Transient Extensional Viscosity Research Articles

Numerical simulation of fiber orientation kinetics and rheology of fiber-filled polymers in uniaxial extension

During processing of fiber composites, the fiber-induced stresses influence the local flow fields, which, in turn, influence the stress distribution and the fiber orientation. Therefore, it is crucial to be able to predict the rheology of fiber-filled polymer composites. In this study, we investigate the fiber orientation kinetics and rheological properties of fiber composites in uniaxial extensional flow by comparing direct numerical finite element simulations to experimental results from our previous study [Egelmeers et al., “In-situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites,” J. Rheol. 68, 171–185 (2023)]. In the simulations, fiber–fiber interactions only occur hydrodynamically and lubrication stresses are fully resolved by using adaptive meshing. We employed a 7-mode and a 5-mode viscoelastic Giesekus material model to describe the behavior of, respectively, a strain hardening low-density polyethylene (LDPE) matrix and a non-strain hardening linear LDPE matrix, and investigated the influence of the Weissenberg number, strain hardening, and fiber volume fraction on the fiber orientation kinetics. We found that none of these parameters influence the fiber orientation kinetics, which agrees with our experimental data. The transient uniaxial extensional viscosity of a fiber-filled polymer suspension is investigated by comparing finite element simulations to a constitutive model proposed by Hinch and Leal [“Time-dependent shear flows of a suspension of particles with weak Brownian rotations,” J. Fluid Mech. 57(4), 753–767 (1973)] and to experimental results obtained in our previous study [Egelmeers et al., “In-situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites,” J. Rheol. 68, 171–185 (2023)]. The simulations describe the experimental data well. Moreover, high agreement is found for the transient viscosity as a function of fiber orientation between the model and the simulations. At high strains for high fiber volume fractions, however, the simulations show additional strain hardening, which we attribute to local changes in microstructure.

Nonlinear rheology and dynamics of supramolecular polymer networks formed by associative telechelic chains under shear and extensional flows

Nonequilibrium computer simulations have been applied to study the shear and extensional flow behavior of supramolecular polymer networks (SPNs) formed by unentangled and weakly entangled associative telechelic chains and their nonassociative polymer melt counterparts. The reversible bonding of the associative end monomers or stickers leads to the formation of percolated transient networks and consequently stronger mechanical properties of the SPNs than their melt counterparts. In startup shear, the transient shear viscosities η ( t ) and first normal stress coefficients Ψ 1 ( t ) of both the SPN and melt systems show overshoot behavior, but only the SPNs demonstrate transient strain hardening at high shear rates. In startup planar extensional flows, all systems demonstrate the characteristic extensional strain hardening behavior. The transient extensional viscosities η E ( t ) of the SPNs undergo a small overshoot before entering the steady state, which was not observed in the nonassociative polymer melts. For both types of polymer systems with unentangled and weakly entangled chain lengths, the steady-state shear viscosities show typical shear-thinning behavior, while the steady-state extensional viscosities demonstrate extension hardening, which are consistent with published simulation and experimental works. The observed flow behavior can be well understood from the flow-induced non-Gaussian chain stretching and segment orientation in all polymer systems studied, as well as the additional relaxation mechanisms in the SPNs, including the flow-induced reduction in the density of elastically active strands, the increment in the probability for the stickers to exchange their associated partners, and the reduction in the average sticky bond lifetimes at high strain rates.

High temperature extensional rheology of commercially available polycarbonate mixed with flame retardant salts

In this paper, we present a study of the dripping properties of polycarbonate (PC) modified with combinations of earth metal salts of inorganic sulfur, potassium perfluorobutane sulfonate (Rimar); non-halogenated flame retardant additives, potassium diphenyl sulfone-3-Sulfonate (KSS); and block co-polymers-polytetrafluoroethylene encapsulated with styrene acrylonitrile resin (T-SAN). Measurements of the extensional rheology of polycarbonate with different concentration of each flame retardant additive were performed using a custom-built high temperature Capillary Breakup Extensional Rheometer (CaBER) at temperatures up to T=400°C. From these measurements, the evolution of the apparent transient extensional viscosity was monitored as a function of time and strain both in air and in an inert nitrogen environment. The evolution of extensional viscosity has been shown to be an excellent tool for predicting the dripping behavior of polymers exposed to heat and a valuable tool for understanding the mechanism of polymer degradation which is typically dominated by either crosslinking or charring. We show that extensional rheology measurements are significantly more sensitive to temperature-induced changes to the polymer microstructure than shear rheology measurements. We have also performed systematic concentration of specific flame retardant salts and through variation in extensional rheology and investigated the optimum concentration required to achieve a V0 rating. Finally, we will show that extensional rheology is a powerful method for predicting the effect of flame retardant modifiers and optimizing their use in new flame resistant materials.

