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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]

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 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]

We present results from a comprehensive investigation of the rheological responses of the gelled waxy crude oils during the yielding transition process by both stress-controlled and strain-controlled tests. If the deformation is within the linear viscoelastic region, G ′ increases slowly with increasing frequency following a power-law relationship. 80% of the total deformation accumulated during creeping is recoverable, and this recoverability remains largely independent of both imposed stress and testing time. The waxy gel relaxes the restored stress slowly with a time scale of ∼100 s. If the induced deformation exceeds the linear viscoelastic region, the elasticity of waxy structure starts to gradually decay with increasing creep stress and creep time, and the plastic contribution has come into play in the nonlinear region. A rapid reduction in the obtained time scale is observed with increasing applied strain. After the structure fractures, both G ′ and G ″ decrease with increasing strain following a power-law relationship. The ratio of the large amplitude shear-thinning exponents of G ′ and G ″ is around 2, indicating a more rapid decay of the elastic property than the viscous property. A brittleness index I is defined to quantitatively describe the brittleness of the waxy gel. The value of I for the waxy gel formed at lower temperatures is smaller, indicating that the waxy gel tends to have a more brittle fracture when yielding. The values of linear storage modulus G ′ ( γ 0 → 0 ) , critical linear strain γ 1 , critical linear stress σ 1 , and yield strain γ y obtained by different rheological testing methods are found to be well consistent. The yielding transition process is found to be strain determined rather than stress determined, and thereby γ 1 and γ y rather than yield stress are suggested to indicate the yielding transition. [ABSTRACT FROM AUTHOR]

A framework for determining the first nonlinear relaxation modulus of a viscoelastic fluid from a medium-amplitude oscillatory shear (MAOS) deformation is constructed. Knowledge of this "MAOS relaxation modulus" allows one to predict the weakly nonlinear stress response of a material under an arbitrary transient deformation via a memory integral expansion. Our framework is demonstrated by explicitly determining the MAOS relaxation modulus for a dilute suspension of Brownian spheroids subject to a dual-frequency oscillatory shear flow. Specifically, we first calculate the second normal stress difference for such a deformation from a corotational memory integral expansion. Second, the microstructural stress response of the model system of Brownian spheroids is determined via a regular perturbation expansion of the orientation distribution function at small dimensionless strain-rate amplitude, or Weissenberg number. An analytical expression for the MAOS relaxation modulus is resolved by comparing the second normal stress difference results of the memory integral expansion and microstructural stress calculation. Finally, using the MAOS relaxation modulus, we reconstruct the stress response of the model system for the start-up and cessation of simple shear and uniaxial extension. In summary, our work offers an approach to utilizing medium (and large) amplitude oscillatory shear results to predict stress dynamics of viscoelastic fluids in other transient, nonlinear flows. [ABSTRACT FROM AUTHOR]

We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) Is steady state attainable during uniaxial extension? (ii) What is the respective transient response in simple shear? and (iii) How does stress relax upon cessation of extension or shear? To accomplish our goal, we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry and cone-partitioned plate shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the branch-on-branch (BoB) algorithm. The data indicate that the extensional viscosity reaches a steady state value, whose dependence on extensional rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox-Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rateindependent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong "elastic memory" of the material. These results are described by BoB semiquantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than three entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers. [ABSTRACT FROM AUTHOR]

Rheologists have expectations for signatures of linear viscoelastic properties, such as shapes of G'(ω) and G?(ω). Medium amplitude (or asymptotically-nonlinear) oscillatory shear (MAOS) provides additional nonlinear rheological information with low dimensional, well-defined material functions [Ewoldt and Bharadwaj, Rheol. Acta 52, 201-209 (2013)]. Here, we develop expectations of signatures (or fingerprints) for the four asymptotically-nonlinear material functions associated with MAOS, [e1](ω), [e3](ω), [v1](ω), [v3](ω). Although the linear fingerprints may be identical for different models, the asymptotically-nonlinear fingerprints may be different in magnitude, frequency-scaling, curve shapes, and sign changes. To perform the analysis, we collect/translate a library of available analytical strain-controlled MAOS fingerprints for seven different constitutive models. Using this library, we identify general trends and highlight key differences of asymptotic-nonlinear viscoelasticity. Asymptotic nonlinearities for all models considered here obey the terminal regime inter-relations and frequency scaling predicted by Bharadwaj and Ewoldt [J. Rheol. 58, 891-910 (2014)]. Unlike the positive linear viscoelastic measures, at least one of the four asymptotic nonlinearities changes signs with Deborah number (De). Following sign interpretations of Ewoldt and Bharadwaj [Rheol. Acta 52, 201-209 (2013)], we show that nonlinearities tend to be driven by strain-rates at small De, and by strains at large De, a trend observed for nearly all the constitutive models studied here, the exception being the model for dilute rigid dumbbell suspensions of Bird et al. [J. Chem. Phys. 140, 074904 (2014)]. Some constitutive models exhibit multiple sign changes at intermediate De and there may be no universal behavior of asymptotically-nonlinear fingerprints in this regime. Therefore, frequency-dependent signatures can be material-specific. This will allow inverse problems to infer structure, select models, and fit model parameters using asymptotically-nonlinear signatures. To illustrate this aspect, we demonstrate a fingerprint matching exercise with experimental measurements on a transiently cross-linked hydrogel system. We find that currently available model fingerprints can match the qualitative magnitudes and frequency dependence, but not the signs of the experimental transient network response. [ABSTRACT FROM AUTHOR]

We propose, in this paper, a model for predicting the rheological response of both vibrated and sheared 3D granular suspensions in stationary and nonstationary conditions. The major assumption of this model is the inherent bimodal behavior of chain forces in granular packings. The model is set up from a kinetic equation describing the dynamic exchange between a population of strongly correlated caged particles and a population of slightly correlated free particles. To compare the predictions of the model to experimental results, the kinetic equation is transformed into a differential constitutive equation, relating stress to strain, by including the effect of the interstitial fluid on the suspension. With only four adjustable parameters intrinsic to the system (i.e., independent of the type of rheological test used), the model is in very close agreement with experiments. Despite the fact that our approach remains at a mean-field level, it is able to predict and describe several rheological behaviors, in stationary, nonstationary conditions, linear and nonlinear regimes, including Newtonian and frictional Coulombian regimes, as well as elastic Hookean and viscoelastic Maxwellian behaviors. It then appears that this two-state approach allows capturing both the viscoelastic behavior of dry granular materials and granular suspensions. Vibrated dense suspensions and granular media are thus unified under a common framework. [ABSTRACT FROM AUTHOR]