol-gel phase transitions (i.e., gelation and dissolution processes). Real-time tracking of piezoelectric-excited millimeter cantilever (PEMC) sensor resonant frequency (fair = 55.4 ± 8.8 kHz; n = 5 sensors) and quality factor (Q; Qair = 23.8 ± 1.5) enabled continuous monitoring of high-frequency hydrogel shear storage and loss moduli (G′f and G″f, respectively) calculated by sensor data and fluid–structure interaction models. Changes in the sensor phase angle, quality factor, and high-frequency shear moduli obtained at the resonant frequency (G′f and G″f) correlated with low-frequency moduli obtained at 1 Hz using dynamic mechanical analysis. Characterization studies were performed using physically and chemically crosslinked hydrogel systems, including gelatin hydrogels (6–10 wt. %) and alginate hydrogels (0.25–0.75 wt. %). The sensor exhibited a dynamic range from the rheological properties of inviscid solutions to hydrogels with high-frequency moduli of 80 kPa and low-frequency moduli of 26 kPa. The sensor exhibited a limit of detection of 260 Pa and 1.9 kPa for changes in hydrogel storage modulus (E′) based on the sensor's phase angle and quality factor responses, respectively. We also show that sensor data enable quantitative characterization of gelation process dynamics using a modified Hill model. This work suggests that cantilever sensors provide a promising platform for the sensor-based characterization of hydrogels, such as quantification of viscoelastic properties and real-time monitoring of gelation processes. [ABSTRACT FROM AUTHOR]

Asphaltenes are a class of high molecular weight aromatic compounds found in crude oil. They adsorb onto toluene-water interfaces and induce a spontaneous emulsification phenomenon, whereby stable water-in-oil emulsions form without the need of an external energy input. This work aims to control and understand the factors affecting spontaneous droplet formation in the presence of asphaltene adsorption. This is particularly useful for crude oil refining, where the presence of a stable emulsion hampers the efficiency of downstream processing operations. We explore the effect of the addition of copolymers designed as crude oil flow improvers as a means to control the extent of emulsion formation. We find that the polymers competitively adsorb onto the toluene-water interface and diminish spontaneous emulsification. We also conduct fluorescence microscopy experiments and measurements of the interfacial energy to determine the mechanism of spontaneous emulsification in asphaltene systems. We conclude that an emulsion forms via the diffusion of molecular water into the oil phase and subsequent binding with asphaltene aggregates, leading to the nucleation of micrometer-sized water droplets. We find that the polymer forms complexes with the dissolved asphaltenes, possibly hampering the ability of diffused water to bind to the asphaltenes and reducing the extent of spontaneous emulsification. Finally, we investigate the role of interfacial shear and dilatational viscoelasticity to better understand which fundamental interfacial properties are important in the emulsification of asphaltene-laden systems. We find that the rate of formation of an interfacial microstructural network is inversely correlated with the extent and rate of spontaneous emulsification. [ABSTRACT FROM AUTHOR]

A challenge for polymer rheology is the reliable determination of shear dependent first normal stress difference (N1 values) at high shear rates (>10 s−1). Here, we evaluate the correctness of the commonly applied exit pressure method focusing on polypropylene and high and low density polyethylene melts at 200 °C. It is demonstrated that the linear extrapolation of pressure values toward the die exit, which is a key step in the application of the exit pressure method, is affordable to determine N1 values despite that these extrapolated exit pressure values are characterized by a relative deviation of 25%–40%. The validity of the exit pressure method is further supported by an excellent match with rheological data from the Laun rule (exponent close to 0.7) and a representative simulation of extrudate swelling data in the width and height direction, considering tuned parameters for the Phan–Thien–Tanner constitutive model. Also, the absence of a significant viscous heating effect near the die exit is highlighted based on numerical analysis. [ABSTRACT FROM AUTHOR]

When injected through a contraction, high molecular weight polymer solutions exhibit a sharp increase in apparent viscosity, which originates from stretching polymer chains above a critical extension rate. This chain stretching can also induce polymer scission, which then decreases the extensional viscosity. In practice, the two phenomena are difficult to separate. Moreover, these phenomena are often observed in situations where flow instabilities appear. In order to disentangle the two effects, we have measured the pressure-flow rate relation for polymer solutions passing through a hyperbolic contraction. The ratio of the pressure drop to that of the (Newtonian) solvent exhibits a maximum due to the competition between polymer extension and scission. We find a geometry-dependent relation between the flow rates at which the maximum occurs for successive passages in a given contraction, which appears to be independent of molecular weight, concentration, solvent quality, and viscosity and can be used to predict the scission under successive passes. [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]

