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Ianniruberto and Marrucci developed a theory whereby entangled branched polymers behave like linear ones in fast elongational flows. In order to test such prediction, Huang et al. performed elongational measurements on star polymer melts, indeed revealing that, in fast flows, the elongational viscosity is insensitive to the molecular structure, provided the molecular weight of the backbone is the same. Inspired by these studies, we here report on results obtained with multi-chain slip-link simulations for symmetric and asymmetric star polymer melts, as well as calculations of the Rouse time of the examined branched structures. The simulations semi-quantitatively reproduce the experimental data if the Kuhn-segment orientation-induced reduction of friction (SORF) is accounted for. The observed insensitivity of the nonlinear elongational viscosity to the molecular structure for the same span molar mass may be due to several factors. In the symmetric case, the calculated Rouse time of the star marginally differs from that of the linear molecule, so that possible differences in the observed stress fall within the experimental uncertainty. Secondly, it is possible that the flow-induced formation of hooked star pairs makes the effective Rouse time of the aggregate even closer to that of the linear polymer because the friction center moves towards the branchpoint of the star molecule. In the asymmetric case, it is shown that the stress contributed by the short arms is negligible with respect to that of the long ones. However, such stress-reduction is balanced by a dilution effect whereby the unstretched arms reduce SORF as they decrease the Kuhn-segment order parameter of the system. As a result of that dilution, the stress contributed by the backbone is larger. The two effects compensate one another so that the overall stress is virtually the same as the other architectures., 19 pages, 6 figures

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.

We present a new, free, and open source reptate (rheology of entangled polymers: toolkit for analysis of theory and experiment) software package for viewing, exchanging, and analyzing rheological and associated data. The main idea of reptate is to propose a powerful and user-friendly platform, which can be installed on the same computer as, e.g., the rheometer and which makes comparing experiments with classical, or latest, theories easy—without the need for a theoretician. The new reptate software offers full compatibility with different operating systems (Windows, Mac, and Linux). We demonstrate the use of reptate by reproducing predictions of recently published articles, from entangled, monodisperse, and polydisperse linear chains to branch-on-branch polymer systems in linear and nonlinear rheology regimes.

We present results of the linear and non-linear rheology of cubic blue phase I (BPI). The elasticity of BPI is dominated by double-twist cylinders assembled in a body-centered cubic lattice, which can be specified by disclination lines. We find that the elasticity of BPI is enhanced by an order of magnitude by applying pre-shear. The shear-enhanced elasticity is attributed to a rearrangement of the disclination lines that are arrested in a metastable state. Our results are relevant for the understanding of the dynamics of disclinations in cubic blue phases., Comment: 12 pages, 8 figures

The yield stress of many yield stress fluids has turned out to be difficult to determine experimentally. This has led to various discussions in the literature about those experimental difficulties, and the usefulness and pertinence of the concept of yield stress fluids. We argue here that most of the difficulties disappear when taking the thixotropy of yield stress fluids into account, and will demonstrate an experimental protocol that allows reproducible data to be obtained for the critical stress necessary for flow of these fluids. As a bonus, we will show that the interplay of yield stress and thixotropy allows one to account for the ubiquitous shear localization observed in these materials. However, due to the thixotropy the yield stress is no longer a material property, since it depends on the (shear) history of the sample.

We report the effect of flow-induced dynamical heterogeneity on the nonlinear elastic modulus of weakly aggregated colloidal gels that have undergone yielding by an imposed step strain deformation. The gels are comprised of sterically stabilized poly(methyl methacrylate) colloids interacting through short-ranged depletion attractions. When a step strain of magnitude varying from γ = 0.1 to 80.0 is applied to the quiescent gels, we observe the development of a bimodal distribution in the single-particle van Hove self-correlation function. This distribution is consistent with the existence of a fast and slow subpopulation of colloids within sheared gels. We evaluate the effect of incorporating the properties of the slow, rigid subpopulation of the colloids into a recent mode coupling theory for the nonlinear elasticity of colloidal gels.

We present direct evidence of the macromolecular network behavior at high deformation rates based on macroscopic simulation of these systems by a group of elastics as a model of flexible-chain polymer concentrated solutions or melts. It was shown that at low deformation rates, the disentanglement process really takes place providing a possibility to irreversible deformations (flow), while at high deformation rates, the dominating effect is the formation of large inhomogeneous structures (“grains” or “bundles”) consisting of flocks of entangled chains. This is a model of the deformation induced flow-to-rubbery transition, which makes the irreversible flow impossible. The attempt to increase the deformation rate leads to the rupture of elastics. So, we constructed a model for the deformation-induced fluid-to-rubber transition at high rates and confirmed it by direct measurements of elastic-to-plastic strain ratio as a function of deformation rate.

