Extensional Viscosity Research Articles

Instrumental characterization of xanthan gum and scleroglucan solutions: Comparison of rotational rheometry, capillary breakup extensional rheometry and soft-contact tribology

Xanthan gum and scleroglucan, two rod-like polysaccharide hydrocolloids, are compared using a wide range of instrumental techniques and methods: steady shear flow, small amplitude oscillatory shear, first normal stress difference, capillary break-up and soft-contact tribology. The aqueous solutions of these two hydrocolloids with similar flow and viscoelastic profile show marked differences in capillary break-up time and apparent extensional viscosity. This result correlates with differences in first normal stress difference and, to a lesser extent, Stribeck curve behaviour. Formulating the hydrocolloids in concentrated sucrose solution (40 wt%) shifts relaxation profiles to longer times which greatly diminishes differences in rheological and lubrication behaviour. With exception of capillary break-up tests, no other methods showed statistically significant differences between the polysaccharides dissolved in the viscosified matrix. The toolbox of techniques is also applied to probe interactions of xanthan gum and scleroglucan with human whole saliva and bovine submaxillary mucin. We report no specific interactions between either hydrocolloid and salivary proteins and suggest that any cumulative effects must stem from specific sets of linear and non-linear rheological properties of saliva/hydrocolloid mixtures. • Rheology and tribology of xanthan gum and scleroglucan are compared. • Capillary break-up provides sensitive discrimination between hydrocolloids. • Xanthan gum and scleroglucan have similar hydrodynamic volume. • Relaxation spectrum of xanthan features faster modes compared to scleroglucan.

Modelling the effect of hydrogen bonding on elongational flow of supramolecular polymer melts

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.

Filament stretching during micro-extrusion of silver pastes enables an improved fine-line silicon solar cell metallization

The metallization of heterojunction solar cells requires a further reduction of silver consumption to lower production costs and save resources. This article presents how filament stretching of polymer-based low-temperature curing Ag pastes during micro-extrusion enables this reduction while at the same time offering a high production throughput potential. In a series of experiments the relationship between the printing velocity and the filament stretching, thus the reduction of Ag-electrode widths and Ag laydown is evaluated. Furthermore, an existing filament stretching model for the parallel dispensing process is advanced further and utilized to calculate the elongational viscosity. The stretching effect enables a reduction of the Ag-electrode width by down to Δwf = − 40%rel. depending on the nozzle diameter and paste type. The Ag laydown has been reduced from mAg,cal. = 0.84 mg per printed line to only mAg,cal. = 0.54 mg per printed Ag-electrode when 30 µm nozzle openings are used, demonstrating the promising potential of parallel dispensing technology for the metallization of silicon heterojunction solar cells.

Improved Polypropylene Thermoformability through Polyethylene Layering.

Due to its low cost, stiffness, and recyclability, isotactic polypropylene (iPP) is an excellent candidate for packaging applications. However, iPP is notoriously difficult to thermoform due to its low melt strength. The addition of just 10 thin layers of high-molecular-weight, linear low-density polyethylene (LLDPE) into iPP sheets by coextrusion significantly increased extensional viscosity and reduced sag. Both LLDPE and iPP were metallocene-catalyzed with excellent adhesion as measured in our previous work. We performed a series of hot tensile tests and sheet sag measurements to determine the properties of the iPP sheet and the multilayer sheet between 130 and 180 °C. To evaluate the thermoformability of these multilayer sheets, truncated conical cups were positive vacuum formed at different temperatures and heating times, and the crush strength was measured. Cups that released easily from the mold with good shape retention and a crush strength within 80% of the maximum value were used to define a temperature-time thermoformability window. We estimated the maximum stress that occurred during the thermoforming process to be 5 MPa. Layer thicknesses before and after thermoforming were used to estimate an average strain of 0.78. The thin LLDPE layers decreased the yield stress below 5 MPa. This enabled thermoforming at sheet temperatures as low as 150 °C. The immiscible LLDPE interfaces increased extensional viscosity, which decreased sag in the multilayer sheets compared to iPP. This broadened the thermoforming range to temperatures as high as 180 °C and allowed longer heating times. These highly thermoformable, layered sheets may be recycled as iPP since they contain only 8% of LLDPE.

