Rheological properties of poly(trimethylene terephthalate) in capillary flow

The shear viscosity, extensional viscosity, and die swell of the PTT melt were investigated using a capillary rheometer. The results showed that the PTT melt was a typical pseudoplastic fluid exhibiting shear thinning and extensional thinning phenomena in capillary flow. There existed no melt fracture phenomenon in the PTT melt through a capillary die even though the shear rate was 20,000 s^?1. Increasing the shear rate would decrease the flow activation energy and decline the sensitivity of the shear viscosity to the melt temperature. The molecular weight had a significant influence on the flow curve. The flow behavior of the PTT melt approached that of Newtonian fluid even though the weight‐molecular weight was below 43,000 s^?1 at 260°C. The extensional viscosity decreased with the increase of the extensional stress, which became more obvious with increasing the molecular weight. The sensitiveness of the extensional viscosity to the melt temperature decreased promptly along with increasing the extensional strain rate. The die swell ratio and end effect would increase along with increasing the shear rate and with decreasing the temperature, which represented that the increase of the shear rate and the decrease of temperature would increase the extruding elasticity of the PTT melt in the capillary die. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 705–709, 2005     

Steady-state behavior of star polymers in dilute flowing solutions via Brownian dynamics

A bead and spring model is considered for the Brownian dynamics simulation of the behavior of regular star polymer chains in a dilute solution under both shear flow and extensional (or elongational) flow. Finite extensibility, excluded volume, and hydrodynamic interaction are taken into account to make the polymer model as realistic as possible. The behavior of star-like chains in flow is similar to that of linear and ring polymers. Thus, dependence of a given property with the arm molecular weight is analogous to that found for linear polymers when using the total molecular weight. In shear flow, the deformation of the chain and the shear rate viscosity dependence (the flow curve), are studied. We find a slope for the shear-thinning region of the flow curve close to −2/3. In elongational flow the coil-stretch transition is characterized by giving the relationship between the critical elongational rate and the arm molecular weight, which turns out to be similar to the power law found in linear chains.     

Shear and extensional flow of reinforced plastics in injection molding. I. Effects of temperature and shear rate with bulk molding compound

Capillary flow studies on bulk molding compound (BMC) using an instrumented injection-molding machine are reported. The significance of extensional flow effects with fiber-reinforced materials is emphasized. The extensional flow behavior in converging dies is modeled, and a means of evaluating both extensional and shear viscosity from capillary flow data is proposed. Methods of correcting results for the effect of deformation heating are discussed. The shear and extensional flow behavior of BMC in the temperature region 18 to 58°C can be fitted to a simplified Arrhenius Law.     

Orifice Flowmeter for Measuring Extensional Rheological Properties

Extensional rheological properties play an important role in processes in which the fluid is subjected to highly decelerated or accelerated flows. This paper describes an orifice flowmeter used to measure extensional properties of rheologically complex fluids at high strain rates. The operating principle of the flowmeter is based on the pressure drop due to the flow through a small size orifice. The flowmeter was first calibrated, by plotting the pressure drop‐flow rate curve of the orifice, in terms of a dimensionless Euler number versus Reynolds number. Newtonian fluids consisting of aqueous solutions of corn syrup were used as calibration fluids. The calibration curve was then used to determine the apparent extensional viscosity of three different paper coating colors. The apparent extensional viscosity is compared to the shear viscosity in terms of the Trouton ratio. The Trouton ratio for one coating color is shown to exceed considerably the theoretical value of 3 expected for Newtonian fluids.     

Necking in isothermal melt spinning and its connection to the vortex formation in entrance flow

We derive the necking condition in isothermal melt spinning employing the model of convected Maxwell fluids with strain-rate dependent material relaxation time. It is found that necking is possible when the extensional viscosity is strain-thinning (strain-softening), and impossible when the extensional viscosity is strain-thickening (strain-hardening). This finding then immediately reveals the correspondence between the spinning process and entrance flow (contraction flow), as several recent articles show that vortex is formed in the entrance flow when the extensional viscosity is strain-thickening. Thus necking in spinning corresponds to no vortex in entrance flow, whereas no net king in spinning to vortex in entrance flow, for the flow mechanism of the both situations is the extensional flow whose behavior is determined by the extensional viscosity.     

