Strain hardening of polymer melts is able to improve the uniformity of items in processing operations with elongational deformation. Of particular interest in this aspect is the dependence of strain hardening on elongational rate. In its first part, the paper presents a review on melt strain hardening obtained in uniaxial extensional experiments. Its dependence on elongational rate is of particular interest insofar as besides non-strain-hardening polymers, strain hardening increasing or decreasing with rate can be found. Results on linear polymers like polystyrene (PS), polypropylene (PP), high-density polyethylene (HDPE), and linear low-density polylethylene (LLDPE) in dependence on molecular parameters are discussed, as well as those of various blends. Particularly interesting are the strain-hardening features of certain HDPEs and LLDPEs, which could be understood by the assumption of a non-homogeneous chemical structure of the samples. Blends of various compositions of a linear and a long-chain branched PP throw light on the complex relation between branching structure and rate dependence of strain hardening. In the second part of the paper, the different strain-hardening behavior of linear polymers is interpreted by assessing the Rouse times as decisive physical quantity. For blends of certain linear species like HDPE and PP and those of linear with long-chain branched polymers, the existence of separate phases in the molten state is postulated. The assumptions are discussed in the light of the various studies on miscibility of linear and branched polyolefins from the literature.Graphical Abstract

Rheological analysis is an important tool to investigate the structural characteristics of materials widely used in the biomedical field, such as polymer solutions, colloids, and hydrogels. In this work, we studied the rheological properties of a colloidal system composed of carboxymethyl cellulose (CMC) and Laponite, both biocompatible materials. Rheological properties of CMC/Laponite aqueous dispersions are influenced by electrostatic interactions and hydrogen bonds between the silanol (Si–O) groups of Laponite and hydroxyl (-OH) of CMC. It was found that the effect of Laponite rheological behavior is strongly affected by CMC concentration, resulting in weak or strong gels. Adding CMC reinforces the blended network, increasing the storage \(\left({G}^{^{\prime}}\right)\) and loss \(\left(G''\right)\) moduli, as well as viscosity. CMC/Laponite gels presented strong shear-thinning and thixotropy due to structural rearrangements when subjected to shear stresses. Moreover, time sweep tests revealed that adding CMC inhibited Laponite aging.Graphical Abstract

AbstractIn flows with re-entrant corners, polymeric fluids can exhibit a recirculation region along the wall upstream from the corner. In general, the formation of these vortices is controlled by both the extensional and shear rheology of the material. More importantly, these regions can only form for sufficiently elastic fluids and are often called “lip vortices”. These elastic lip vortices have been observed in the flows of complex fluids in geometries with sharp bends. In this work, we characterize the roles played by elasticity and shear thinning in the formation of the lip vortices. Simulations of the Newtonian, Bird-Carreau, and Oldroyd-B models reveal that elasticity is a necessary element. A systematic study of the White-Metzner, finitely extensible non-linear elastic (FENE-P), Giesekus and Rolie-Poly models shows that the onset and size of the elastic lip vortex is governed by a combination of both the degree of shear thinning and the critical shear rate at which the thinning begins.Graphical Abstract(left) Contour plots of velocity magnitude for the FENE-P model showing the decrease in size of the elastic lip vortex as maximum extensibility decreases. (right) Length of the elastic vortex as a function of a modified Carreau number showing a modelindependent effect of the degree and onset of shear thinning.