Extrusion foaming of linear and branched polypropylenes – input of the thermomechanical analysis of pressure drop in the die

Abstract This paper aims at a better understanding of the polypropylene (PP) physical extrusion foaming process with the objective of obtaining the lowest possible foam density. Two branched PPs were compared to the corresponding linear ones. Their shear and elongation viscosities were measured as well as their crystalline properties. Trials were conducted in a single screw extruder equipped with a gear pump and a static mixer cooler to adjust the melt temperature at the final die. The effect of decreasing this temperature on the PP foamability and on the pressure drop in the die was analyzed. The foam density of branched PPs varies from high to low values while decreasing the foaming temperature. In the same processing conditions, the foam density of linear PPs does not decrease so much, as already evidenced in the literature. The foamability transition coincides with an increase of the pressure drop in the die. The originality of the work lies in the thermomechanical analysis of the polymer flow in the die which allows the identification of the relevant physical phenomena for a good foamability. The comparison of the experimental pressure drops in the die and the computed ones with the identified purely viscous behavior points out the influence of the foaming temperature and of the PP structure. At high foaming temperature the discrepancy between experimental measurements and the computed pressure drops remains limited. It increases when decreasing the foaming temperature, but the mismatch is much more important for branched PPs than for linear ones. This difference is analyzed as a combination of the activation energy of the viscosity, the elongational viscosity in the convergent geometry of the die which is much more important for branched PPs than for linear ones, and the onset of crystallization which occurs at higher temperature for branched PPs than for linear PPs.

On the role played by extensional viscosity in peristaltic transport of circular solid particles suspended in Oldroyd-B liquids

The efficiency of the peristalsis mechanism is numerically investigated for the transport of circular solid particles suspended in viscoelastic liquids obeying the Oldroyd-B model. Having modeled the solid particle as a viscoplastic droplet obeying the bi-viscous model, we have relied on the finite-element method for solving the equations of motion (at low Reynolds numbers) for the carrier liquid and the viscoplastic droplet. Viscoelasticity of the carrier liquid is predicted to impede the particle's peristaltic transport with its severity depending on the Deborah number, the size of the particle, and the wave parameters. The obtained numerical results suggest that, when suspended in viscoelastic liquids, smaller-sized particles are more suitable for peristaltic drive. It is also predicted that at a critical Deborah number around unity, particles that are too large might exhibit a sudden drop in their transport velocity. We have interpreted the hampering effect of elasticity in terms of the extensional viscosity and the strain-hardening behavior of the carrier liquid, which is shown to be controlled by the Deborah number, the size of the particle, and the wave parameters.

Principles and Guidelines for In-Line Viscometry in Cereal Extrusion.

In the food industry, extrusion cooking finds numerous applications thanks to its high productivity and nutrient retention. More specifically, cereal extrusion, e.g., for savory snacks and breakfast products has an important market share. For such applications, rheology, which addresses viscous and elastic contributions, plays an important role in developing, optimizing, and controlling the extrusion manufacturing technique. In this context, conventional off-line rheometers are not ideal for providing data, as the goal is to replicate the exact thermomechanical history to which the food is subjected in the extrusion process. Hence, to achieve reliable analyses, in-line viscometers that have mostly been tested using oil-based polymers were introduced. Biopolymers (e.g., starch), however, are highly sensitive to both heat and mechanical degradation, and the viscometer design has to be adapted accordingly to produce an accurate measurement. Alongside a discussion of the different designs available, this review will address the most common methodologies for measuring the steady shear viscosity, extensional viscosity, and the first normal stress difference for food applications, providing researchers in the biopolymer and food engineering fields with a general introduction to this emerging topic.