The depletion attraction, induced upon addition of a nonadsorbing polymer to a colloidal solution, can lead to gel formation at sufficiently high polymer concentrations, which corresponds to strong attractive interactions. We have investigated the nonlinear rheological response, in particular the yielding, of colloidal gels with an intermediate volume fraction and variable interparticle attraction. Two distinct yielding processes are observed in both oscillatory experiments, namely, dynamic strain sweeps and transient experiments, here step rate, creep, and recovery tests. The first yielding process occurs at strains similar to the range of the interparticle potential and is interpreted as the breaking of bonds, which destroys the particle network and leads to individual clusters. The process of bond breaking is successfully modeled as the escape of a particle from the potential well of its nearest neighbor. The second yield point occurs at larger strains and is related to the deformation and fragmentatio...

Research on soft materials, including colloidal suspensions, glasses, pastes, emulsions, foams, polymer networks, liquid crystals, granular materials, and cells, has captured the interest of scientists and engineers in fields ranging from physics and chemical engineering to materials science and cell biology. Recent advances in rheological methods to probe mechanical responses of these complex media have been instrumental for producing new understanding of soft matter and for generating novel technological applications. This review surveys these technical developments and current work in the field, with partial aim to illustrate open questions for future research.

International audience; Shear step strain experiments with various strain amplitudes have been performed on poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA) melts using both stress-controlled and strain-controlled rheometers. Firstly, the onset of the rheological nonlinearity, i.e., nonlinear stress damping behavior, occurring after a large step strain is found to be a phenomenological consequence of an abrupt stress decline within the transient period of strain actuation. Such a feature, analogous to the stress overshoot in a fast startup shear with sufficiently high rates, is interpreted based on theoretical frameworks concerning chain disentanglement/re-entanglement arising from chain retraction. Furthermore, this work infers that full technical considerations in step strain experiments are indispensable for acquisition of accurate stress relaxation data, as some common but easily overlooked technical problems are influential, probably introducing errors. For instance, a too long finite rise time and a stress overload enable to hinder the nonlinearity onset in the transient period, resulting in inaccurate experimental data. In this sense, the stress-controlled rheometer is advantageous relative to the strain-controlled one, although the inertia in the stress-controlled mode incurs a strain overshoot effect. Nevertheless, the amplitude-dependent strain overshoot offers a very subtle effect on the stress damping behavior. Moreover, transducer compliance problems need to be taken into account, especially for high stiffness polymers. Overall, the effects of such technical factors are dictated by their ability to influence the chain stretching/retraction and the disentanglement. A well-considered experimental methodology is necessary to achieve confidence windows in step strain experiments for analysis accuracy.

Thanks to extensive observations of strain localization upon startup or after stepwise shear, a conceptual framework for nonlinear rheology of entangled polymers appears to have emerged that has led to discovery of many new phenomena, which were not previously predicted by the standard tube model. On the other hand, the published theoretical and experimental attempts to test the limits of the tube model have largely demonstrated that the most experimental data appear consistent with the tube-model based theoretical calculations. Therefore, the field of nonlinear rheology of entangled polymers is at a turning point and is thus a rather crucial area in which further examinations are needed. In particular, more molecular dynamics simulations are needed to delineate the detailed molecular mechanisms for the various nonlinear rheological phenomena.

Aqueous solutions of thread-like micelles of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) are known to be classified into three types depending on their rheological properties that change with the concentration ratio of salt to detergent: When the concentration of NaSal, CS, is much lower than that of CTAB, CD, the dynamic modulus, G*, is similar to that of dilute polymer solutions without entanglements (Type I). With increasing salt concentration (CS < CD), G* becomes similar to that of entangled semidilute polymer solutions (Type II). For the case of CS ≥ CD, G* is described with the Maxwell model having a single relaxation time (Type III). In this study, nonlinear viscoelastic behavior of type II solutions was examined. G* for the solution with CD = 1.0×10−1 molL−1 and CS = 3.25 ×10−2 molL−1 was very similar to that of the ordinary entangled polymer solutions. The damping function determined from the stress relaxation experiments was close to that of the entangled polymers and well described with the Doi-Edwards model. The characteristic time for nonlinear rheology, τeq, was determined from the stress overshoot of viscosity growth function. τeq was found to be about thirty times smaller than the characteristic time for nonlinear stress relaxation. These features were in accord with those of the ordinary entangled polymer solutions. However, shear rate dependence of the steady viscosity was not described with the Cox-Merz rule, suggesting that a shear induced structure might have been developed at long times during a steadily flowing state.

