Extensional Viscosity Research Articles

Modelling elongational viscosity overshoot and brittle fracture of low-density polyethylene melts

The Hierarchical Multi-mode Molecular Stress Function (HMMSF) model predicts the elongational and multiaxial extensional viscosities of polydisperse linear polymer melts based exclusively on their linear viscoelastic characterization and a single nonlinear material parameter, the so-called dilution modulus {G}_{D}. For long-chain branched (LCB) polymer melts such as low-density polyethylene (LDPE), the HMMSF model describes quantitatively the elongational stress growth coefficient up to the maximum of the elongational viscosity but fails to predict the existence of the maximum and the following steady-state viscosity. By taking into account branch point withdrawal in elongational flow of LCB melts, we extend the HMMSF model and show that the maximum of the elongational viscosity can be characterized by a single additional parameter, the characteristic stretch {overline{lambda }}_{m}, while the steady-state tensile stress and the elongational viscosity depend only on the dilution modulus {G}_{D} as in the case of linear polydisperse melts. Comparison of predictions of the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model to experimental data of 5 LDPE melts with widely different molecular weights, polydispersities and densities, and a model polystyrene pom-pom polymer shows good agreement within experimental accuracy in constant elongational-rate flow as well as stress relaxation after steady and reversed elongational flow. For the LCB melts considered, we report differences in the specific Hencky strain at the maximum of the tensile stress as quantified by the characteristic stretch {overline{lambda }}_{m}, and we discuss correlations between polydispersity, dilution modulus {G}_{D}, and strain hardening potential of the LDPE melts. We also extend the fracture criterion for brittle fracture of monodisperse polymer melts to the case of polydisperse polymers and find reasonable agreement with experimental evidence.

Effects of residual wax content on the thermal, rheological, and mechanical properties of high‐density polyethylene

AbstractThe influence of residual wax content on the thermal, rheological, and mechanical behavior of two high‐density polyethylene (HDPE) samples from different lots of the same supplier was characterized. HDPE with a low wax content presented a higher melting temperature and a wider melting endotherm. A decrease in the degree of crystallinity and thermal stability of HDPE with a higher wax content was observed. Thermograms obtained by DSC indicated a small additional exothermic transition associated with the exclusion of residual wax. A higher wax content in HDPE produces a decrease in its viscosity due to a lubricating effect, which allows the sliding of HDPE chains of high molecular weight. In contrast, HDPE with lower wax content achieves greater elongational viscosity and melt strength. The mechanical testing results show that HDPE with higher wax content presented lower Young's modulus, tensile strength, elongation at break, and Izod impact strength than HDPE with lower wax content. The results obtained show that a relatively slight difference in wax content significantly affects HDPE properties.

Extensional rheology and CO2 foaming of thermoplastics vulcanizates: Influence of the crosslinking chemistry

The objective of this study is to investigate the ability of thermoplastic vulcanizates (TPVs) (materials based on PP/EPDM blend) to foam under CO2 batch conditions. The EPDM phase, which is dispersed into the PP phase, was dynamically crosslinked either by a phenolic resin (Resol) or by a radical peroxide (dicumyl peroxide). The results show an influence of the crosslinking chemistry on the extensional viscosity of the TPV. Regarding radical chemistry, the peroxide induces polypropylene degradation by β-scission reaction during the dynamic crosslinking process. As a result, the ability of the TPV to deform under extensional flow (Hencky deformation at break <0.5) is greatly reduced. On the contrary, the Resol-based TPV has demonstrated a non-linear viscosity behaviour (strain hardening) and a great ability to deform (Hencky deformation at break >1.5). This unexpected result for a non-homogeneous system can be explained by the confinement of the PP phase between EPDM nodules which gives to the PP chains a gel rheological behaviour. In addition, the influence of the addition of carbon black filler has also been studied. Finally, the relationship between extensional viscosity and physical foaming has been investigated. As for a homogeneous polymer, the extensional viscosity has been proved to be a key factor to estimate the foaming behaviour of complex systems like TPV. Hence, the importance of non-linear viscosity for a multi-phasic polymer to ensure foaming ability has been demonstrated.