The colloidal suspension of magnesium lithium phyllosilicate (MLPS), a synthetic clay that shows complex rheological behaviors, is a promising analogue for natural soft clay. The significant thixotropy of MLPS colloidal suspension controls the solid-liquid transition and affects the application of the material. In this work, the thixotropic yielding behaviors of MLPS with concentrations of 3, 4, 5, and 6 wt% were investigated utilizing rheological testing methods. The static and dynamic yield stresses measured by different methods were analyzed and compared. The flow curves of shear rate ramp tests show inapplicability in determining yield stresses due to shear banding, while the yield stresses obtained by shear stress ramp and oscillatory shear tests exhibit satisfactory consistency. Coupled with a structural kinetics equation, a thixotropic visco-plastic model incorporating static and dynamic yield stress was established to describe the thixotropic yielding behavior of MLPS suspension. The model parameters were conveniently determined via shear ramp tests and step change in shear rate tests with good fitting performance, and the concentration-dependent characteristics of the parameters were also discussed. Based on model prediction and experimental results, the interactions between shear stress, shear rate, and microstructure were analyzed in steady and transient states.

A Pom-Pom polymer with qa side chains of molecular weight Mw,a at both ends of a backbone chain of molecular weight Mw,b is the simplest branched polymer topology. Ten nearly monodisperse polystyrene Pom-Pom systems synthesized via an optimized anionic polymerization and a grafting-onto method with Mw,b of 100 to 400 kg/mol, Mw,a of 9 to 50 kg/mol, and qa between 9 and 22 are considered. We analyze the elongational rheology of the Pom-Poms by use of the hierarchical multi-mode molecular stress function (HMMSF) model, which has been shown to predict the elongational viscosity of linear and long-chain branched (LCB) polymer melts based exclusively on the linear-viscoelastic characterization and a single material parameter, the so-called dilution modulus GD. For the Pom-Poms considered here, we show that GD can be identified with the plateau modulus \({G}_{N}^{0}={G}_{D}\), and the modeling of the elongational viscosity of the Pom-Poms does therefore not require any fitting parameter but is fully determined by the linear-viscoelastic characterization of the melts. Due to the high strain hardening of the Pom-Poms, brittle fracture is observed at higher strains and strain rates, which is well described by the entropic fracture criterion.Graphical abstract

Shear thickening fluids (STFs) exhibit a liquid–solid-like transition under impact because of the formation and evolution of shear jamming in the STFs. This study aims to develop a computational fluid dynamics (CFD) model to simulate the shear jamming formation and evolution in a concentrated STF under impact for the optimum design of the STF applications. The STF was defined with a strain rate–dependent viscosity and compressibility. In the CFD model, the interface between air and STF was modelled by the volume of fluid method to solve the multiphase flow problem. In addition, the impact penetration process of an impactor was reproduced by the change of the fluid domain shape with a dynamic mesh method. The shear jamming was demonstrated clearly by a high strain–rate region caused by the impact. The numerical results were comparable to the experimental observations of shear jamming evolution using a high-speed camera. Furthermore, the numerical results showed that the effect of the STF’s dimensions (depth and diameter) on the expansion rate of the shear jamming was insignificant.

The viscosity of aqueous suspensions of 25 nm titanium dioxide nano-particles was studied as a function of shear rate, temperature, and particle concentration. It is suggested that the complex behaviour of the material could be explained by the interplay of three factors, each having activation energy and activation entropy components. These are the intrinsic viscosity which was shown to obey a semi-empirical form of DLVO equation plus two shear rate–dependent mechanisms, one (thinning) changing the structure from an ordered to a disordered state, the other (thickening) an activation action term due to energy dissipated in particle collisions.

We investigated the rheological properties of bidisperse entangled-polymer blends under high-deformation-rate flows by slip-link simulations with a friction reduction mechanism. The friction reduction mechanism induced by the stretch and orientation (SORF) is important to predict the viscoelasticity under uniaxial elongational flows. To test the applicability of this mechanism for bidisperse systems, we incorporated an expression of friction reduction (Yaoita et al. Macromolecules 45:2773–2782 2012) into the Doi-Takimoto slip-link model (DT model) (Doi and Takimoto Philos Trans R Soc Lond A 361:641–652 2003). For six experimental bidisperse systems, i.e., four polystyrene blends and two polyisoprene blends, the extended DT model where the order parameter of the friction reduction mechanism is evaluated through the component averages succeeds in reproducing the data under uniaxial elongation and shear. This success is due to the suppression of the stretch of the longer chains using the statistical average over each component. Through this study, the SORF expression improves the rheological prediction for bidisperse entangled polymer melts under uniaxial elongational flows with strain rates comparable to or larger than the inverse of the Rouse relaxation time of the longer chains. Additionally, the predictions with the SORF using the component average for the stretches reproduce the steady viscosities because under elongational flows, the states of the components with different molecular weights clearly differ from each other depending on their Rouse relaxation time. The finding means that for chain dynamics, the friction coefficient is determined by the state of the surrounding polymer chains and the state of the chain.