In recent years, large amplitude oscillatory shear (LAOS) has become a prime tool to investigate the nonlinear rheology of complex fluids. More specifically, most studies use LAOS data as a macroscopic probe for hypothetical microscopic changes, sometimes successfully. Nevertheless, we would like to raise awareness on the potential impact of secondary flows triggered by instabilities in LAOS performed in curved shear flows exemplified by the Taylor–Couette geometry. First, we show that even for Newtonian fluids, where no micro-structural changes are expected, complex flow patterns can emerge in the LAOS data. Second, we stress the potential impact of similar effects in complex fluids by studying LAOS flows of a well-known shear-banding surfactant solution. Our hope is that our thorough study of the Newtonian case together with preliminary experiments on a complex fluid will reinforce the already successful analogy existing between inertial and elastic instabilities, suggest caution for future LAOS studies focused solely on a structural perspective, and open new research avenues combining flow instabilities and unsteady flows in complex fluids.

Some topics in nonlinear rheology are discussed for polymeric systems: constitutive equation for dilute solutions; strain hardening in elongational flow; chain retraction in entangled systems; stress overshoot of non-entangled systems; entanglement molecular weight.

We discuss the linear and nonlinear rheology of concentrated microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from a liquid to a highly compressed yet disordered solid.

Time-dependent nonlinear flow behavior was investigated for a model hard-sphere suspension, a 50 wt% suspension of spherical silica particles (radius = 40 nm; effective volume fraction = 0.53) in a 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The suspension had two stress components, the Brownian stress σ B and the hydrodynamic stress σ H After start-up of flow at various shear rates $$\dot \gamma $$ , the viscosity growth function η+ (t, $$\dot \gamma $$ ) was measured with time t until it reached the steady state. The viscosity decay function η− (t, $$\dot \gamma $$ ) was measured after cessation of flow from the steady as well as transient states. At low $$\dot \gamma $$ where the steady state viscosity η ( $$\dot \gamma $$ ) exhibited the shear-thinning, the η− (t, $$\dot \gamma $$ ) and η+ (t, $$\dot \gamma $$ ) data were quantitatively described with a BKZ constitutive equation utilizing data for nonlinear relaxation moduli G (t, γ). This result enabled us to attribute the thinning behavior to the decrease of the Brownian contribution η B = σ B / $$\dot \gamma $$ (considered in the BKZ equation through damping of G (t, γ)). On the other hand, at high $$\dot \gamma $$ where η ( $$\dot \gamma $$ ) exhibited the thickening, the BKZ prediction largely deviated from the η+ (t, $$\dot \gamma $$ ) and η+ (t, $$\dot \gamma $$ ) data, the latter obtained after cessation of steady flow. This result suggested that the thickening was due to an enhancement of the hydrodynamic contribution η H = σ H / $$\dot \gamma $$ (not considered in the BKZ equation). However, when the flow was stopped at the transient state and only a small strain (

We have conducted a real time, two-dimensional light scattering study of the nonlinear dynamics of field-induced structures in an electrorheological fluid subjected to oscillatory shear. We have developed a theoretical description of the observed dynamics by considering the response of a fragmenting/aggregating particle chain to the prevailing hydrodynamic and electrostatic forces. This structural theory is then used to describe the nonlinear rheology of ER fluids.

We present a phenomenological theory for the rheological behavior of ordered mesophases of mixed diblock and triblock copolymer under shear. This theory is based on a coupled multilayer model for mesophase dynamics, and represents the extension of an earlier theory [Doi et al., Macromolecules 26, 4935 (1993)] for pure diblock copolymer mesophases. We show that added triblock copolymer suppresses yielding behavior in copolymer mesophases. We discuss the possible relevance of our model to experimental rheological and structural studies of microphase‐separated diblock+triblock copolymer solutions in selective solvents.