Experimental study on the entry of solid spheres into Newtonian and non-Newtonian fluids

This study experimentally investigates the entry of hydrophobic/hydrophilic spheres into Newtonian and Boger fluids. By considering solution of 82% glycerin and 18% water and solution of 80% glycerin, 20% water and 100 ppm polyacrylamide, Newtonian and Boger fluids are made, respectively. It has been tried that liquids' surface tension, density, and viscosity are almost the same. Thus, all dimensionless numbers are approximately the same at a similar impact velocity except for the elasticity number. A PcoDimaxS highspeed camera captures the spheres' trajectory from the impact to the end of the path. Regarding the range of released height (0.5–100 cm), the impact velocities are approximately in the range of 0.31–4.43 ms−1. The role of fluid elasticity in combination with the sphere surface wettability on the air cavity formation/evolution/collapse is mainly studied. Also, the kinetics of the sphere motion (velocity, acceleration, and hydrodynamic force coefficient) is studied. The results show that air drawn due to the sphere's impact with the Newtonian liquid is more, and the pinch-off takes place later. Also, shedding bubbles are cusped-shaped in the Boger fluid, while in the Newtonian fluid, they are elliptical. In addition, the most significant impact of surface wettability is observed in the Newtonian fluid. Finally, the results reveal that the sphere in the Newtonian fluid can move faster and travel a longer distance in a specific time interval. The differences observed are closely related to the viscoelastic fluid's elasticity property and extensional viscosity.

On the assessment of shear and extensional rheology of thickened liquids from commercial gum-based thickeners used in dysphagia management

In order to promote safe swallowing in dysphagia patients, it is of interest to study the rheological properties of thickened liquids from various commercial gum-based thickening powders using small amplitude oscillatory shear, steady shear and extensional measurements. The active hydrocolloid of the studied samples included xanthan gum, guar gum or tara gum. Shear rheology measurements showed that all samples exhibited shear thinning behaviour that can be described by the Cross model. With comparable viscosity at shear rate 50 s −1 , the xanthan gum-based samples exhibited higher zero shear viscosity and longer relaxation time than the guar gum and tara gum-based samples. Furthermore, they behaved as weak gels while the other samples showed viscoelastic liquid behaviour at IDDSI (International Dysphagia Diet Standardisation Initiative) level 1 to 3. Extensional rheology revealed that the breakup time of these samples were xanthan gum > guar gum > tara gum, suggesting more superior cohesiveness of xanthan gum-based compared to the others. • Water thickened with different types of thickeners can have similar shear viscosity at shear rate 50 s -1 but very different extensional viscosity. • Xanthan gum-based thickened water behaves as concentrated solutions with higher extensional viscosity than guar gum and tara gum-based samples. • Xanthan gum-based thickened water is less likely to fracture during swallowing compared to the guar gum and tara gum-based samples. • The characteristic fluid relaxation time (λ E ) may be used to describe the cohesiveness of thickened fluid/bolus. • Extensional rheology may be an essential tool to define a safe-swallow bolus.

Analysis of Elongational Viscosity of Entangled Poly (Propylene Carbonate) Melts by Primitive Chain Network Simulations.

It has been established that the elongational rheology of polymers depends on their chemistry. However, the analysis of experimental data has been reported for only a few polymers. In this study, we analyzed the elongational viscosity of poly (propylene carbonate) (PPC) melts in terms of monomeric friction via primitive chain network simulations. By incorporating a small polydispersity of materials, the linear viscoelastic response was semi-quantitatively reproduced. Owing to this agreement, we determined units of time and modulus to carry out elongational simulations. The simulation with constant monomeric friction overestimated elongational viscosity, whereas it nicely captured the experimental data if friction decreased with increasing segment orientation. To see the effect of chemistry, we also conducted the simulation for a polystyrene (PS) melt, which has a similar entanglement number per chain and a polydispersity index. The results imply that PPC and PS behave similarly in terms of the reduction of friction under fast deformations.

Rheological Properties of MWCNT-Doped Titanium-Oxo-Alkoxide Gel Materials for Fiber Drawing.