The focus of the present paper is the rheological study of poly(D,L-lactic-acid) (PDLLA) towards a modeling of their healing properties during 3D direct pellet printing extrusion (DPPE). The viscoelastic properties of PDLLA and the filament temperature during deposition are first characterized. The influence of DPPE processing conditions is investigated in terms of temperature, time, and printing speed. For this, we propose a modeling of the process-induced interphase thickness between two deposited layers considering the non-isothermal polymer relaxation and accounting for the contribution of entanglement rate through the Convective constraint release model. Hence, taking into account the induced chain orientation and mobility coming from filament deposition, this model quantifies the degree of healing between 3D-printed layers. Eventually, the proposed model is validated by comparing the theoretically calculated degree of healing with experimental tensile properties and lap shear results.Graphical Abstract

This study investigates the effect nano-silica particle additive with different concentrations and sizes on magneto-rheological behavior of carbonyl iron particle suspensions from the tribological point of view. The lubrication states between particle–particle contacts and particle-plate contacts affected the magnetorheological behaviors. The silica particle additive leads to a larger friction coefficient at boundary lubrication conditions of the base carrier fluid which results in solid–solid contact states between the particles and plate and improves the yield stress. The normal stress and plate gap reflect that the nano-silica particles prevent the end of the ferromagnetic particle from sliding at the plate under high magnetic field, which enhance the friction effect between the particle and plate. The normalization methods based on the concept of tribology disclosed the influence of silica particle additives on the structural evolution of iron particles. It provides an effective guidance for the formulation design of MRF considering the effect of additives on the lubrication performance of the base carrier fluid.

The hydrodynamics of thin films is an important factor when it comes to the stability and rheology of multiphasic materials, such as foams, emulsions, and polymer blends. However, there have so far been only limited experimental studies addressing the dynamics of individual free-standing thin films at conditions similar to those encountered on macroscopic scales. In this article, we study a well-characterized system of a water-in-oil emulsion stabilized by a non-ionic surfactant (SPAN80) close to its CMC. We employ a dynamic thin film balance, to study the dynamics of freestanding films under both constant and time-varied pressure drops. We compare with the recently published results of Narayan et al. (2020) on colliding droplets of the same system with a hydrodynamic microfluidic trap, and show for the first time that agreement between the two lengthscales is possible, which indicates that the coalescence is indeed dominated by the dynamics in the film. We then address the scatter in the coalescence times and show that it can be affected by extrinsic factors, as well as by variations in the collision angle. Finally, we discuss the difficulties of extracting insight on the coalescence mechanism from coalescence time distributions when different effects such as impurities, small pressure variations, collision angle variations, and possible Marangoni-related instabilities are at play.

A myriad of empirical and phenomenological constitutive models that describe different observed rheologies of complex fluids have been developed over many decades. With each of these constitutive models' strength in recovering different rheological responses, algorithms that allow the data to automatically select the appropriate constitutive relations are of great interest to rheologists. Here, we present a rheology-informed neural network (RhINN) that enables robust model selection based on available experimental data with minimal user intervention. We train our RhINN on a series of experimental data for different complex fluids and show that it is capable of finding the appropriate model with the lowest number of fitting parameters for each data set. Finally, we show that uniform selection of a handful of data over the entire accessible shear rates does not affect the RhINN's accuracy, while providing a specific range of data (and omitting the rest) results in an erroneous model determination.