In a recent article [Lee et al., J. Rheol. 63, 863–881 (2019)], the start-up of stress-controlled oscillatory flow both theoretically and experimentally was considered. In particular, they derive an analytical expression for the nonzero value around which the resulting strain (relative to the configuration before start-up) ultimately oscillates. Their derivation is based on the concept of recovery rheology, in which strain is decomposed into a sum of recoverable and unrecoverable components. Here, the same problem is treated based directly on the general theory of linear viscoelasticity. In this analysis, a transiently decaying contribution emerges that is not present in the Lee expression. This contribution is important since it gives an assessment of the time scale on which steady time-periodic oscillatory flow is established. [ABSTRACT FROM AUTHOR]

A particulate molecular model in which the solvent particles are considered explicitly is developed for studying the linear viscoelasticity of nanocolloidal suspensions using molecular dynamics simulations. Nanocolloidal systems of volume fractions ranging from 0.10 to 0.49 are studied. The hydrodynamics in these model systems are governed by interparticle interactions. The volume fraction dependence of the relative zero shear viscosity exhibited by this molecular model is consistent with that reported in the literature experiments and simulations. Over the range of frequencies studied, the relative dynamic viscosity values follow the same qualitative trend as that seen in the literature experiments. The time-concentration superposition (TCS) principle is successfully applied to construct the viscoelastic master curves that span nine decades of frequency in the case of the elastic modulus and more than four decades of frequency in the case of the loss modulus. The TCS principle was observed to fail at high volume fractions that are near the glass transition concentration; this finding is consistent with the literature experimental and simulation observations. The volume fraction dependence of the shift factors used in the construction of the viscoelastic master curves is in good quantitative agreement with that of the viscosity of the nanocolloidal systems. Our results demonstrate that molecular simulations in conjunction with an explicit solvent model can be used to quantitatively represent the viscosity and the viscoelastic properties of nanocolloidal suspensions. Such particulate models will be useful for studying the rheology of systems whose properties are governed by specific chemical interactions. [ABSTRACT FROM AUTHOR]

The rheological properties (viscosity, plasticity, viscoelasticity, and elasticity) of noncolloidal suspensions with varying concentrations of a solid phase (Al powder) in oligomeric polyethylene glycol have been studied in the shear mode of deformation. All typical types of rheological behavior have been observed. In the concentration range up to approximately 30%, suspensions are Newtonian liquids, while at a certain concentration, non-Newtonian and viscoelastic effects appear. With further increases in concentration, the flow curves become a power-law type, though the yield stress can be found only for suspensions with a high solid phase content. The elasticity of the suspensions can be detected at concentrations in the order of 55%. In a narrow range of concentrations, the rheological state of the suspensions can be treated as viscoplastic, wherein they preserve fluidity and become elastic. This concentration threshold, determined by the change in various rheological characteristics including the loss tangent, corresponds to the gelation or "colloid" glass transition. The most detailed experiments were devoted to the concentration range of 60–70 vol. %, which are treated as highly concentrated suspensions (HCSs). A concentration of 70% is the upper limit, because mixtures with higher concentrations do not keep their continuity and crumble. The rheological state of HCSs corresponds to the elastoplastic type of behavior. The separation of the total deformation into plastic and elastic components showed that plastic deformations (but not the flow) in the shearing of HCSs are small. Repeated shearing in the loading-unloading mode has been performed. In this case, a decrease in the elastic deformation and a remarkable growth of the shear elastic modulus was observed. This effect is presumably explained by the orientation of the particles and shear-induced anisotropy. A stress-concentration diagram of the physical states of suspensions has been proposed. The concentration range somewhat below that of the HCS state is of special interest for the powder injection molding technology, which is limited by the domain of plasticity. [ABSTRACT FROM AUTHOR]

Many industrial polymer melts are entangled and undergo crystallization during processing. Several recent studies have reported experimental data for the rheology of crystallizing entangled polymers. Meanwhile, over the past few years, slip-link models have been demonstrated to describe the rheology of entangled melts under a variety of nonlinear deformation conditions. In this work, we present a modification of the slip-link model to describe the rheology of an entangled melt undergoing crystallization. The partially crystallized melt is represented by a blend of linear chains with free ends and cross-linked, bridgelike chains with fixed ends that resemble the tie molecules between developing crystallites. Two new parameters are introduced: the fraction of cross-linked chains and a modulus shift factor, both of which are functions of the degree of crystallinity. The model captures the evolution of viscosity and elasticity simultaneously over the whole range of available frequencies in the linear regime. The model is validated using experimental datasets for isotactic polypropylene. [ABSTRACT FROM AUTHOR]