聚丙烯熔体拉伸流变行为的研究

采用双料筒毛细管流变仪,对两种不同摩尔质量的等规聚丙烯的剪切及拉伸流变行为进行了研究,并采用Cogswell方法计算了熔体的拉伸强度。结果表明：聚丙烯为假塑性流体,随着剪切速率的增加,熔体的表观剪切黏度下降,呈现出假塑性流体典型的“剪切变稀”行为。在相同的温度和剪切速率下,平均摩尔质量较小、分布较宽的聚丙烯的表观剪切黏度及拉伸黏度均较小,但熔体的拉伸强度较大,意味着其具有较好的流动性能,并具有较高的可拉伸性,可以达到较大的拉伸比。     

PIV技术测试聚合物流体拉伸流动的实验研究

针对低相对分子质量、低黏度的牛顿流体（如聚异丁烯）和非牛顿流体（如3 %苯甲酸钠溶液）,采用粒子成像速度仪（PIV）系统测试了2种流体在同一流率下流经渐变收缩流道时的速度分布,并研究比较了壁面处的纯剪切流动与流道中心轴线上的拉伸流动。通过实验测试与有限元模拟比较发现,牛顿流体和非牛顿流体的速度分布形态具有一定的差异。在确定速度分布的情况下,根据渐变收缩流动的特点,可以得到流体流动时中心轴线上的拉伸速率和边界处的剪切速率。     

Effect of molecular weight distribution on elongational viscosity of undiluted polymer fluids

A combination of the Bersted model, giving the relaxation spectrum in terms of the molecular weight distribution (MWD), and the rubberlike-liquid model of I odge is used to describe the elongational viscosity for constant extensional strain rates in terms of the MWD. Predictions of this hybrid model are in reasonable agreement with experimental results for polystyrene, if one assumes a strain rate dependent truncation of the relaxation spectrum. The predicted effects of varying molecular weight and breadth of the molecular weight distribution on the extensional viscosity are presented. At constant weight average molecular weight and constant strain, a narrower MWD is predicted to yield an extensional viscosity-strain rate curve that is essentially shifted to higher strain rates relative to a broader MWD. Furthermore, at constant weight, average molecular weight, constant strain, and high strain rates, a narrower MWD is predicted to yield a higher extensional viscosity.     

Study of the rheology of aqueous radiation curable polyurethane dispersions modified with associative thickeners

The chemistry of radiation curable polyurethane dispersions is outlined with an emphasis on the microstructure of the aqueous polymer dispersion and the possible interactions with associative thickeners. The steady-shear flow was studied for two model dispersions prepared from the same unsaturated polyurethane but showing significantly different particle size distributions. A hydrophobically modified ethoxylated urethane (HEUR) associative thickener with a linear structure was incorporated at different amounts to the dispersions with varying particle volume fractions. The steady-state viscosity at 25 and 10 °C was always reached quickly after instant flow rate changes so that no significant thixotropic effects were reported within the experimental timescale. Without thickener, the flow curves of the two model dispersions exhibited a Newtonian behavior except at the highest volume fractions where shear thinning became apparent. The maximum packing values determined from the Krieger–Dougherty relationship were essentially the same for the two systems. In the presence of thickener, the flow curves were characterized by a Newtonian plateau followed by a marked shear thinning region even at low particle volume fractions. This behavior typically suggests the formation of a physical network between polyurethane particles and thickener molecules partly adsorbed onto the polymer surface. The zero-shear viscosity of the two dispersions was compared with respect to: (i) particle volume fraction and (ii) particle surface area at different HEUR concentrations. At a given volume fraction, the particle size affects the viscosity of thickened models. As a corollary, a relationship is found between the particles size and the level of thickener required to reach a target viscosity. This study offers practically relevant data in terms of application conditions and provides a better insight into the thickening protocol.     