A strategy of doping by multi-walled carbon nanotubes (MWCNT) to enhance mechanical strength and the electrical conductivity of ceramic fibers has nowadays attracted a great deal of attention for a wide variety of industrial applications. This study focuses on the effect of MWCNTs on rheological properties of metal alkoxide precursors used for the preparation of nanoceramic metal oxide fibers. The rheological behavior of MWCNT-loaded titanium alkoxide sol precursors has been evaluated via an extensional rheometry method. A substantial decrease in elongational viscosity and relaxation time has been observed upon an introduction of MWCNTs even of low concentrations (less than 0.1 wt.%). A high quality MWCNT/nanoceramic TiO2 composite fibers drawn from the specified precursors has been validated. The MWCNT percolation, which is mandatory for electrical conductivity (50 S/m), has been achieved at 1 wt.% MWCNT doping.

Modification of polylactide by reactive blending with polyhydroxybutyrate oligomers formed by thermal recycling through E1cB-elimination pathway

This study aimed to thermally recycle polyhydroxybutyrate (PHB), a microbial polyester with low thermal stability and limited re-processability, into crotonate-ended oligomers through the E1cB-elimination pathway. The resulting products were used as a functional additive to improve the mechanical and rheological properties of polylactide (PLA), which has intrinsic brittleness and low melt stability. The PLA was modified through a reactive blending process in an internal mixer. The quantitative 1H NMR analysis confirmed the crotonate functionality of the oligomers and their consumption during the reactive blending process. Tensile testing revealed that reactive blending 20 wt% PHB oligomers with PLA improve tensile toughness 24 times over pure PLA while keeping the elastic modulus above 1 GPa. Oscillatory-shear rheometry confirmed the improved shear-thinning behavior of reactive blends, while extensional viscosity measurements revealed a significant strain hardening behavior. The increase in melt stability was attributed to the formation of high molecular weight structures as a result of possible chain extension and branching reactions. DSC traces showed that branching and grafting points acted as nucleation sites, accelerating PLA melt crystallization. It was also found that increasing the PLA crystallinity above 44% gives rise to crystallization-induced phase separation, despite initial miscibility.

When Polymer Chains Are Highly Aligned: A Perspective on Extensional Rheology

We provide a Perspective on recent findings in extensional rheology for polymer melts and solutions with different macromolecular architectures. For linear polymer systems, we focus on the argument of flow-induced friction reduction and provide our comments from an experimental point of view. For branched polymers, we provide our understanding on how to control extensional viscosity for polymers with different zero-shear-rate viscosity based on recent experimental results of star and comb polymer melts. For ring polymers, we summarize the recent progress in extensional rheology and provide our view on what would be interesting for further investigation. On the basis of the above results and discussions, we show that extensional rheology is complicated for even very simple molecular architectures. More data from both experiments and simulations are important for improvement of a fundamental understanding and development of theories, which is essential for molecular design of polymer materials.

Characterization of silver nanoparticle inks toward stable roll-to-roll gravure printing

The rheological properties of silver inks are analyzed, and the printing results are presented based on the inks and roll-to-roll (R2R) printing speed. The shear viscosity, shear modulus, and extensional viscosity of the inks are measured using rotational and extensional rheometers. The inks exhibit the shear thinning power law fluids because the concentration of dispersed nanoparticles in the solvent is sufficiently low, which minimizes elasticity. After the inks are printed on a flexible substrate through gravure printing, the optical images, surface profiles, and electric resistances of the printed pattern are obtained. The width and height of the printed pattern change depending on the ink viscosity, whereas the printing speed does not significantly affect the widening. The drag-out tail is reduced at high ink viscosities and fast printing speeds, thereby improving the printed pattern quality in the R2R process. Based on the results obtained, we suggest ink and printing conditions that result in high printing quality for complicated printings, such as overlay printing registration accuracy, which imposes pattern widening and drag-out tails in printed patterns.

