Rheo-optical measurements of the elongational flow of aqueous polymer solutions

An opposed jets rheometer was used to investigate the elongational viscosity as a function of the strain rate for dilute aqueous solutions of polyvinylformamide and polyacrylamide. Critical strain rates at which the enhancement in elongational viscosity occurs were determined for both systems. The influence of the polymer concentration on the elongational viscosity was investigated. The measurements were performed with polymer concentrations less than the critical polymer concentration c_p^* c_p^* . In order to assess the deformation and orientation of the macromolecules, flow-induced birefringence was measured simultaneously.     

Measurements and model predictions of transient elongational rheology of polymeric nanocomposites

Transient elongational rheology of two commercial-grade polypropylene (PP) and the organoclay thermoplastic nanocomposites is investigated. A specifically designed fixture consisting of two drums (SER Universal Testing Platform) mounted on a TA Instruments ARES rotational rheometer was used to measure the transient uniaxial extensional viscosity of both polypropylene and nanoclay/PP melts. The Hencky strain rate was varied from 0.001 to 2 s^− 1, and the temperature was fixed at 180°C. The measurements show that the steady-state elongational viscosity was reached at the measured Hencky strains for the polymer and for the nanocomposites. The addition of nanoclay particles to the polymer melt was found to increase the elongation viscosity principally at low strain rates. For example, at a deformation rate of 0.3 s^− 1, the steady-state elongation viscosity for polypropylene was 1.4 × 10⁴ Pa s which was raised to 2.8 × 10⁴ and 4.5 × 10⁴ Pa s after addition of 0.5 and 1.5 vol.% nanoclay, respectively. A mesoscopic rheological model originally developed to predict the motion of ellipsoid particles in viscoelastic media was modified based on the recent developments by Eslami and Grmela (Rheol Acta 47:399–415, 2008) to take into account the polymer chain reptation. We show that the orientation states of the particles and the rheological behavior of the layered particles/thermoplastic hybrids can be quantitatively explained by the proposed model.     

Rheological properties of long glass fiber filled polypropylene

Long glass fiber-filled polypropylene (PP) composites are produced by pultrusion, and the extrudate is cut at different lengths producing composites containing long fibers of controlled length. The rheological properties of such composites in the molten state have been studied using different rheometers. A capillary rheometer has been constructed and mounted on a molding-injection machine. The shear viscosity of filled PP determined from the capillary rheometer, after corrections for entrance effects, was found to be very close to that of unfilled PP. However, large excess pressure losses at the capillary entrance were observed and these data have been used to obtain an apparent elongational viscosity. The apparent elongational viscosity was shown to be considerably larger than the shear viscosity for PP and filled PP, and it increased markedly with fiber length and fiber content. Rotational rheometers with a parallel-plate geometry were used to investigate the viscoelastic properties of these composites and their behavior was found to be non-linear, exhibiting a yield stress. A model is proposed to describe the shear viscosity from a solid-like behavior at low stresses to fluid-like behavior at high shear stresses taking into account fiber content and orientation. A modified model, proposed for elongational flow, describes relatively well the apparent elongational data.     

Multilayer film casting of modified Giesekus fluids Part 2. Linear stability analysis

A linear stability analysis of the multilayer film casting of polymeric fluids has been conducted. A modified Giesekus model was used to characterize the rheological behaviors of the fluids. The critical draw ratio at the onset of draw resonance was found to depend on the elongational and shear viscosities of the fluids. Extensional-thickening has a stabilizing effect, whereas shear-thinning and extensional-thinning have destabilizing effects. The critical draw ratios for bilayer films of various thickness fractions are bounded by those for single layer films of the two fluids. When the two fluids have a comparable elongational viscosity, the critical draw ratio at a given Deborah number varies linearly with thickness fraction. When one fluid has a much larger elongational viscosity, it dominates the flow and the critical draw ratios at most thickness fractions remain close to its critical draw ratio as a single layer film. When the dominating fluid exhibits extensional-thickening, a film with a certain thickness fraction has more than one critical draw ratio at a given Deborah number and may not exhibit draw resonance within some range of the Deborah number.     