Linear and Non-linear Rheology of Bread Doughs Made from Blends of Wheat (Triticum aestivum L.) and Rye (Secale cereale L.) Flour

Strain hardening of wheat flour (WF) proteins during fermentation and baking is at the basis of the excellent quality of wheat breads. Yet, there are good reasons to use rye flour (RF), such as its high content of dietary fiber and other bioactives. However, rye proteins lack the ability to form dough with sufficient strain hardening capacity under extension, which partially explains the inferior quality of rye breads. A promising strategy to make high-quality breads with high nutritional value is the use of WF and RF blends. Despite this, the rheological behavior of WF/RF bread doughs has not yet been investigated. This study examines their rheology by non-linear uniaxial extensional and small-amplitude oscillatory shear measurements, and relates these measurements to the quality of the resulting breads. The strain hardening index (SHI), derived from extensional measurements, is expressed as the transient extensional viscosity at maximum strain [ηe+(εmax)] relative to the linear extensional viscosity extrapolated to maximum strain [ηe0+(εmax)]. Both the SHI and bread volume decreased when the level of RF in the blend increased. As an example, replacing 60% WF by RF led to a relative decrease of the SHI and bread volume of 34 and 64%, respectively. The decrease of the SHI is correlated to an increase in ηe0+(εmax). Comparison of the extensional curves of doughs made with blends of WF and RF and doughs made with blends of WF and wheat starch (WS) further revealed that RF components play a major role in the rheology of the doughs. In conclusion, it was found that WF/RF blends need to contain at least 60% WF to obtain bread of proper quality.

Uniaxial extensional viscosity of semidilute DNA solutions

The extensional rheology of polymeric liquids has been extensively examined through experiments and theoretical predictions. However, a systematic study of the extensional rheology of polymer solutions in the semidilute regime, in terms of examining the effects of concentration and molecular weight, has not been carried out so far. Prior studies of the shear rheology of semidilute polymer solutions have demonstrated that their behaviour is distinctively different from that observed in the dilute and concentrated regimes. This difference in behaviour is anticipated to be even more pronounced in extensional flows. In this work, the extensional rheology of linear, double-stranded DNA molecules, spanning an order of magnitude of molecular weights (25 to 289 kilobasepairs) and concentrations (0.03 to 0.3 mg/ml), has been investigated. DNA solutions are now used routinely as model polymeric systems due to their near-perfect monodispersity. Measurements have been carried out with a filament stretching rheometer since it is the most reliable method for obtaining an estimate of the elongational stress growth of a polymer solution. Transient and steady-state uniaxial extensional viscosities of DNA dissolved in a solvent under excess salt conditions, with a high concentration of sucrose in order to achieve a sufficiently high solvent viscosity, have been determined in the semidilute regime at room temperature. The dependence of the steady state uniaxial extensional viscosity on molecular weight, concentration and extension rate is measured with a view to determining if data collapse can be observed with an appropriate choice of variables. Steady state shear viscosity measurements suggest that sucrose-DNA interactions might play a role in determining the observed rheological behaviour of semidilute DNA solutions with sucrose as a component in the solvent.