Effects of viscoelasticity on the onset of vortex shedding and forces applied on a cylinder in unsteady flow regime

The present paper aims to investigate the effect of viscoelasticity on the onset of vortex shedding of a high concentration polymer solution over a cylinder using the finite volume method for the first time. To describe the behavior of the viscoelastic fluid, mathematically, the Phan–Thien–Tanner (PTT) model is employed. The convergence problems are resolved using the rheoFoam solver developed by previous researchers based on the log-conformation method. The exact critical Reynolds number (Recr), which corresponds to the onset of vortex shedding, is estimated by implementing numerous unsteady simulations at each elasticity number (El). The Recr is also calculated at every retardation ratio (β) and elongational viscosity. The results revealed a significant impact of viscoelasticity on Recr so that the flow of a high viscosity ratio PTT becomes unstable at higher Re (at very low El) or lower Re (at higher El), compared to a Newtonian fluid. In addition, Recr decreases linearly with β according to Recr=−34.5β+46.525 and increases with extensional viscosity. It is also found that β plays a vital role in the effect of viscoelasticity on the flow parameters. The averaged drag coefficient (CD¯) and the amplitude of lift coefficient (CLmax) do not have similar behaviors for low and high β. Moreover, viscoelasticity enlarges the vortices and increases the shedding frequency. A comprehensive physical analysis of flow structures is carried out using the distribution of time-averaged stress components and pressure over the cylinder. The numerical results demonstrated the three regimes of drag reduction at El < 0.015, drag enhancement at 0.015 < E1 < 1, and a Newtonian behavior at El > 1 that is an opposite trend compared to a steady regime. The variations of CLmax with El are also similar to CD¯, but at different critical elasticity numbers (El = 0.005 and 2). It is found that the normal stress changes the drag force by the variation of pressure distribution over the cylinder, while the shear stress directly affects the drag and lift forces. In addition, the viscoelasticity decreases the size of the vortices behind the cylinder and increases their vorticity, and changes the position of maximum normal stress, which leads to drag variations. It was also concluded that the higher the elongational viscosities, the lower the shedding frequency.

Lubrication of saliva layer on oral and throat mucosa and its friction reduction effect of swallowing

Swallowing disorder has been becoming a serious issue with increasing in elderly people. Disorder sometimes appears with a decrease in saliva, because saliva has an important role in lubrication over the oral cavity and throat. Though the structure of biological mucosa has been studied physiologically, there are only few studies that examined the influence of its oral and throat mucosa on fluid lubrication. Therefore, we investigated the friction reduction effect on the oral cavity and pharynx. There is a thin liquid phase with a thickness of about 0.1 mm called saliva layer on oral and throat mucosa. It is necessary to evaluate the rheological properties of mucus with low viscosity and high spinnability like saliva layer using a PEO solution, because of the viscosity characteristics different from the shear viscosity. The PEO solution concentration was determined from the measurement of the viscous characteristic by the rotational viscometer to set the same viscosity as that of saliva. Therefore, we investigated the rheological characteristics by measuring the extensional viscosity to make a mucus using a PVA coating. We measured friction torque on the artificial mucosa lubricated by PEO solution. The effect of torque reduction of friction by high-viscosity liquids (100% glycerin solution) on the artificial mucosa was clarified in this study. We considered apparent slip occurs in the saliva layer. However, there was no effect of friction reduction on the low viscosity (40% glycerin aqueous solution). Even if apparent slip occurs in the artificial mucosa, the viscosity on the artificial mucosa is the same as that of the liquids.

Variations of the viscous properties of a sponge cake artificial bolus with some physiological parameters

Artificial boluses were prepared from sponge cake by grinding the food to a given particle size and hydrating with artificial saliva. The shear viscosity of the artificial food bolus was then measured by capillary rheometry, and its variations with shear rate were studied as a function of four main factors: bolus water content, particle size, temperature and saliva viscosity. The flow curves can be fitted according to the Herschel-Bulkley model, which allows for the derivation of two main properties: yield stress and consistency. Saliva plasticizing coefficients are defined by the variations of these properties as a function of the water content. Their value, close to 12, is in good agreement with values obtained for molten starch (10 < α < 20). Particle size has little influence, whereas the effect of temperature and saliva viscosity is not monotonous. They underline the complexity of the structure of the bolus and the interplay between the saliva, acting as a lubricant and a swelling agent. Finally, the extensional viscosity of the artificial bolus is also determined by capillary rheometry, and it is shown to be of importance when comparing the viscous properties of the artificial bolus with those of real ones from literature.

