Apparent Elongational Viscosity Research Articles

Numerical simulation of the fiber spinning with the viscoelastic Giesekus constitutive model

The numerical simulation of the first stage of fiber-spinning process was performed. The single-mode Giesekus model was used for polymer fiber stress calculations. Fiber profiles, longitudinal velocity, tensile stress and apparent elongational viscosity were analyzed depending on the stretch speed and the degree of anisotropy of the polymer.

Concept of an Evaluation Technique for Planar Elongational Stress and Relaxation Time Using Hoop Stress in Swirling Flow

The paper reports a novel idea of an experimental approach to estimate the apparent planar elongational viscosity and the relaxation time of low viscosity fluids. A two-dimensional swirling contraction channel is designed to maintain a constant elongation rate to the flow direction. The hydrodynamic focusing creates a stable planar elongation flow field. The flow is injected into the center of the channel and a sheath flow is injected through both sides. The sample fluid is stretched in the flow field, and then forms the ribbon-shaped filament. In the swirling contraction part, a static force balance between the hoop force caused by the planar elongational stress and the centrifugal force determines the radial position of the filament. The distribution of the planar elongational stress can be estimated by observing this position, and then the apparent planar elongational viscosity was calculated using developed simplified expressions. On the other hand, when a channel with a constant width swirling part is used, the elongational stress generated in the straight contraction part gradually decreases passing through the constant width part. The sample filament position is then shifted based on the stress relaxation. The relaxation time can be evaluated by observing this variation.

Modifying the rheological properties of polypropylene under elongational flow by adding polyethylene

Adding polyethylene greatly affects the rheological response of isotactic polypropylene (PP) under uniaxial elongational flow. Though strain hardening in the transient elongational viscosity barely appeared in pure PP, we induced strain hardening by adding low-density polyethylene (LDPE) to PP, even though the blends showed a phase-separated structure. During elongational flow, LDPE droplets dispersed in the PP were deformed in the flow direction. Because LDPE shows marked strain hardening in the elongational viscosity, the deformed LDPE droplets behaved as rigid fibers as the strain increased. Consequently, the PP between the fibrous LDPE droplets experienced excess localized deformation, which increased the apparent elongational viscosity. Furthermore, adding the high-density polyethylene (HDPE) increased the drawdown force—defined as the force required for uniaxial stretching of a molten polymer in the nonisothermal condition. This behavior comes from the rapid crystallization of HDPE, which causes the deformed HDPE particles to act as rigid fibers in the molten PP and enhances the PP crystallization, which increases the elongational stress.

Textural behavior of gels formed by rice starch and whey protein isolate: Concentration and crosshead velocities

ABSTRACT Fabricated food gels involving the use of hydrocolloids are gaining polpularity as confectionery/convenience foods. Starch is commonly combined with a hydrocolloid (protein our polyssacharides), particularly in the food industry, since native starches generally do not have ideal properties for the preparation of food products. Therefore the texture studies of starch-protein mixtures could provide a new approach in producing starch-based food products, being thus acritical attribute that needs to be carefully adjusted to the consumer liking. This work investigated the texture and rheological properties of mixed gels of different concentrations of rice starch (15%, 17.5%, and 20%) and whey protein isolate (0%, 3%, and 6%) with different crosshead velocities (0.05, 5.0, and 10.0 mm/s) using a Box-Behnken experimental design. The samples were submitted to uniaxial compression tests with 80% deformation in order to determinate the following rheological parameters: Young’s modulus, fracture stress, fracture deformation, recoverable energy, and apparent biaxial elongational viscosity. Gels with a higher rice starch concentration that were submitted to higher test velocities were more rigid and resistant, while the whey protein isolate concentration had little influence on these properties. The gels showed a higher recoverable energy when the crosshead velocity was higher, and the apparent biaxial elongational viscosity was also influenced by this factor. Therefore, mixed gels exhibit different properties depending on the rice starch concentration and crosshead velocity.