Rheology of polymer multilayers: Slip in shear, hardening in extension

The nonlinear rheology of multilayer stacks of alternating isotactic polypropylene (PP) and polyethylene (PE) films with N layers was measured in shear and uniaxial extension. We show that the force to extend N − 1 interfaces can lead to strain hardening. We studied three PE/PP pairs: a Ziegler–Natta catalyzed pair and two metallocene pairs, one with high density PE and one with linear low density PE. Interfacial tension was measured on matrix/droplet blends of each pair using small amplitude oscillatory shear measurements fitted with the Palierne model. Multilayer coextrusion was used to fabricate bilayers and sheets with hundreds of layers for each polyolefin pair. Under shear deformation, disentangling of chains in the N − 1 interfaces led to a decrease in the overall shear viscosity, which is interpreted as an interfacial slip velocity and is in agreement with previous studies on multilayer films. Under extensional flows, the multilayers exhibited an increased transient extensional viscosity (tensile stress growth coefficient, η E , M +) and pronounced strain hardening, even when the constituent homopolymers exhibited no strain hardening behavior. A model based on a force summation was developed to predict this behavior with interfacial tension as a fitting parameter; the extracted interfacial tensions agreed reasonably well with those from the Palierne model. The “slip in shear” and “hardening in extension” behaviors highlight the role of interfacial polymer physics during rheological measurements and polymer processing.

Investigating the dynamics of droplet breakup in a microfluidic cross-slot device for characterizing the extensional properties of weakly-viscoelastic fluids

A microfluidic device, deemed the Plateau-Rayleigh microfluidic extensional rheometer (PRIMER), is presented that uses a cross-slot geometry to observe a two-phase droplet-breakup event in which the viscoelastic fluid is in the dispersed (or droplet) phase. For viscoelastic fluids, we report that a cylindrical filament forms between droplet segments with a diameter that decays exponentially in time. In optically tracking this decay, both transient extensional viscosity and extensional relaxation times can be evaluated. For validating and optimizing the device, a range of poly(ethylene oxide) (PEO) solutions and Newtonian solutions were tested. Comparisons of the evolution profiles as a result of the presence of elasticity are made, and these results are compared with the results from dripping-onto-a-substrate (DoS), another emerging extensional technique.

Shear and extensional rheology of aqueous solutions of cocamidopropyl betaine and sodium dodecyl sulfate mixture

The paper presents the results obtained for aqueous solutions of a mixture of cocamidopropyl betaine (CAPB) and sodium dodecyl sulfate (SDS) in rheological tests in the shear and extensional flow. The rheological measurements in the extensional flow were conducted using a capillary breakup extensional rheometer. The description of the mechanical spectra required the application of the multi-mode Maxwell model, which demonstrates that stress relaxation occurs via reptation – as in entangled polymer solutions. The rheological properties of aqueous CAPB/SDS solutions in the extensional flow were also found to be qualitatively consistent with the properties of entangled polymer solutions. The ratio of the extensional relaxation time to the transient shear relaxation time was considerably lower than one, and the range of elasto-capillary thinning appeared at a Weissenberg number of 2/3. The difference between polymer solutions and CAPB/SDS solutions is noted at late times, when the transient extensional viscosity of the solutions of polymers and wormilke cationic surfactants reaches a constant value, whereas in CAPB/SDS solutions it drops rapidly. The decrease in transient extensional viscosity in this range may be due to the break-up of wormlike micelles under the influence of high transient extensional stresses.

Macromolecular relaxation, strain, and extensibility determine elastocapillary thinning and extensional viscosity of polymer solutions

Delayed capillary break-up of viscoelastic filaments presents scientific and technical challenges relevant for drop formation, dispensing, and adhesion in industrial and biological applications. The flow kinematics are primarily dictated by the viscoelastic stresses contributed by the polymers that are stretched and oriented in a strong extensional flow field resulting from the streamwise gradients created by the capillarity-driven squeeze flow. After an initial inertiocapillary (IC) or viscocapillary (VC) regime, where elastic effects seem to play no role, the interplay of capillarity and viscoelasticity can lead to an elastocapillary (EC) response characterized by exponentially-slow thinning of neck radius (extensional relaxation time is determined from the delay constant). Less frequently, a terminal visco-elastocapillary (TVEC) response with linear decay in radius can be observed and used for measuring terminal, steady extensional viscosity. However, both IC/VC-EC and EC-TVEC transitions are inaccessible in devices that create stretched necks by applying a step strain to a liquid bridge (e.g., capillary breakup extensional rheometer). In this study, we use dripping-onto-substrate rheometry to obtain radius evolution data for unentangled polymer solutions. We deduce that the plots of transient extensional viscosity vs. Hencky strain (scaled by the respective values at the EC-TVEC transition) emulate the functional form of the birefringence-macromolecular strain relationship based on Peterlin's theory. We quantify the duration and strain between the IC/VC-EC and the EC-TVEC transitions using measures we term elastocapillary span and elastocapillary strain increment and find both measures show values directly correlated with the corresponding variation in extensional relaxation time.

