Empirical rules play a crucial role in industrial and experimental settings for efficiently determining the rheological properties of materials, thereby saving both time and resources. An example is the Cox–Merz rule, which equates the steady-shear viscosity with the magnitude of the complex viscosity obtained in oscillatory tests. This empirical rule provides access to the steady-shear viscosity that is useful for processing conditions without the instabilities associated with experiments at high shear rates. However, the Cox–Merz rule is empirical and has been shown to work in some cases and fail in others. The underlying connection between the different material functions remains phenomenological and the lack of a comprehensive understanding of the rheological physics allows for ambiguity to persist in the interpretation of material responses. In this work, we revisit the Cox–Merz rule using recovery rheology, which decomposes the strain into recoverable and unrecoverable components. When viewed through the lens of recovery rheology, it is clearly seen that the steady-shear viscosity comes from purely unrecoverable acquisition of strain, while the complex viscosity is defined in terms of contributions from both recoverable and unrecoverable components. With recovery tests in mind, we elucidate why the Cox–Merz rule works only in a limited set of conditions and present an approach that could allow for universal comparisons to be made. This work further highlights the significance of recovery rheology by showing how it is possible to extend beyond phenomenological approaches through clear rheophysical metrics obtained by decomposing the material response into recoverable and unrecoverable components.

The ability to accurately predict the rheological behavior of the blends of two incompatible polymers is critical to the polymer industry. The constitutive modeling of incompatible polymer blends requires understanding the structure and dynamics of the blends across different length scales. The polydispersity of chain length at the molecular level and nonuniformity of flow field due to dispersed domains at the mesoscopic level present significant challenges to this industrially relevant problem. This work proposes a modeling framework for linear and nonlinear rheology of industrial incompatible polymer blends with sea-island morphology. For the individual components, we adopt the Rolie-Double-Poly model and generate the relaxation spectrum from an optimized molecular weight distribution. We derive a new mixing rule without empirical parameters from the flow field analysis inside and outside the droplets. The phase interface, modeled by an ellipsoidal model, contributes to the apparent rheology only at low shear rates. Our modeling approach is verified by the shear and extensional rheology of eight polymer blends with a broad range of viscosity ratios (0.01–100). We also show that the model has the ability to predict the nonlinear rheological behaviors of incompatible polymer blends with known molecular weight distributions and phase morphology.

The demand for fiber-filled polymers has witnessed a significant upswing in recent years. A comprehensive understanding of the local fiber orientation is imperative to accurately predict the mechanical properties of fiber-filled products. In this study, we experimentally investigated the fiber orientation kinetics in uniaxial extensional flows. For this, we equipped a rheometer with a Sentmanat extensional measurement device and with an optical train that allows us to measure the fiber orientation in situ during uniaxial extension using small angle light scattering. We investigated an experimental system with glass fibers for the suspended phase (L/D=8−15), and for the matrix either low density polyethylene, which shows strain hardening in extension, or linear low density polyethylene, which shows no strain hardening. For these two polymer matrices, the fiber orientation kinetics were investigated as a function of fiber volume fraction (ϕ=1%, 5%, and 10%) and Weissenberg number (by varying the Hencky strain rate, ϵ˙H=0.01−1s−1). We found that all these parameters did not influence the fiber orientation kinetics in uniaxial extension and that these kinetics can be described by a multiparticle model, based on Jeffery’s equation for single particles. Our results show that, in uniaxial extension, fiber orientation is solely determined by the applied strain and that, up to the concentrated regime (ϕ≈D/L), fiber-fiber interactions do not influence the fiber orientation. The extensional stress growth coefficient of these composites, which is measured simultaneously with the orientation, shows high agreement with Batchelor’s equation for rodlike suspensions.

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.

The dynamics of charged and hard-sphere silica colloidal suspensions are measured using diffusing wave spectroscopy and are interpreted by the Generalized Stokes–Einstein Relation (GSER). At high concentration, the resulting moduli are in good qualitative agreement with bulk rheology, including the frequency response, but are higher by a quantitative factor. We show that the “two-point” GSER, which derives from the correlated motion of the colloidal particles, provides a better quantitative agreement between bulk and microrheology. The two-point GSER applies generally when the average scattering vector sampled by the multiple scattering events corresponds to a length scale greater than the scatterer diameter. We discuss applications for characterizing colloid interactions by measuring the high-frequency moduli of suspensions and extend the two-point analysis to tracer particle microrheology measurements of a semiflexible biopolymer network.