Thermorheological properties of LLDPE/LDPE blends

The thermorheological behavior of a number of linear low-density polyethylene and low-density polyethylene (LLDPE/LDPE) blends was studied with emphasis on the effects of long chain branching. A Ziegler–Natta, LLDPE (LL3001.32) was blended with four LDPEs having distinctly different molecular weights. The weight fractions of the LDPEs used in the blends were 1, 5, 10, 20, 50, and 75%. Differential scanning calorimetry (DSC) analysis has shown that all blends exhibited more than one crystal type. At high LDPE weight fractions, apart from the two distinct peaks of the individual components, a third peak appears which indicates the existence of a third phase that is created from the co-crystallization of the two components. The linear viscoelastic characterization was performed, and mastercurves at 150 °C were constructed for all blends to check miscibility. In addition, Van Gurp Palmen, zero-shear viscosity vs composition, Cole–Cole, and the weighted relaxation spectra plots were constructed to check the thermorheological behavior of all blends. In general, good agreement is found among these various methods. The elongational behavior of the blends was studied using a uniaxial extensional rheometer, the SER universal testing platform from Xpansion Instruments. The blends exhibit strain-hardening behavior at high rates of deformation even at LDPE concentrations as low as 1%, which suggests the strong effect of branching added by the LDPE component.     

Rheology of SiO 2 /(acrylic polymer/epoxy) suspensions. III. Uniaxial elongational viscosity

Uniaxial elongational viscosity of SiO₂/(acrylic polymer/epoxy (AP/EP)) suspensions with various SiO₂ volume fractions (?) in a blend of acrylic polymer and epoxy was investigated at various temperatures (T). The matrix polymer ((AP/EP) blend) contained 70?vol.% of EP. At ?????35?vol.% at T????80°C, where the suspensions were in sol state, strain-hardening behavior was observed. This strain hardening of the suspensions is attributable to the elongational flow properties of (AP/EP) medium. At critical gel state (??=?35?vol.% and T?=?100°C) and in gel state (?????40?vol.%), the elongational viscosity exhibited the strain-softening behavior. These results strongly suggest that the strain softening results from the strain-induced disruption of the network structure of the SiO₂ particles therein.     

Influence of viscoelasticity on drop deformation and orientation in shear flow: Part 1. Stationary states

The influence of matrix and droplet viscoelasticity on the steady deformation and orientation of a single droplet subjected to simple shear is investigated microscopically. Experimental data are obtained in the velocity–vorticity and velocity–velocity gradient plane. A constant viscosity Boger fluid is used, as well as a shear-thinning viscoelastic fluid. These materials are described by means of an Oldroyd-B, Giesekus, Ellis, or multi-mode Giesekus constitutive equation. The drop-to-matrix viscosity ratio is 1.5. The numerical simulations in 3D are performed with a volume-of-fluid algorithm and focus on capillary numbers 0.15 and 0.35. In the case of a viscoelastic matrix, viscoelastic stress fields, computed at varying Deborah numbers, show maxima slightly above the drop tip at the back and below the tip at the front. At both capillary numbers, the simulations with the Oldroyd-B constitutive equation predict the experimentally observed phenomena that matrix viscoelasticity significantly suppresses droplet deformation and promotes droplet orientation. These two effects saturate experimentally at high Deborah numbers. Experimentally, the high Deborah numbers are achieved by decreasing the droplet radius with other parameters unchanged. At the higher capillary and Deborah numbers, the use of the Giesekus model with a small amount of shear-thinning dampens the stationary state deformation slightly and increases the angle of orientation. Droplet viscoelasticity on the other hand hardly affects the steady droplet deformation and orientation, both experimentally and numerically, even at moderate to high capillary and Deborah numbers.     

Determination of elongational viscosity of polymer melts by RME and Rheotens experiments

Several linear (LLDPE, HDPE, PS) and long-chain-branched (LDPE, PP) polymer melts were investigated by an elongational rheometer (RME Rheometrics) and by Rheotens (Göttfert). The Molecular Stress Function (MSF) theory is briefly reviewed and used to extrapolate the steady-state elongational viscosity. To evaluate Rheotens experiments, a new process model is introduced which assumes that the elongational viscosity in the Rheotens test is a function of the draw ratio only. The apparent elongational viscosities extracted from Rheotens curves are found to lie in between the steady-state elongational viscosity and three times the shear viscosity.     

The effect of viscoelasticity on the extrusion drawing in film-casting process

The governing rheological property for extrusion drawing in film-casting process is proposed in this study. The experiment of film-casting process using the high-pressure process low-density polyethylene (LDPE) was performed. The non-isothermal viscoelastic simulation of the film casting experiment was also carried out to explain the experimental results. Film width reduction phenomenon in an air gap, so-called neck-in behavior, was investigated by using the simulation of the LDPE and the model fluids exhibiting specific viscoelasticity. The neck-in phenomenon was also examined using theoretical model based on force balance and deformation type of a film. As a result, the neck-in normalized by the air gap was in good correlation with the ratio of planar to uniaxial elongational viscosity rather than the strain hardening nature of uniaxial elongational viscosity.     