Dripping-onto-substrate capillary breakup extensional rheometry of low-viscosity printing inks

In this manuscript, the capillary thinning dynamics of a series of solutions containing polymers commonly used in the coating industry as low-viscosity printing inks were studied. Four different polymer binders were studied in methyl-ethyl ketone. These included one acrylic polymer, one cellulose polymer and two vinyl polymers of different molecular weights. The dripping-onto-substrate capillary breakup extensional rheometry (CaBER-DoS) method was used to characterize the extensional rheology for solutions with viscosities as low as 3.5mPa.s. This technique is based on the measurement of the decay of a fluid filament under the influence of surface tension and has been shown to be capable of measuring relaxation times as low as 20 µs for weakly elastic liquids. The influence of the polymer concentration on the dynamics of filament breakup was investigated for each polymer solution and the results were compared to those obtained with different polymer binders. With an increase in polymer concentration, a critical polymer concentration was identified for the transition between the inertio-capillary, the visco-capillary and the elasto-capillary breakup regimes. With the onset of elasto-capillary breakup at moderate to high polymer concentrations, a delay in the filament breakup was observed due to an increase of the viscous and elastic stresses. This viscoelastic breakup delay would be detrimental to most ink jet printing applications. Within the elasto-capillary breakup regime, the transient extensional viscosity resulted in Trouton ratios ranging from just above the Newtonian limit of Tr = 3 to values close to Tr = 100.

Unraveling the Bimodality of Polypropylene Film Grades Using Rheological Shear and Elongational Measurements: Inconsistent Results of Gel Permeation Chromatography

As the main parameter to describe the molecular structure of a linear polymer, molecular weight distribution of five different polypropylene grades was evaluated through measurements of gel permeation chromatography and rheology experiments. From their dynamic shear data, the relaxation spectra, h(τ), were calculated from which molecular weight distribution was estimated using molecular viscoelastic theories and then compared with the gel permeation chromatography results. Generally good agreement, yet with narrower molecular weight distribution rheology curves was found. Exception was observed for one grade for which rheological data predicted bimodal distribution curve comprising a small shoulder of high molecular weight, not seen in the corresponding gel permeation chromatography curve. Additionally, a higher value of the generalized mixing parameter (i.e. β) was found for this bimodal grade which was attributed to an increase in the number of entanglements per chain and better network connectivity. Furthermore, measurements of the transient extensional viscosity also revealed enhanced strain hardening and melt strength for this particular grade. The results showed that small amount of high molecular weight fraction of linear chains could drastically alter the processing behavior of polypropylene film grades.

Influence of in situ reactive interphase with graft copolymer on shear and extensional rheology in a model bilayered polymer system

Influence of an in situ reactive interphase composed of graft copolymer on the melt shear and extensional rheology was systematically studied with a model bilayer of polyamide-6 (PA6)/maleic anhydride grafted poly(vinylidene fluoride) (PVDF-g-MAH). Firstly, small-amplitude oscillatory shear was used in situ to probe the development of reactive interphase from the interfacial reactions by tracking the changes of viscoelastic responses. Secondly, shear (start-up shear, shear stress relaxation) and extensional rheology was comparatively performed on the healed bilayers to evaluate the effects of reactive interphase. Interestingly, shear stress relaxation and especially extensional rheology were pretty sensitive to the presence of reactive interphase, whereas start-up shear showed negligible sensitivity. Specifically, the reactive interphase retarded the stress relaxation of healed bilayers subjected to step strains. Particularly, extensional rheology provided a more direct and quantitative view of the contribution of reactive interphase to melt rheology in both linear and nonlinear regimes. The remarkable increase in transient extensional viscosity and enhanced strain hardening resulting from the interfacial reaction in bilayer were demonstrated in terms of the interfacial stress. Besides, effect of reaction extent on extensional rheology was further examined, where it was found that interfacial stress increased with reaction time. The observed changes in rheology were attributed to the in situ formed interphase with graft copolymers and the resulting increased entanglements between neighboring layers. This study highlights the remarkable sensitivity of shear stress relaxation and especially extensional rheology to a reactive interphase.