Dynamics of falling droplet and elongational properties of dilute nonionic surfactant solutions with drag-reducing ability

The dynamics of the falling droplet through a nozzle for dilute nonionic surfactant (oleyl-dimethylamine oxide, ODMAO) aqueous solutions with viscoelastic and drag-reducing properties were investigated at different concentrations of ODMAO solutions Cs = 500, 1000, and 1500 ppm by weight. The effects of the flow rate and tube outer diameter on the length of the filament, which was the distance between the tube exit and the lower end of a droplet at the instant when the droplet almost detached from the tube, were clarified by flow visualization measurements by a high-speed video camera. Two types of breaking-off processes near the base of the droplet and within the filament were classified by the Ohnesorge number Oh and the Weber number We. In the regime of the higher Oh and We, the length of the filament became drastically larger at Cs = 1000 and 1500 ppm, whose high spinnability represented the strong viscoelasticity of ODMAO solutions. In the case where the filament was broken up near the lower end of the neck and thinning in time, the thinning of the diameter of the filament was measured by a light-emitting diode micrometer. As for the elasto-capillary thinning of dilute nonionic surfactant solutions, the initial necking process was similar to that of Newtonian fluids and then followed the exponential thinning like polymer solutions. The apparent elongational viscosity of the dilute nonionic surfactant solution was evaluated in the elasto-capillary thinning regime, in which the elongation rate was almost constant. At Cs = 1000 and 1500 ppm, the Trouton ratio, which was the ratio of the apparent elongational viscosity to the shear viscosity, was found to be several orders of magnitude larger than that of Newtonian fluids, while the shear viscosity measured by the capillary viscometer was almost the same order of the Newtonian fluids. The higher elongational property would be closely related to the higher drag-reducing ability of dilute nonionic surfactant solutions.

Controlling micro‐ and nanofibrillar morphology of polymer blends in low‐speed melt spinning process. Part I. Profiles ofPLA/PVA‐filament parameters along the spinline

ABSTRACTThe profiles of PLA/PVA filament parameters (e.g., temperature, velocity, tensile stress, and apparent elongational viscosity) along the spinline in the low‐speed melt spinning process under various spinning conditions were investigated. Owing to the combination of the filament velocity and filament temperature measurements using laser doppler velocimetry (LDV) and infrared thermography, respectively, the fiber formation zone was determined. The length of the fiber formation zone obtained from filament velocity profilesis always shorter than that obtained from the filament temperature profiles(. Obviously, this unexpected phenomenon occurs for low spinning speeds due to the axial heat conduction effect of the filament along the spinline and the nonuniform radial temperature distribution through the cross‐sectional thick filament. Another remarkable finding is related to the Nusselt number which has been found as nearly constant along the spinline in the low‐speed melt spinning process. Thus, mathematical simulations of the filament temperature profiles will be simplified drastically. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci.2016,133, 44258.

Experimental study on the capillary thinning of entangled polymer solutions

The transient elongation behavior of entangled polymer and wormlike micelles (WLM) solutions has been investigated using capillary breakup extensional rheometry (CaBER). The transient force ratio X = 0.713 reveals the existence of an intermediate Newtonian thinning region for polystyrene and WLM solutions prior to the viscoelastic thinning. The exponential decay of X(t) in the first period of thinning defines an elongational relaxation time λ x which is equal to elongational relaxation time λ e obtained from exponential diameter decay D(t) indicating that the initial stress decay is controlled by the same molecular relaxation process as the strain hardening observed in the terminal regime of filament thinning. Deviations in true and apparent elongational viscosity are discussed in terms of X(t). A minimum Trouton ratio is observed which decreases exponentially with increasing polymer concentration leveling off at Trmin = 3 for the solutions exhibiting intermediate Newtonian thinning and Trmin ≈ 10 otherwise. The relaxation time ratio λ e/ λ s, where λ s is the terminal shear relaxation time, decreases exponentially with increasing polymer concentration and the data for all investigated solutions collapse onto a master curve irrespective of polymer molecular weight or solvent viscosity when plotted versus the reduced concentration c[ η], with [ η] being the intrinsic viscosity. This confirms the strong effect of the nonlinear deformation in CaBER experiments on entangled polymer solutions as suggested earlier. On the other hand, λ e ≈λ s is found for all WLM solutions clearly indicating that these nonlinear deformations do not affect the capillary thinning process of these living polymer systems.