We present a novel approach to perform passive microrheology. A method to measure the rheological properties of fluids from the Brownian motion of suspended particles. Rheological properties are found from the particles' mean square displacements (MSDs) as a function of measurement time lag. Current state-of-the-art approaches find the MSD by tracking multiple particles' trajectories. However, particle tracking approaches face many limitations, including low accuracy and high computational cost, and they are only applicable to low particle seeding densities. Here, we present a novel method, termed particle image rheometry (PIR), for estimating the particle ensemble MSD from the temporal evolution of the probability density function of the displacement as a function of measurement time lag. First, the probability density function (PDF) of the particle displacements for each time lag is found using a generalized ensemble image cross-correlation approach that eliminates the need for particle tracking. Then, PDFs are used to calculate the MSD from which the complex viscosity of the solution is measured. We evaluate the performance of PIR using synthetic datasets and show that it can achieve an error of less than 1% in passive microrheology measurements, which corresponds to a twofold lower error than existing methods. Finally, we compare the measured complex viscosity from PIR with bulk rheometry for a polymeric solution and show agreement between the two measurements.

From a mechanical perspective, blood is a complex fluid with a rate- and time-dependent response to an applied deformation. At small deformation rates, cell aggregations owing to the bridging of fibrinogen proteins result in the formation of rouleaux structures manifesting in a large increase in the overall viscosity of the blood viscosity and the emergence of measurable yield stress. At elevated deformation rates, these internal aggregated mesostructures are broken down in a dynamical fashion, giving rise to a thermokinematic memory and thixotropic behavior of the blood. These rich and complex rheological features of blood are primarily governed by the interactions between different cells as well as the fraction of red blood cells (RBCs). Here, using a series of detailed computational tools and benchmarking experimental measurements, we present a constitutive model that accurately describes the rate- and time-dependent rheology of blood based on two physiological metrics of the blood: the hematocrit and fibrinogen concentration. We show that the model is capable of accurately predicting blood flow, not only under simple steady flows but also under different flow protocols relevant to a real circulatory system.

We formulate a particle and force level, activated dynamics-based statistical mechanical theory for the continuous startup nonlinear shear rheology of ultradense glass-forming hard sphere fluids and colloidal suspensions in the context of the elastically collective nonlinear Langevin equation approach and a generalized Maxwell model constitutive equation. Activated structural relaxation is described as a coupled local-nonlocal event involving caging and longer range collective elasticity which controls the characteristic stress relaxation time. Theoretical predictions for the deformation-induced enhancement of mobility, the onset of relaxation acceleration at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady-state structural relaxation time and viscosity, a nonvanishing activation barrier in the shear thinning regime, an apparent Herschel–Buckley form of the shear rate dependence of the steady-state shear stress, exponential growth of different measures of a yield or flow stress with packing fraction, and reduced fragility and dynamic heterogeneity under deformation were previously shown to be in good agreement with experiments. The central new question we address here is the defining feature of the transient response—the stress overshoot. In contrast to the steady-state flow regime, understanding the transient response requires an explicit treatment of the coupled nonequilibrium evolution of structure, elastic modulus, and stress relaxation time. We formulate a new quantitative model for this aspect in a physically motivated and computationally tractable manner. Theoretical predictions for the stress overshoot are shown to be in good agreement with experimental observations in the metastable ultradense regime of hard sphere colloidal suspensions as a function of shear rate and packing fraction, and accounting for deformation-assisted activated motion appears to be crucial for both the transient and steady-state responses.

The present work investigates nonlinear behavior in large amplitude oscillatory shear (LAOS) of unsaturated wet granular materials using pressure-imposed rheometric measurements that enable to explore how the material properties characterizing the flow response depend on both strain amplitude and frequency of deformation. Away from the quasistatic limit, we show that the energy dissipated per unit volume in a single LAOS cycle, which can be visualized by the area enclosed by the Lissajous curve of stress versus strain, is an increasing function of the viscosity of the wetting liquid and is also influenced by the reduced pressure (comparing the cohesive to confining forces) and the frequency. Introducing the inertial number I and the viscous number Iv as previously done, it is shown that the influence of surface tension, viscosity, and driving frequency can be captured by plotting the dissipated energy per unit volume versus the viscous number: a good collapse is obtained. It is shown that an increase in liquid content shifts the whole curve of the dissipated energy upwards, indicating that the overall dissipation mechanism does not change with liquid content, only the energy dissipation related to the internal structure and its breakdown changes.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Coutouly et al.: Exploiting the lower disorder-to-order temperature in polystyrene-b-poly(n-butyl acrylate)-b-polystyrene triblock copolymers to increase their flow resistance at high temperature. J. Rheol. 1 November 2022; 66 (6): 1319–1320. https://doi.org/10.1122/8.0000565 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentThe Society of RheologyJournal of Rheology Search Advanced Search |Citation Search