聚合物熔体延伸粘度的研究方法

聚合物熔体的延伸粘度是影响聚合物熔体流动特性和成型制品性能的重要因素。本文较为系统地介绍了聚合物熔体延伸粘度的理论和实验研究方法,着重介绍了Cogswell、Gibson、Binding和Berstered等人的理论研究工作,为进一步研究熔体的延伸粘度提供思路。     

Shear and extensional rheology and flow‐induced orientation of carbon nanofiber/polystyrene melt composites

The rheological behavior and morphology of polystyrene/carbon nanofiber (PS/CNF) composites in their melt phase have been characterized through experimental measurements. Viscosity measurements of the PS/CNF composites in the linear viscoelastic regime show the ratio of the transient extensional viscosity to the transient shear viscosity to be greater than three, the Trouton ratio. This behavior is due to differences in the flow‐induced orientation of CNFs in shear and extensional flow. The orientation development of the CNFs in shear and extensional flow was analyzed through a method utilizing transmission electron microscopy and was used to explain observed rheological phenomena. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Influence of carbon black on processability of rubber stocks. V. Extrusion

A study of postextrusion relaxation (shrinkage) rates identified two separate processes, only one of which is influenced by carbon black structure and surface area. One of these processes is thought to be a solidlike fast elastic recovery and was found to be influenced by carbon black and polymer characteristics. The other process reflected slow randomization of oriented molecular chains: it was mainly influenced by polymer nature and carbon black had almost no effect. In the previous paper of this series, work with various carbon blacks in SBR–1500 indicated that both types of polymer deformation originate within the converging flow region at the die entrance, where extensional flow takes place. In the present work the extensional flow behavior of five polymers (filled with various carbon blacks) was examined at elevated temperatures. The magnitude of shrinkage caused by molecular alignment was related to extensional viscosity of the rubbers. This confirms the hypothesis stated above. Extensional viscosity was measured using the previously described instrument, which is inexpensive to construct, easy to operate, and can be attached to any standard stress–strain tester. The characteristics of extensional flow are defined and it is shown that for polymeric materials it differs substantially from shear flow, since a rapid orientation of the molecular chains takes place during the extensional flow. The effect of carbon black on the extensional viscosity at elevated temperatures is illustrated.     

Compression molding of glass reinforced thermoplastics: Modeling and experiments

The shearing and extensional behavior of glass mat‐thermoplastic (GMT) material under compression molding was investigated with a special model being developed for the case of non‐lubricated mold‐plate surfaces. Mathematical expressions for the radial and through‐thickness flow velocities were derived that enabled the derivation of extensional and shear strain rates. The GMT non‐lubricated (no‐slip wall conditions) compression molding was modeled as a combination of extensional and shearing flow and the two extensional and shear viscosities were determined. Scott's approach was used in this work to determine the radial velocit in the r‐direction, which depends on the shear power‐law expression. The velocity component in the z‐direction was then calculated using the continuity equation. The velocity profiles were used to calculate the shear and extensional strain rates. Scott's shear viscosity did not satisfy the constitutive equation for the extensional part, but a power‐law expression with new parameters depending on the deformation tensors was successfully used to calculate an independent extensional viscosity using the same non‐lubricated squeezing experiment. Lubricated squeezing flow was carried out for the same material to achieve a pure extensional flow, and the extensional viscosity calculated using this approach agreed with the extensional viscosity determined using the non‐lubricated experiment. GMT material used in this study is confirmed to have two layers of continuous long fibers orientated randomly inplane, separated by short chopped fibers in the middle, which suggests that the material can be treated as an isotropic material, and the fiber‐matrix separation is seen to be high at the extremities of the flow.     

Elongational,hysteresis, and oscillatory flows of complex fluids

The simple model proposed earlier to describe te rheological properties of complex fluids is used to calculate (a) the extensional viscosity, (b) the hysteresis loops, and (c) the complex viscosity. It has been found that the rheological properties predicted by the model agree with experimental observations. It is shown that for some viscoelastic fluids the extensional viscosity is always finite and for some other fluids the extensional viscosity tends t infinity at finite extensional rate. In the latter case, steady flow is not attainable. The shape of the hysteresis loops depends on the maximum shear-rate. It also depends on the material properties. In a small amplitude oscillatory flow, our model reduces t a linear viscoelastic fluid.     