Strain and strain rate dependence of gellan, agar and agar–gellan gels as model systems

Gellan, agar and their combination gels (1:1, 2g/100g) as model systems were subjected to strains up to 0.8 while varying the crosshead speed between 0.01 and 10mms−1 to determine different textural characteristics (Young’s modulus, rigidity constant, degree of concavity and apparent biaxial elongational viscosity, ηbe) and fracture characteristics. The compression curves usually consisted of 6 zones, and the gels were sensitive to strain rate and the extent of applied strain. Agar gel showed higher fracture force and energy compared to gellan and agar–gellan samples. However, the fracture strain for gellan was highest (44.6–70.7%) followed by agar (22.8–40.3%) and agar–gellan (24.3–37.3%) gels indicating more brittleness in agar/agar–gellan gels but toughness in gellan samples. The degree of concavity of gellan gel was less than 1 indicating strain-softening characteristics; the agar gel exhibited strain-hardening phenomenon as it was more than 1. However, marginal strain-softening behaviour was observed for gellan–agar combination gel (0.856⩽n⩽0.999). A power law type model linked ηbe and the biaxial extensional rate at fracture. Gellan gels are suitable to prepare chewable fabricated juicy gels, while brittle products resulted from agar/agar–gellan. It is proposed that ηbe at fracture is a good index for characterising gels in relation to product development and compression-spreading.

Flow Drawing Behavior of Poly (ethylene terephthalate) Fiber Heated by CO2 Laser Irradiation

Poly (ethylene terephthalate) fiber was continuously flow drawn with heating by CO2 laser irradiation. The flow drawing behavior was discussed with the view point of the irradiated laser energy and draw ratio. The drawing behavior can be classified into 4 categories ; (1) only stable neck drawing can be observed, (2) both neck and flow drawing can be observed, (3) only stable flow drawing can be observed, and (4) melt down or break. The fiber temperature and the fiber speed profile on the flow drawing process were measured. As the results, it revealed that the maximum fiber temperature on the drawing process was the range of 210 to 225 o C, and the length of deformation region increase with the draw ratio. The apparent elongational viscosity of the flow drawing process was also estimated by the measured fiber speed profiles, and was compared with the reported values of the neck drawing process and the meltspinning process. The minimum value of the apparent elongational viscosity was about 10 - 20 kPa·s regardless of the draw ratio.

Melt-spinning and thermal stability behavior of TiO2 nanoparticle/polypropylene nanocomposite fibers

The elongational flow properties of TiO2 nanoparticle/polypropylene (PP) nanocomposite fibers were studied via melt spinning. The diameter, tension, and flow rate of fibers were directly measured and used to calculate the apparent elongational viscosity and apparent elongational strain rate using Cogswell’s theory. Thermal gravimetric analysis (TGA) was used to demonstrate that the TiO2 nanoparticles improved the thermal stability of the PP fibers. With a 1–3 wt % loading of the TiO2 nanoparticles, the PP fiber decomposition temperatures ranged from 338 °C for the pristine polymer to 342, 349, and 367 °C; the decomposition was accompamied by an initial 95 wt % weight loss. In addition, the well-distributed morphology of the TiO2 nanoparticles on the side surface of the PP matrix was observed using atomic force microscopy (AFM). At 1 wt % loading of the TiO2 nanoparticles, the surfaces of the PP nanofibers contained mono-disperse nanoparticles with sizes of 20–50 nm. Furthermore, the TiO2 nanoparticle/PP nanocomposite fibers were shown to be thermally stable and are suitable for application as an antibacterial polymer.

Rheological properties of blends of linear and long‐chain branched polypropylenes

AbstractBlends of a long‐chain branched polypropylene (LCB‐PP) and a linear polypropylene (L‐PP) were prepared using a twin‐screw extruder. Linear viscoelastic properties such as complex viscosity, storage modulus, and weighted relaxation spectrum were determined as functions of LCB‐PP content. Shear data obtained from commercial rheometers as well as from a slit‐die rheometer were used to verify the Cox‐Merz relation for the neat components as well as for a blend. Elongational properties were obtained using a Sentmanat Extensional Rheometer (SER) unit mounted on an Advanced Rheometric Expansion System (ARES) rheometer and the converging die. A significant strain hardening was observed for the neat LCB‐PP as well as for all the blends, but the strain hardening decreased with increasing strain rate. The apparent steady elongational viscosity values evaluated using the converging die were observed to be comparable at high deformation rates to those obtained from the SER unit, but the differences increased as the strain rate decreased. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers

Rheology and properties of melt-processed poly(ether ether ketone)/multi-wall carbon nanotube composites