The stress versus strain curves in dense colloidal dispersions under start-up shear flow are investigated combining experiments on model core-shell microgels, computer simulations of hard disk mixtures, and mode coupling theory. In dense fluid and glassy states, the transient stresses exhibit first a linear increase with the accumulated strain, then a maximum ('stress overshoot') for strain values around 5%, before finally approaching the stationary value, which makes up the flow curve. These phenomena arise in well-equilibrated systems and for homogeneous flows, indicating that they are generic phenomena of the shear-driven transient structural relaxation. Microscopic mode coupling theory (generalized to flowing states by integration through the transients) derives them from the transient stress correlations, which first exhibit a plateau (corresponding to the solid-like elastic shear modulus) at intermediate times, and then negative stress correlations during the final decay. We introduce and validate a schematic model within mode coupling theory which captures all of these phenomena and handily can be used to jointly analyse linear and large-amplitude moduli, flow curves, and stress-strain curves. This is done by introducing a new strain- and time-dependent vertex into the relation between the the generalized shear modulus and the transient density correlator., 21 pages, 13 figures

One of the hallmarks of biopolymer gels is their nonlinear viscoelastic response to stress, making the measurement of the mechanics of these gels very challenging. Various rheological protocols have been proposed for this; however, a thorough understanding of the techniques and their range of applicability as well as a careful comparison between these methods are still lacking. Using both strain ramp and differential prestress protocols, we investigate the nonlinear response of a variety of systems ranging from extracellular fibrin gels to intracellular F-actin solutions and F-actin cross-linked with permanent and physiological transient linkers. We find that the prestress and strain ramp results agree well for permanently cross-linked networks over two decades of strain rates, while the protocols only agree at high strain rates for more transient networks. Surprisingly, the nonlinear response measured with the prestress protocol is insensitive to creep; although a large applied steady stress can lead to significant flow, this has no significant effect on either the linear or nonlinear response of the system. A simple model is presented to provide insight into these observations. © 2010 The Royal Society of Chemistry.

We image semi-flexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 micron. The degree of nonaffine strain depends on polymer length and crosslink density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk., Comment: 9 pages (double-spaced) of text, 4 figures + 1 supplementary figure

The mode coupling theory (MCT) for the glass transition is in reasonable accord with observations on attractive colloids at high densities. This paper presents a brief review of the MCT. This is followed by a more detailed discussion of two recent extensions of it. These address (i) nonlinear rheology and jamming in colloids under shear and (ii) weak gelation of colloids at low densities.

We report our studies of the linear and nonlinear rheology of aqueous solutions of the surfactant cetyl trimethylammonium tosylate (CTAT) with varying amounts of sodium chloride (NaCl). The CTAT concentration is fixed at 42mM and the salt concentration is varied between 0mM to 120mM. On increasing the salt (NaCl) concentration, we see three distinct regimes in the zero-shear viscosity and the high frequency plateau modulus data. In regime I, the zero-shear viscosity shows a weak increase with salt concentration due to enhanced micellar growth. The decrease in the zero-shear viscosities with salt concentration in regimes I I and III can be explained in terms of inter-micellar branching. The most intriguing feature of our data however, is the anomalous behavior of the high frequency plateau modulus in regime II (0.12 $\le \frac{[NaCl]}{[CTAT]} \le$ 1. 42). In this regime, the plateau modulus {\it increases} with an increase in NaCl concentration. This is highly counter-intuitive, since the correlation length of concentration fluctuations and hence the plateau modulus $G_{\circ}$ are not expected to change appreciably in the semi-dilute regime. We propose to explain the changes in regime II in terms of the unbinding of the organic counterions (tosylate) from the CTA$^{+}$ surfaces on the addition of NaCl. In the nonlinear flow curves of the samples with high salt content, significant deviations from the predictions of the Giesekus model for entangled micelles are observed., Comment: 27 pages, inclusive of 9 eps figures

An optical visualization apparatus has been designed to measure the particle velocity of concentrated particle suspensions in a stress controlled rheometer equipped with a quartz parallel-plate. Suspensions with high and low matrix viscosity were used to investigate the nonlinear rheology and the local flow mechanism, as well as the correlations between particle velocity profiles and transition behaviors. Herein, it is shown that the sedimentation has great effects on the flow behavior of suspensions and on the particle velocity profiles. Local flow behaviors e.g. shear banding, drift in the center position of oscillatory shear and dynamic wall slip, have been studied comprehensively. By Fourier-transform rheology (FTR) analysis, the shear banding phenomenon is proved to be strongly linked with the nonlinear rheology of suspensions.

Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states., Review article