Hydrogen bonding is the most common noncovalent reversible interaction leading to supramolecular polymeric assemblies. Shabbir et al. (Macromolecules 48:5988–5996, 2015) reported both linear and nonlinear rheological data for a model system consisting of pure poly(n-butyl acrylate) (PnBA) homopolymer and three PnBA-poly(acrylic acid) (PnBA-PAA) copolymers with different numbers of acrylic acid (AA) side groups. Hydrogen bonds between the AA groups not only cause the storage and loss modulus to shift in the direction of a power law scaling of 0.5 in the terminal relaxation regime, but also the elongational viscosity shows increasing strain hardening with a strongly nonlinear dependence on the number of hydrogen bonding groups. Based on the “Sticky Rouse” model and a constitutive equation of the Doi-Edwards type with consideration of chain stretch, we model the effect of hydrogen bonding on the elongational viscosity of the PnBA-AA copolymers. We show that the elongational viscosity data are consistent with a Sticky Rouse relaxation modulus of the AA associations characterized by a constant modulus \(G_{A}\) and a constant sticker life time \(\tau_{A}\), while the complexity of the hydrogen assemblies as quantified by the Sticky Rouse time increases with the concentration of AA groups from the order of seconds (3% AA) to hours (6%AA) and to 1 day (13%AA), and leads to extreme strain hardening. The elongational stress shows a steady state at large strains and the stretch reaches a limiting value independent of strain rate. At the highest concentration of AA groups investigated (38%AA), the PnBA-AA copolymer is a weak gel fracturing at a critical strain, and the sticker life time loses its significance. The effect of the Sticky Rouse time on self-healing is discussed.

Adsorption of asphaltene molecules at the oil-water interface induces the formation of a complex microstructure that stabilizes emulsions and impairs the efficiency of crude oil refining. We explore the contribution of polar and non-polar solvents to the rheology and self-aggregation of indigenous asphaltenes from a crude oil sample. We aim to assess the rheological properties of adsorbed layers by designing a set of protocols to explore the mechanical properties of asphaltene laden interfaces. The asphaltenes are also characterized by optical and SEM microscopy, besides surface-area isotherms. Our findings indicate that asphaltenes are a polycondensed aromatic island-type structure that are able to reversibly adsorb when toluene is placed onto the air-water interface. They also show that low aromatic solvents may lead to greater viscoelastic moduli due to disturbances on the asphaltene film. We find that the network growth and asphaltene self-arrangement are directly related to the solvent aromatic content.

3D printing is changing the way we conceive, design, and build 3D objects in mechanical, biomedical, aerospace, construction, automotive and maritime industries. In the current work, the nonlinear rheological behaviour of polymer melts is measured through a table-top 3D printer (3D RheoPrinter) that, smartly modified, allows inline investigation of viscosity, extrudate swell and melt fracture. By using a piezoresistive mini-transducer, the innovative system is designed to be applicable to all Fused Deposition Modelling (FDM) 3D printers by a simple and cost-effective modification of a state-of-art nozzle. The measurements of the nonlinear rheological behaviour are compared with traditional, rotational rheology. Two biodegradable polymers, i.e. polylactic acid and polycaprolactone, are investigated as model systems to test the 3D RheoPrinter. The results of the shear viscosity and the first normal stress difference coefficient, as function of shear rate, show a good agreement between the 3D RheoPrinter and rotational rheometer with an error of about 6% for a confidence interval of 96%. Moreover, the 3D RheoPrinter can still be used as 3D printer. In the last part of this work, it is presented a printing test for building 3D structures in which the results show controllable resolution by means of the measured rheological information such as the extrudate swell. The vision of this work is that an inline rheological characterization, possible with the developed 3D RheoPrinter, can enable automatic process optimization and quality assurance to the 3D printing community. The social and scientific impacts of this work are maximized by the cost-efficiency and simplicity of the design that makes it within reach of the general public. The 3D RheoPrinter opens for a rheological experimentation to a broad audience and it offers important insights to bring FDM to the next level of resolution.