Poly(ether ether ketone) (PEEK)/multi-wall carbon nanotube (MWNT) composites containing up to 17wt% filler were prepared using a twin screw extruder. Transmission electron microscopy (TEM) images reveal that the MWNTs were homogeneously dispersed in the PEEK matrix. Linear viscoelastic measurements show that both complex viscosity and moduli increase with increasing MWNT concentration. The storage modulus, G′ exhibits a dramatic seven order increase in magnitude around 1wt%, leading to a solid-like low-frequency behaviour at higher loadings; the effect can be attributed to network formation at a rheological percolation threshold. Rheotens measurements show that the melt strength also increases significantly on addition of nanotubes, however, the drawability decreases. An analytical Wagner model was used to calculate the apparent elongational viscosity over a wide range of elongational rates, and to reveal significant increases on addition of MWNTs, with a similar threshold behaviour. The electrical response is also dominated by percolation effects, increasing by nearly 10 orders of magnitude from 10−11 to 10−1S/cm, on the addition of only 2wt% MWNTs. In contrast, the thermal conductivity and tensile elastic modulus of the composites increased linearly with nanotube content, rising by 130% and 50%, at 17wt% MWNTs, respectively.

Rheological behaviour of nano-composites based on polyamide 6 under shear and elongational flow at high strain rates

In this work, the rheological behaviour of high molecular mass polyamide 6 (PA6)/organo-montmorillonite nano-composites, obtained via melt blending, was investigated under shear and extensional flow. Capillary rheometry was used for the measurement of high shear rate steady state shear viscosity and die entrance pressure losses; further, by the application of a converging flow method (Cogswell model) to these experimental results, elongational viscosity data were indirectly calculated. The extensional behaviour was directly investigated by means of melt spinning experiments, and data of apparent elongational viscosity were determined. The results evidenced that the presence of the organo-clay in filled PA6 melts modifies the rheological behaviour of the material, with respect to the unfilled polymer, in dependence on the type of flow experienced by the fluid. In shear flow, the nano-composites showed a slightly lower viscosity than neat PA6, whereas in elongation, they appeared much more viscous, in dependence on the organo-clay content.

Pressure Loss of Viscoelastic Surfactant Solutions under the Flow in a Packed Bed of Particles

The objective of this study is to examine the property of pressure loss under the flow of surfactant solutions in a packed bed of particles. Three mixtures of CTAB and NaSal in distilled water were used as test fluids. The flow property of surfactant solution in the packed bed was expressed by a wall shear stress and an apparent shear rate, which were defined in a model channel for a packed bed. The flow curve, a plot of the shear stress versus the shear rate, shows a sigmoidal shape. The first bending point in flow curve occurs because of the sudden increase in shear stress, which looks like the shear-thickening in shear viscosity. However, the surfactant solutions in the packed bed was affected by a stretch deformation due to a converging-diverging flow. We estimated an apparent elongational viscosity by means of the difference in pressure loss between the packed bed and the capillary flow data. As a result, it is found that the obtained elongational property demonstrates a significant change, that is the transition from a stretch-thickening property to stretch-thinning one with the increase in stretch rate. It is considered that the property of elongational viscosity for surfactant solutions is closely related to the transition of micellar network structure.

Analysis of the rheotens experiment with viscoelastic constitutive equations for probing extensional rheology of polymer melts

A model for the rheotens experiment is proposed to probe extensional rheology of polymer melts relevant to fabrication. The philosophy of the model is the coupling of the filament transport phenomena equations with kinetic theory constitutive equations of the differential type. A modified Giesekus (MG) constitutive equation seems to outperform other constitutive equations of the kinetic theory type, such as original Giesekus (OG) and finitely extensible non-linear elastic (FENE)-like, in terms of fitting and predictive capability of force rheotens curves at different process conditions for (i) substantially linear homogeneously branched polymers (AFFINITY™ polyolefin plastomers), (ii) linear low density polyethylene (LLDPE) (ASPUN™ fiber grade resins) and (iii) dow LDPE melts, with a variety of melt indexes and polydispersities (Mw∕Mn). The model is a useful tool for estimation of an apparent elongational viscosity versus strain rate curve from raw rheotens data. It predicts a dominating extension thinnin...