Elongational viscosity by fiber spinning

Isothermal melt, fiber-spinning was recently analyzed by means of a nonlinear, integral, constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear-thinning, and extension thinning or thickening when either the drawing force or the draw ratio is specified. The predictions agreed with experimental data on spinning of polystyrene, low-density polyethylene, and polypropylene melts. The predicted apparent elongational viscosity along the threadline (which, as shown in this work, must be identical to that measured experimentally by fiber spinning type of elongational rheometers) is compared with the true elongational viscosity predicted by the same constitutive equation under well-defined experimental conditions of constant extension rate, independent of any strain history. It is concluded that the apparent elongational viscosity, as measured by fiber-spinning, approaches the true elongational viscosity at low Weissenberg numbers (defined as the product of the liquid's relaxation time multiplied by the extension rate). At moderate Weissenberg numbers, the two viscosities may differ by an order of magnitude and their difference grows even larger at high Weissenberg numbers.     

Isothermal elongational behavior of liquid-crystalline polymers and LCPs based blends

The rheological behavior of two flexible thermoplastics, Nylon-6 (Ny) and bisphenol-A polysulfone (PSu), and two wholly aromatic liquid crystalline polymers, Vectra-A900 (VA) and Vectra-B950 (VB), as well as that of Ny/VB and PSu/VA blends with 10% LCP, has been investigated by the use of capillary viscometers equipped with cylindrical dies having different length-to-diameter ratios. The elongational viscosity of all materials was calculated, from the results of isothermal measurements carried out at 290°C, by means of the Cogswell's analysis, based on the estimation of the pressure drop due to the converging flow at the die inlet. The behavior in elongational flow was compared with the rheological behavior in shear flow conditions. It was found that the elongational viscosities of VA and VB are very large and account for a fairly marked pressure drop at the die entrance, due to the orientation of the LCP domains taking place in the converging flow zone. For these materials, the ratio of the elongational viscosity to the Newtonian shear viscosity is up to two orders of magnitude higher than the value expected on the basis of the Trouton rule. For the flexible resins, the Trouton ratio is 3 and ca. 3–10, are common values for high molar mass linear polymers. The addition of 10% LCP into the flexible resins strongly increases their elongational viscosity and makes the blends resemble neat LCPs in their extensional flow behavior. In shear flow, on the contrary, the addition of LCP was shown to induce a marked reduction of the melt viscosity, even when, as for the Ny/VB blend, the LCP is more viscous than the matrix.     

The langevin approach to the dumbbell kinetic problem in rheology

An alternative formalism to the dumbbell kinetic problem is proposed which is believed to be more fundamental than the classical Liouville one. The new formulation provides a logical approach to non-conservative systems and systems with varying frictional coefficients. A non-linear dumbbell with internal viscosity and varying frictional factor for the beads is examined. It is proved that the centre of gravity of the dumbbell must move affinely with the solvent continuum. A useful class of approximation is suggested to reduce the constitutive equation to an explicit form. The response of the model is computed for a number of flow fields. For shear flows, the introduction of the internal viscosity results in a shear-thinning phenomenon. The onset of non-Newtonian behaviour occurs at the correct order of magnitude of the dimensionless shear rate. Also, a negative second normal stress difference is found which varies with shear rate. In an oscillatory shear flow, the internal viscosity leads to a finite limiting value of the dynamic viscosity at high frequencies. In elongational flow the effects of the varying frictional coefficient dominate that of the internal viscosity. Interesting phenomena include the presence of a hysteresis loop and the ability of the dumbbell to maintain an extended configuration at moderate elongational rates. Clearly, these are relevant in turbulent drag reduction applications. The model has sufficient merits to deserve more investigation.     

On the “viscosity overshoot” during the uniaxial extension of a low density polyethylene

An experimental investigation of the viscosity overshoot phenomenon observed during uniaxial extension of a low density polyethylene is presented. For this purpose, traditional integral viscosity measurements on a Münstedt-type extensional rheometer are combined with local measurements based on the in-situ visualization of the sample under extension. For elongational experiments at constant strain rates within a wide range of Weissenberg numbers (Wi), three distinct deformation regimes are identified. Corresponding to low values of Wi (regime I), the tensile stress displays a broad maximum, but such maximum is observed with various polymeric materials deformed at low rates and it should not be confused with the “viscosity overshoot” phenomenon. Corresponding to intermediate values of Wi (regime II), a local maximum of the integral extensional viscosity is systematically observed. Moreover, within this regime, a strong discrepancy between integral measurements and the space average of the local elongational viscosity is observed which indicates large deviations from an ideal uniaxial deformation process. Images of samples within this regime reinforce this finding by showing that, corresponding to the maximum of the integral viscosity, secondary necks develop along the sample. The emergence of a maximum of the integral elongational viscosity is, thus, related to the distinct inhomogeneity of deformation states and most probably not to the rheological properties of the material. In the fast stretching limit (high Wi, regime III), the overall geometric uniformity of the sample is well preserved, no secondary necks are observed and both the integral and the space averaged transient elongational viscosity show no maximum. A detailed but yet incomplete comparison of the experimental findings with results from the literature is presented and several open questions are stated.     