In this work, we investigate the large amplitude oscillatory shear (LAOS) behavior of white-wheat, wholegrain-wheat and chickpea flour doughs experimentally and theoretically. In order to accurately model the LAOS behavior of those doughs, it was important to study their linear viscoelastic as well as stress relaxation behaviors. We analyzed the linear viscoelastic behavior theoretically through the single spring-pot model, the fractional Maxwell model (FMM) and the fractional Kelvin-Voigt model. We found that the FMM is best suited to describe the LVE of the doughs we investigated. The damping function form was chosen based on stress relaxation and strain sweep experiments. We found that the Soskey-Winter (SW) equation is suitable for accurately describing the damping behavior of doughs. The LAOS experimental results were obtained at a set of strain amplitude and frequency values to build the Lissajous-Bowditch curves in Pipkin space. We modeled the LAOS stress response using the Kay-Bernstein Kearsley and Zapas (K-BKZ) model coupled with the FMM and SW models. The SW parameters were optimized for each dough by fitting the LAOS Lissajous-Bowditch curves in Pipkin space. The obtained fits to LAOS stress response were very good and illustrate that the FMM-SW-K-BKZ model provides an excellent description of the LAOS behavior of the different variety of doughs examined in this work. Moreover, the study shows that LAOS Lissajous-Bowditch curves provide characteristically different shapes for wheat and chickpea flour doughs.

We used mixture design to predict rheological parameters, namely the storage and loss modulus \(G'\) and \(G''\) and the critical stress \(\sigma _{c}\), of mixtures of Laponite EP and bentonite clay. Laponite EP is an organically coated laponite displaying unusual rheological behaviour compared to its unmodified form. We examined the effect of salt (magnesium chloride) and of surfactant (Tween 20) varying the pH between 4 and 9. We found reliable complex models with significant higher order terms showing that the rheological behaviour of the gels was not a function of each single compound, but instead the result of multiple interactions. Such interactions had an antagonistic effect on \(G'\) and \(G''\). Stronger gels were found at low concentrations of magnesium chloride and Tween 20. The gel stability in response to stress increased with the amount of Tween 20, but decreased with magnesium chloride. Such distinct behaviour may be the result of interactions between the platelet charges and the different components, as well as salting in versus salting out effects. We identified the conditions for which the values of \(G'\) were suitable for agrochemical products. The method presented here is a quick and reliable approach to formulate products with targeted rheological properties.

Extensional rheology of a variety of linear and branched polymer melts is investigated using entry flow measurements and 15:1 axisymmetric contraction flow simulations. Using a Cogswell model analysis, we show that log−log plots of entrance pressure drop versus wall shear stress display three distinct power-law regimes, the intermediate one of which is observed beyond a critical stress associated with the onset of chain stretching effects. Our observations suggest that this stress threshold is a chain architecture-dependent property characteristic of entangled polymers. Converging flow methods are used to analyze the excess pressure losses to predict the uniaxial extensional viscosity. As the temperature is increased, the progressive shift of the kink to higher strain rates seen in the flow curves can be captured by a proposed Trouton ratio model, where the characteristic time of the fluid is assumed to follow the empirical William–Landel–Ferry (WLF) equation. Experimental pressure drops in converging flows for Weissenberg numbers up to about 105 are used to evaluate predictions of an extended generalized Newtonian fluid (GNF-X) model, where a weighted viscosity for mixed flows has recently been derived and a weighting function classifies flows intermediate between shear and shearfree flows. Judging from its success in predicting the nonlinear extensional response of both linear and branched polymers, as well as its ability to differentiate the respective flow patterns, the GNF-X model should be useful for simulations of commercial polymer processing.Graphical abstract