Establishment of the Melt Spinning Dynamics Model for Polymeric Nanocomposites

A model suitable to polymeric nanocomposites was developed for the simulation of both low‐ and high‐speed melt spinning. Considering the different content of nanoparticles, different TiO2 modifications, and different take‐up speeds, various spinning parameters along the spinline, such as velocity gradient, tension, relative crystallinity, etc., were predicted. Calculations based on the model indicated that the addition of nanoparticles has a large effect on the spinning parameters, especially relative crystallinity, apparent elongational viscosity, and tensile force

Transient uniaxial orientation of flexible polymer chains in a wide range of elongation rates

Affine evolution of chain end-to-end vectors distribution function is derived analytically for non-linear polymer liquids subjected to uniaxial elongational flow, controlled by time-evolution of chain deformation coefficients. Peterlin approximation for non-Gaussian chain elasticity is applied, with Padè approximation for the inverse Langevin function. The approach enables calculations of transient molecular deformation coefficients in entire range of elongation rates and times.Equations controlling time evolution of the molecular deformation coefficients in elongational flow are solved analytically with an assumption of dominating elongational component. The approach allows to decouple evolution equations and obtain an approximate closed form analytical formula describing time evolution of the molecular deformation with high accuracy, in particular at higher elongation rates, above the Gaussian limit.Predictions of the analytical formula are compared with numerical computations to evaluate the approximation and ranges of its validity.The analytical formula enables predicting evolution of average functions in non-linear systems, such as free energy, tensile stress, molecular orientation, etc. The formula is used to discuss molecular vs. macroscopic deformation in wide range of elongation rates and times, as well as evolution of stress, axial orientation factor, apparent elongational viscosity.

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.

Relationships between processing conditions and rheological behavior of polyethylenes

AbstractThe rheological properties of high‐density polyethylene melts were found to change drastically after treatment with oxygen or peroxide. Unusual features of the treated melts in shear flow (190°C) included (a) increase in length of time to reach steady state values of shear stress in start‐up experiments; (b) a non‐reproducibility of the low‐shear rate sections of the flow curves measured at increasing and decreasing shear rate; (c) an increase of viscosity at low shear rates compared to the neat sample. Under non‐stationary extensional flow (a regime of constant force) the treatment leads to a change in shape of the strain development with time, an increase of the apparent elongational viscosity, and an increase in time to break. At 150–170°C, the rheological behavior of the treated polyethylenes is completely identical to the corresponding behavior of the untreated. These results, together with data from IR‐spectroscopy and GPC suggest the following mechanism: The oxidation or peroxidation leads to reactive sites in the polymer chain that incorporate a few long branches during the initial contact with oxygen or peroxide. These reactive sites remain in the polymer after cooling/solidification and can become activated again upon heating to 190°C causing additional changes in molecular structure. Formation of the long‐chain branches results in an increased resistance of the melt to extensional deformation, and an improvement in processing behavior, as well as the quality of bottles produced by the blow‐molding process. Polym. Eng. Sci. 44:615–624, 2004. © 2004 Society of Plastics Engineers.

Diameter Profile Measurements for CO2 Laser Heated Drawing Process of PET Fiber

Abstract Poly (ethylene terephthalate) (PET) fiber was heated by carbon dioxide laser radiation in the continuous drawing process. By this procedure, the position of the deformation region could be fixed precisely in the air. The location of neck-like deformation fluctuated within a range of about 0.2 mm for draw ratios of 4.0 to 4.5 and within a range of about 0.5 mm for draw ratios of 5.5 to 6.0, but the location fluctuated over a range of 1.0 mm for a draw ratio of 5.0. Fiber diameter profiles, which were used to calculate Hencky strain rate profiles and apparent elongational viscosity profiles, were obtained from high-speed video camera images of the deformation region. Regardless of draw ratio, apparent elongational viscosity exhibited almost the same minimum value. Apparent elongational viscosity is much lower than the value obtained by measurement at a low, constant strain rate, but the elongational stress acting at the point where apparent elongational viscosity begins to increase steeply (Hencky strain of about 1.0) is of the same order of magnitude as the reported value. For draw ratios less than 5.0, the temperature where apparent viscosity is lowest is about 100 to 120°C, which corresponds to the flow temperature of amorphous PET, whereas for draw ratios exceeding 5.0 the temperature where apparent viscosity is lowest is about 80°C, which corresponds to the glass transition temperature. Thus, the former corresponds to so-called neck-like deformation typically observed in high-speed spinning, and the latter corresponds to necking typically observed in cold drawing. These two types of deformation appear in turns for a draw ratio of 5.0, and therefore the location of the deformation region fluctuates greatly. This measurement system can be used as a high-strain-rate elongational rheometer for analyzing practical polymer processing systems, which can easily measure the precise on-line deformation history with a time resolution in the μs level.