3D simulation of the hierarchical multi-mode molecular stress function constitutive model in an abrupt contraction flow

• First simulation of the hierarchical multi-mode molecular stress function model. • The model is compared to experiment for a 3D contraction flow of Lupolen LDPE. • Striking agreement shown for vortex opening angles over a large range of flow rates. • Simulated and experimental birefringence show very good correspondence. • Variation of apparent stress optical coefficient with flow rate shown to be low. A recent development of the Molecular Stress Function constitutive model, the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model has been shown to fit a large range of rheometrical data with accuracy, for a large range of polymer melts. We develop a 3D simulation of the HMMSF model and compare it to experimental data for the flow of Lupolen 1840H LDPE through an abrupt 3D contraction flow. We believe this to be the first finite element implementation of the HMMSF model. It is shown that the model gives a striking agreement with experimental vortex opening angles, with very good agreement to full-field birefringence measurements, over a wide range of flow rates. A method to give fully-developed inlet boundary conditions is implemented (in place of using parabolic inlet boundary conditions), which gives a significantly improved match to birefringence measurements in the inlet area, and in low stress areas downstream from the inlet. Alternative constitutive model parameters are assessed following the principle that extensional rheometer data actually provides a ‘lower bound’ for peak extensional viscosity. It is shown that the model robustly maintains an accurate fit to vortex opening angle and full-field birefringence data, provided that both adjustable parameters are kept such that both shear and extensional data are well fitted.

Do-it-yourself rheometry

We describe the structure and outcomes of a course project for do-it-yourself (DIY) rheometry. Although the project was created in response to the shelter-in-place orders of the COVID-19 pandemic, the student learning outcomes were so positive that we have continued implementing the project even when students have access to laboratory rheometers. Students select an interesting complex fluid, collect qualitative visual evidence of key rheological phenomena, and then produce their own readily available flows that they quantitatively analyze to infer rheological properties, such as yield stress, extensional viscosity, or shear viscosity. We provide an example rubric, present example student project outcomes, and discuss learning outcomes that are achieved with DIY measurements.

Analysis of elongational flow of star polymers

Star polymers with three arms are the simplest example of branched polymers. Elongational rheology data of three well-characterized monodisperse polystyrene melts, a symmetric star, an asymmetric star, and a linear polymer with the same span molecular weight of 180 kg/mol reported by Huang et al. (Macromolecules 49:6694−6699, 2016) are analyzed by the enhanced relaxation of stretch (ERS) model (Wagner and Narimissa, J Rheol 65:1413–1421, 2021). All three melts show the same elongational stress growth coefficient and the same steady-state elongational viscosity in fast extensional flows when the stretch-related Weissenberg number {Wi}_R=dot{varepsilon}{tau}_R>1. Excellent agreement between experimental data of elongational stress growth coefficient and model predictions is obtained, based exclusively on the linear-viscoelastic characterization of the polymer systems. Stress relaxation following steady elongational flow depends on the presence of the branch point and the length of the arm, and a new process regarding relaxation of the orientation of the stars is identified.

Nonlinear rheology of entangled wormlike micellar solutions predicted by a micelle-slip-spring model

We examine linear and nonlinear shear and extensional rheological properties using a “micelle-slip-spring model” [T. Sato et al., J. Rheol. 64, 1045–1061 (2020)] that incorporates breakage and rejoining events into the slip-spring model originally developed by Likhtman [Macromolecules 38, 6128–6139 (2005)] for unbreakable polymers. We here employ the Fraenkel potential for main chain springs and slip-springs to address the effect of finite extensibility. Moreover, to improve extensional properties under a strong extensional flow, stress-induced micelle breakage (SIMB) is incorporated into the micelle-slip-spring model. Thus, this model is the first model that includes the entanglement constraint, Rouse modes, finite extensibility, breakage and rejoining events, and stress-induced micelle breakage. Computational expense currently limits the model to micellar solutions with moderate numbers of entanglements (≲7), but for such solutions, nearly quantitative agreement is attained for the start-up of the shearing flow. The model in the extensional flow cannot yet be tested owing to the lack of data for this entanglement level. The transient and steady shear properties predicted by the micelle-slip-spring model for a moderate shear rate region without significant chain stretch are fit well by the Giesekus model but not by the Phan–Thien/Tanner (PTT) model, which is consistent with the ability of the Giesekus model to match experimental shear data. The extensional viscosities obtained by the micelle-slip-spring model with SIMB show thickening followed by thinning, which is in qualitative agreement with experimental trends. Additionally, the extensional rheological properties of the micelle-slip-spring model with or without SIMB are poorly predicted by both the Giesekus and the PTT models using a single nonlinear parameter. Thus, future work should seek a constitutive model able to capture the behavior of the slip-spring model in shear and extensional flows and so provide an accurate, efficient model of micellar solution rheology.