Solvent Effects on the Elasticity of Electrospinnable Polymer Solutions.

Ultrafine fibers manufactured through electrospinning are a frontrunner for advanced fiber applications, but transitioning from potential to commercial applications for ultrafine fibers requires a better understanding of the behavior of polymer solutions in electrospinning to enable the design of more complex spinning dopes. In complex fluids, there are viscoelastic stresses and microstructural transitions that alter free surface flows. These may not be seen in shear rheology; therefore, an in-depth analysis of the extensional rheological behavior must be performed. In this work, we use dripping-onto-substrate rheometry to characterize the extensional viscosities of electrospinning dopes from four polymer solutions commonly used in electrospinning (low- and high-molecular-weight polyvinylpyrrolidone in methanol and water as well as poly(ethylene oxide) and poly(vinyl alcohol) in water). We link the electrospinnability, characterized through fiber morphology, to the extensional rheological properties for semidilute and entangled polymer solutions and show that high-surface-tension solvents require higher extensional viscosities and relaxation times to form smooth fibers and that the Deborah and Ohnesorge numbers are a promising method of determining electrospinnability. Through this tie between solvent characteristics, viscoelasticity, and electrospinnability, we will enable the design of more complex spinning dopes amenable to applications in wearable electronics, pharmaceuticals, and more.

Using Computational Modelling to Study Extensional Rheometry Tests for Inelastic Fluids

The present work focuses on the extensional rheometry test, performed with the Sentmanat extensional rheometer (SER) device, and its main objectives are: (i) to establish the modelling requirements, such as the geometry of the computational domain, initial and boundary conditions, appropriate case setup, and (ii) to investigate the effect of self-induced errors, namely on the sample dimensions and test temperature, on the extensional viscosity obtained through the extensional rheometry tests. The definition of the modelling setup also comprised the selection of the appropriate mesh refinement level to model the process and the conclusion that gravity can be neglected without affecting the numerical predictions. The subsequent study allowed us to conclude that the errors on the sample dimensions have similar effects, originating differences on the extensional viscosity proportional to the induced variations. On the other hand, errors of a similar order of magnitude on the test temperature promote a significant difference in the predicted extensional viscosity.

Extensional rheometry of model liquids: Simulations of filament stretching

Polymeric liquid bridges are known to fail during extension. This phenomenon of failure seemingly calls into question the operating principle of filament stretching rheometers. In these devices, a polymeric sample is initially placed between two plates. The sample is then stretched into a liquid bridge by moving the plates apart in a specified way. We here show that a steady extensional viscosity can be measured if the plates are separated in such a way that the stretch rate in the filament symmetry plane is kept constant, even for liquids highly prone to instability. Moreover, reliable measurements of the stress during a relaxation phase can be obtained as well. The conclusions are based on simulations for a number of constitutive equations, including the Newtonian liquid, the Oldroyd-B model, the differential non-stretch Rolie–Poly model, and the integral Doi–Edwards model with and without associated stretch relaxation dynamics.

Full linear Phan-Thien–Tanner fluid model: Exact analytical solutions for steady, startup, and cessation regimes of shear and extensional flows

Exact, fully explicit, purely real analytical expressions for the material functions describing steady, startup, and cessation regimes of shear flows and of planar, uniaxial, and biaxial extensional flows of full linear Phan-Thien–Tanner fluids are obtained. These expressions, which have no analogs in the literature, are formulated in compact, beautiful forms, partially due to the unique scaling procedure reducing the number of the model parameters from four to one. The properties of the material functions are investigated in detail. For steady extensional flows, the possible shapes of the extensional viscosity curves are described and the conditions for these shapes to occur are determined. For startup flows, it is found when exactly the stress dynamics is oscillatory, and, in this case, a detailed characterization of oscillations is given, which includes expressions for the position and magnitude of stress overshoots and undershoots.