A nonlinear shear and elongation rheological study of interfacial failure in compatible bilayer systems

This work aims to examine whether or not interfacial failure can occur in a compatible polymer bilayer system under large shear and elongation deformations, as well as to probe the sensitivity of nonlinear transient rheology to the presence of interface/interphase at neighboring layers. For this, stress relaxation after a step strain and fast startup in simple shear and uniaxial extension experiments have been performed on healed and coextruded poly(methyl methacrylate)/poly(vinylidene fluoride) bilayers with the presence of a robust diffuse interphase as evaluated by energy dispersive X ray. For unhealed bilayers, interfacial failure occurred in shear flows at intermediate deformations, while for healed bilayers the interphase greatly delayed the onset of interfacial failure to larger deformation steps and to a higher deformation rate in the startup shear. Extensional rheology demonstrated that the presence of an interphase in the bilayers greatly enhanced the transient extensional viscosity ηE+(t) as well as the tensile relaxation modulus E(t) of the structure, even though the entanglement density was relatively low. Moreover, models are presented to predict the nonlinear relaxation behavior of bilayers and to estimate the relaxation behavior of the interphase. Fitting of the tube model to the shear relaxation indicates a dilated tube diameter in the interphase, confirming its weak entanglement intensity and its readiness to flow-induced disentanglement under large external deformations. Finally, the physics of the interfacial failure was assessed based on some recent molecular dynamic theories.

Study on extensional viscosity of acrylic adhesive

In this paper, transient extensional viscosities of acrylic adhesives were studied using Extensional Viscosity Fixture (EVF) in rotation rheometer at 120°C under different extensional rates. Extensional viscosity is an important parameter to evaluate extensional behavior of adhesives. Strain hardening was observed during extension for tested adhesives. Effects of molecular weight and tackifi er addition on transient extensional viscosities were also investigated. Addition of tackifier would decrease transient extensional viscosities of tested acrylic adhesives. In addition, extensional viscosities were compared to complex viscosities obtained from linear oscillation shear tests at 120°C. Extensional viscosity is more sensitive to addition of tackifier compared to shear viscosity.

Comparative Analysis of the Effect of Organoclay, Boron Nitride, and Fluoropolymer on the Rheology and Instabilities in the Extrusion of High Density Polyethylene

The effect of different processing additives on the extrusion instabilities of high density polyethylene (HDPE) was investigated. The concentration of each processing additive was fixed at 0.05 wt%. Organoclay, boron nitride, and fluoropolymer reduced transient shear and extensional viscosities of HDPE melt. Drop in extrusion pressure occurred during the extrusion experiment. The initial loss of glossiness in HDPE was restored with the addition of these additives. However, the fluoropolymer did not succeed in eliminating the stick-slip fracture. Despite the inclusion of the processing additives, gross-melt fracture in HDPE reappeared at apparent shear rate of 141 s−1. Both moment and distortion factor methods of analyses were employed and their findings support the observed visual trends of the extrudate surface. The quantifying tools indicated that combined organoclay and fluoropolymer reduced the pressure fluctuations and its performance surpassed that of the individual additives.

High strain extensional rheometry of polymer melts: Revisiting and improving the Meissner design

A new extensional rheometer limited in achievable strain only by sample rupture is presented. The rheometer is based on the Meissner design of two pairs of counter-rotating rollers pulling a sample of fixed length but is small enough to fit inside the oven of a standard rotational rheometer and thus is dubbed the Meissner Extensional Rheometry Accessory (MERA). The true strain rate is calculated by visually accessing the sample during deformation using a high-speed digital camera. Extensional experiments were performed on three materials representing a wide range expected rheological behavior, a styrene-butadiene rubber blend, a linear polystyrene, and a branched low-density polyethylene. The MERA was able to accurately replicate the results of the well-known Sentmanat extensional rheometer (SER) design in terms of onset of strain-hardening and absolute transient extensional viscosity values. However, due to its design, it was possible to achieve homogeneous extensional flow up to real Hencky strains in excess of 8, which corresponds to a linear stretch in excess of 3000. By comparison, the SER is limited to one drum revolution, which corresponds to a Hencky strain of 3.5–4.0 or a maximum linear stretch of approximately 50. Previously the highest Hencky deformations reported in the literature are for the filament stretching extensional rheometer and Rheometric Scientific RME apparatus and in both cases approach 7, which corresponds to a linear stretch of approximately 1000.