Relation between polymer transitions and the extensional viscosity of dough systems during thermal stabilization assessed by lubricated squeezing flow

Polymer transitions occurring during the thermal processing of dough are defining the rheological behaviour of solidifying dough. Yeast, an essential ingredient in breadmaking, plays an important role in this transformation process, but its impact on the transitional behavior of the polymers remains unknown. Therefore, the aim of this study was to elucidate the impact of hydrothermally induced polymer transitions on the elongational rheological behavior of dough under process-relevant strain-strain-rate combinations transitions in dependence of the presence of yeast. Using elongational rheology together with DSC, TD-NMR and microscopy, yeast-induced degradation on the microstructural level (average decrease of protein strand length of 46%) and microstructural level were shown to affect the course of the starch gelatinization process and the functionality of gluten while baking. These findings can be used to relate oven rise performance to fundamental rheological behavior based on occurring phase transitions, leading to a more comprehensive process understanding.

Viscoelastic Properties of Fully Biomass-Based Transparent Plastic Comprising Cellulose Acetate and Citrate Ester.

Viscoelastic properties including melt processability were evaluated for a fully biomass-based glassy plastic comprising cellulose acetate (CA) and triethyl citrate (TEC). The TEC exerted an excellent plasticizing effect without dissolving the CA crystals. Pure CA has poor melt processability. In contrast, the TEC-plasticized CA had good melt-processability at 205 °C, which is lower than the degradation temperature of CA. Extrusion was possible even at 1000 s−1 without any flow instabilities, similar to conventional plastics showing good processability at extrusion. Furthermore, there was marked strain-hardening behavior in the transient elongational viscosity, suggesting that various processing operations are possible, such as a long-chain branched polymer. This biomass-based plastic can be used as a substitute for conventional glassy plastics because it is highly transparent and its softening temperature is above 100 °C.

Novel High‐Speed Elongation Rheometer

AbstractThe elongational viscosity of polymers can be determined by utilizing different devices such as extensional rheometer after Sentmanat (SER), oil bath rheometer after Meissner or tensile rheometer after Münstedt (MTR), with strain rates up to 10 s–1. Although these investigations are already complex, they do not depict real fiber spinning processes where higher elongation strain rates occur. Therefore, a novel method is developed to calculate the elongational viscosity of polymers during the fiber spinning process. To reduce the complexity of the system, two polymethylmethacrylates (PMMAs) with different molar masses are investigated using a capillary rheometer to exclude crystallization effects. The diameter of the polymeric strand is determined via a high‐speed camera from the die exit to the aspirator. In addition, simulations are carried out to describe the temperature profile of the polymeric strand along the spinline. It is possible to determine the elongational viscosity of the polymers in dependence of temperature and strain rates up to 100 s–1, by calibration of the force in an aerodynamic stretching device (aspirator).

Direct-Ink-writing of liquid metal-graphene-based polymer composites: Composition-processing-property relationships

This paper presents a study of the solvent-based precursors (inks) derived from composites of polyethylene oxide, graphene flakes and micro-scale spherical Eutectic Gallium Indium (EGaIn) fillers and their processing through direct-ink-writing (DIW). The presented studies focus on the influence of EGaIn fillers on ink rheology, DIW process mechanisms as well as electrical conductivity of the printed structures. The results show that EGaIn fillers vary the ink rheology towards a more elastic behavior with lower extensional viscosity. This leads to ink filaments capable of withstanding large extensional strains during DIW, forming continuous prints even when printing speed is higher than ink flow speed, and producing features with line width smaller than the nozzle diameter. Electrical conductivity of the prints reduces with increasing strain due to the deformation of the liquid EGaIn fillers along the printing direction. These findings can be utilized to control the DIW process and the properties of the conductive polymer composites.

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.

Optimization of a Flat Die Including Elongational Viscosity Effects

Abstract A software package for optimization of polymer extrusion dies is developed. Die geometry is optimized such that a uniform velocity distribution is obtained at the die exit without excessively increasing the pressure drop in the die. The software uses the BFGS optimization algorithm, and employs the adjoint method to obtain the design sensitivities. The optimization software is successfully used to optimize the geometry of a flat die for polymer sheet extrusion such that a uniform velocity distribution is obtained at the die exit, without increasing the pressure drop in the die.

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.