Modelling elongational and shear rheology of two LDPE melts

Experimental data of two low-density polyethylene (LDPE) melts at 200°C for both shear flow (transient and steady shear viscosity as well as transient and steady first normal stress coefficient) and elongational flow (transient and steady-state elongational viscosity) as published by Pivokonsky et al. (J Non-Newtonian Fluid Mech 135:58–67, 2006) were analysed using the molecular stress function model for broadly distributed, randomly branched molecular structures. For quantitative modelling of melt rheology in both types of flow and in a very wide range of deformation rates, only three nonlinear viscoelastic material parameters are needed: Whilst the rotational parameter, a ₂, and the structural parameter, β, are found to be equal for the two melts considered, the melts differ in the parameter describing maximum stretch of the polymer chains.     

Effect of interfacial modifier on single drop deformation and breakup in step increasing shear flow

This work deals with in situ visualisation of deformation and breakup of a copolymer modified single Newtonian drop immersed in a Newtonian homogenous matrix. The experiments were carried out on a model system made of poly-isobutylene as the suspending fluid and two poly-dimethylsiloxanes with different molecular weights as the drop phase with viscosity ratios 0.036 and 1.13, below and above but close to unity. Three weight concentrations 0.5%, 2% and 10% of the block copolymer laying below, close to and above the critical concentration of the total drop surface coverage were examined. Single drop deformation experiments were carried out in a home-designed Couette quartz cell connected to a home-modified Paar Physica Rheometer. The variation in the length-to-diameter ratio (L/D) versus shear rate and capillary number was measured both in steady and in transient regimes till breakup. The results indicated a weaker resistance of copolymer modified drops against hydrodynamic stresses at both viscosity ratios as compared to the clean drop. However, the drop deformation was found to be complex and depends on the copolymer concentration and the viscosity ratio.     

Linear and non-linear nature of the flow of polypropylene filled with ferrite particles: from low to concentrated composites

The flow behavior of a filled suspension consisting of ferrite particles suspended in a polypropylene matrix with and without the addition of a commercial dispersant (Solplus DP310) was studied. The composites were filled with 10, 20, 30, and 40 vol.%. Both capillary and parallel disk rotational flows were employed. On the one hand, dynamic results confirm general trends found for highly concentrated systems. The higher is the filler level, the lower is the linear viscoelastic domain. When adding the dispersant agent, it was shown a larger linear viscoelastic domain, lower moduli values and thus, lower viscosity. Also, the critical strain, G′ and G′′ showed a power law dependency on the volume fraction. On the other hand, the capillary results showed no dependency of the flow properties on the die. Thus, no slip of the suspension at the wall was observed. Actually, this experimental finding elucidated that the significant decrease on viscosity produced by the addition of the dispersant agent at 40 vol.% is principally due to lubricant effects and not at all to slip contributions. The results also reveal three distinct flow regimes. Low, moderate, and high shear rates lead to different microstructure under flow.     

On the predictive/fitting capabilities of the advanced differential constitutive equations for branched LDPE melts

Predictive/fitting capabilities of the XPP, PTT–XPP and modified Leonov constitutive equations are compared in both steady as well as transient shear and uniaxial elongational flows using two, highly branched LDPE materials (Escorene LD165BW1 and Bralen RB0323). It has been found that even if all three tested models exhibit very good fitting capability for steady uniaxial extensional viscosity curve, their predicting capabilities may differ significantly for shear viscosity as well as first and second normal stress coefficients.     

Morphology development in polystyrene/polyethylene blends during uniaxial elongational flow

The deformation of linear low-density and low-density polyethylene particles dispersed in a polystyrene matrix was studied during defined uniaxial elongational flow conditions for different capillarity numbers and different temperatures. The morphology of the elongated samples was analysed by quenching the specimens in liquid nitrogen directly after the deformation. Furthermore, morphology development after recovery was investigated. By measuring the transient elongational viscosity of the blend matrix the true hydrodynamic stress during the flow process was calculated. Using a modified critical capillarity number, the fibril formation of the dispersed phase could be described at all test conditions. Virtually no break-up processes were observed. This finding could be explained by calculating the characteristic time of fibril break-up due to Rayleigh instabilities. By annealing the elongated samples a spherical shape of the dispersed droplets was regained. Compared with the initial sample morphology a pronounced increase of the particle sizes due to coalescence processes during elongation was observed.