Effect of viscoelasticity on the foaming behaviour of long-chain branched polypropylene with different branching degrees analysed by using bubble-growth modelling

Long-chain branched polypropylene (LCB-PP) was generated by a melt grafting reaction with trimethylolpropane triacrylate (TMPTA) as the grafting monomer and zinc dimethyldithiocarbamate (ZDMC) or styrene (St) as the co-monomers. High-temperature size exclusion chromatography (HT-SEC) was used to characterize the molecular mass, molecular mass distribution and branching degree of the modified PP. Subsequently, linear and nonlinear viscoelasticity data were obtained by a small amplitude oscillatory shear (SAOS) test and uniaxial extensional viscosity measurement. The pressure balanced bubble-growth (PBB) model was used to calculate the critical coalescence radius (CCR) curves for PP to quantitatively correlate the viscoelasticity and foamability and evaluate the foamability of PP combined with batch foaming. It is shown that with increasing branching degree, the foam shows a better resistance to bubble coalescence, resulting in a more regular bubble structure and a higher expansion ratio. Moreover, viscosity should be controlled over an appropriate range for realising good foamability; otherwise, excessive viscosity can suppress bubble growth and limit the expansion ratio. MPPZ4 modified with 4 wt% TMPTA and 0.4 wt% ZDMC showed the best foamability. A combination of the PBB model and batch foaming experiment is used to quantitatively explain the contribution of LCB to foaming.

Structure development in high-speed melt spinning of high-molecular weight poly(ethylene terephthalate)/polypropylene islands-in-the-sea bicomponent fibers

High-speed melt spinning of island-in-the-sea (SI) type bicomponent fibers with 74 islands consisting of high-molecular-weight poly(ethylene terephthalate) (HMW-PET) and polypropylene (PP) was achieved. The structure and mechanical properties of the HMW-PET component (islands) in the SI fibers were significantly enhanced with increasing the take-up velocity, while those of PP component (Sea) were suppressed. These results were attributed to the concentration of spinning stress on the HMW-PET component exhibiting higher elongational viscosity in the spinline. Considerable interaction between the two components in the SI fibers contributed to uniform structure development of the island parts in the fibers and improvement of the melt structure in the spinline. These results further enhanced the mechanical property and spinnability of the island parts. The thermoplastic composites, manufactured using the high-speed spun SI fibers with the islands of fine diameter (approximately 1.9 μm), exhibited a high tensile strength of approximately 1.0 GPa by microfiber-reinforced effect.

Synergistic Behavior of Anionic Surfactants and Hydrolyzed Polyacrylamide under an Extensional Field: Effect of Hydrophobicity.

Surfactant-polymer interaction has been studied by many academic and industrial researchers. Associative polymers have attracted attention, especially in enhanced oil recovery due to their ability to generate higher resistance than parental polyacrylamide (HPAM) at a lower concentration. The effect of hydrophobicity on the associative polymer-surfactant interaction has been studied through many means including rheology. Previous rheological studies were restricted to shear-based behavior, and no efforts were undertaken to study the effect of hydrophobicity on the extensional rheological behavior of the surfactant-HPAM system. In this work, the extensional behavior of anionic surfactant-polyacrylamide systems was studied for varying levels of hydrophobicity. The concentration of the surfactant used in the surfactant-polymer formulation ranged from 0 to 0.3%, and the polymer concentration was fixed at 1000 ppm. Extensional rheology was performed using a capillary breakup extensional rheometer. Surface tension studies were also conducted. The results revealed that the parental HPAM-surfactant system shows the maximum extensional viscosity for the concentration range studied here. This is contrary to shear behavior reported in the literature, and it appears that electrostatic repulsive interaction associated with HPAM-surfactant systems becomes dominant in the extensional field. Associative polymer-surfactant systems characterized by higher hydrophobicity showed the least maximum extensional viscosity, as opposed to the literature-reported behavior in the shear field. Hydrophobic interaction associated with associative polymer-surfactant systems appears to become weaker in the extensional field.