Studying the origin of “strain hardening”: Basic difference between extension and shear

This work studies the origin of the so called observed when comparing the transient stress response of entangled melts to uniaxial extension with that to simple shear. Strain hardening occurs when the transient extensional viscosity measured from a startup uniaxial extension of finite rate deviates upward from the zero-rate transient viscosity. Our theoretical analysis shows that polymer melts would always exhibit strain hardening at sufficient high Hencky rates because the entanglement network can be effectively strengthened during extension and can only be weakened during shear for linear chains. The kinematic difference between simple shear and uniaxial extension has two effects: (a) The force resulting from the startup deformation is measured from an increasingly shrinking area in uniaxial extension instead of a constant area as in simple shear; and (b) the tendency of the entanglement network to yield, i.e., to undergo chain disentanglement is partially suppressed during startup extension at high Hencky rates. In short, the phenomenon of strain hardening reflects the reality that entangled melts are not fluids but temporary solids and that the conventional description of their uniaxial extension in terms of the Cauchy stress contains a geometric condensation factor.

Effect of biaxial drawing on morphology and properties of copolyamide nanocomposites produced by film blowing

In this work, extensional behavior in non-isothermal and isothermal conditions of copolyamide-based nanocomposites was analyzed and correlated to bubble stability in the film blowing processing of these materials. The higher values of transient extensional viscosity and melt strength of the nanocomposites, compared to the neat matrix, imply that they are able to better resist the extensional external force during bubble formation. Oxygen barrier and mechanical properties of the films were investigated and correlated to the resulting polymer crystal structure and filler morphology. At the higher draw ratios and blow up ratios the nanocomposite specimens were present essentially in the mesomorphic β-form, nevertheless, significant improvements in barrier and mechanical properties of the hybrid films were observed, likely due to a good dispersion and orientation of the silicate platelets in the polymer matrix.

Sedimentation of a sphere in a viscoelastic fluid: a multiscale simulation approach

AbstractA long-standing problem in non-Newtonian fluid mechanics, namely the relationship between drag experienced by a sphere settling in a tube filled with a dilute polymeric solution and the sphere sedimentation velocity, is investigated via self-consistent multiscale flow simulations. Comparison with experimental measurements by Arigo et al. (J. Non-Newtonian Fluid Mech., vol. 60, 1995, pp. 225–257) have revealed that the evolution of the drag coefficient as a function of fluid elasticity can be accurately predicted when the macromolecular dynamics is described by realistic micromechanical models that closely capture the transient extensional viscosity of the experimental fluid at high extension rates. Specifically, for the first time we have computed the drag coefficient on the sphere at high Weissenberg number $\mathit{Wi}$ utilizing multi-segment bead–spring chain models with appropriate molecular parameters and have demonstrated that a hi-fidelity multiscale simulation is not only capable of accurately describing the drag on the sphere as a function of $\mathit{Wi}$ at various sphere-to-tube diameter ratios but also it can closely reproduce the experimentally observed velocity and stresses in the wake of the sphere.

Elongational viscosity of LDPE with various structures: employing a new evolution equation in MSF theory

Molecular stress function theory with new strain energy function is used to analyze transient extensional viscosity data of seven low-density polyethylene (LDPE) melts with various molecular structures as published by Stadler et al. (Rheol Acta 48:479–490, 2009) Pivokonsky et al. (J Non Newton Fluid Mech 135:58–67, 2006) and Wagner et al. (J Rheol 47(3):779–793, 2003). The new strain energy function has three nonlinear viscoelastic material parameters and assumes that the total stored energy of a branched molecule is given by different backbone and side chains stretching. The model parameters have been fitted for each LDPE in order to correlate with the supposed macromolecular structure expected from the type of synthesis. Most probable molecular structures for these LDPEs are comb and Cayley tree structures for respectively low- and high-molecular weight parts.