Flow-induced crystallization from solution: The relative effects of extension and shearing flow fields

Calculations have been performed to evaluate the relative effects of extensional and shearing flow fields on both the chain elongation and crystal nucleation rate enhancement for polyethylene crystallizing from xylene solutions. Rheological behavior was evaluated by means of the elastic dumbbell model modified for nonlinear effects at high elongations, and nucleation rate effects were considered from an essentially phenomenological view point. Molecular weight effects were also incorporated explicitly in the computations. Results show that chain elongation and nucleation rate enhancement is far greater for extensional than for shearing flows. Semiquantitative comparisons with experimental results reported in the literature for various aspects of the flow induced process, including the important fractionation effects, are discussed. Modification of the dumbbell model to account for shear rate effects on the intrinsic viscosity is also discussed.     

Use of Carbopol 980 and carboxymethyl cellulose polymers as rheology modifiers of sodium-bentonite water dispersions

The effects of polymer addition on the rheological parameters of sodium bentonite water dispersions at ambient conditions were studied using high molecular mass carboxymethylcellulose (CMC) and Carbopol 980. Adsorption isotherms using the batch equilibrium technique of the polymers onto the bentonite particles were Langmuir isotherms of the L1 type, indicating monolayer adsorption of the polymers onto the surface of the bentonite particles. The aqueous dispersions of 3% and 4% sodium bentonite exhibited Herschel–Bulkley rheological behavior. Addition of CMC up to 1.5% by mass to the 3% sodium bentonite dispersions decreased the yield stress and the flow consistency index because of the steric effects caused by the adsorption of the polymer. This state was then followed by a plateau of the yield stress and a considerable increase of the flow consistency index, indicating that after a particular polymer concentration, further addition merely increased the liquid viscosity of the mixture. The flow behavior index was not affected by CMC addition. Addition of Carbopol 980 to the 3% and 4% sodium bentonite dispersions up to 0.15% by mass again firstly decreased the yield stress and the flow consistency index, then increased the yield stress and the flow consistency index with increasing polymer concentration. The high shear viscosity of bentonite–Carbopol dispersions showed also a minimum followed by a drastic increase. The flow behavior index was not affected significantly by the polymer addition.     

Elongational viscosity of microbead suspensions

A ‘tubeless syphon’ was used as an elongational viscometer for the purpose of measuring elongational viscosities of glass bead suspensions in dilute polymer solutions. It was found that while the shear viscosities increased, the elongational viscosities decreased very sharply with increasing bead concentration. The conclusions from the present data are then compared with the observed changes in the elastic properties of two phase molten polymer systems. A double shift procedure has been successfully adopted to correlate the experimental data.     

Molecular degradation of concentrated polystyrene solutions in a fast transient extensional flow

The extensional degradation of concentrated polymer solutions is studied. Extensional flows are prevalent in the polymer processing industry, but their effect on polymer degradation is often overlooked. Previous research into dilute solution extensional degradation proved that this type of flow is much more effective than shear flow in causing chain scission. This research extends these dilute solution studies into the concentrated regime, where intermolecular entanglements are expected to affect chain scission. A concentrated polystyrene solution is degraded in an opposed pistons device. This device cycles the solution across a sharp contraction, imposing a strong extensional flow. The flow field is modeled to determine the extension rate along the centerline, and the degradation is quantified by measuring the zero shear viscosity and the molecular weight distribution. The results show that degradation is more significant compared to dilute solutions. The zero shear viscosity drops 30% after a single pass across the orifice at high strain rates. As in a dilute solution, the extensional flow leads to preferential cleavage of the high molecular weight chains. All chains longer than a measured critical molecular weight are ruptured. Multiple passes across the orifice increase chain scission, although degradation is the most significant in the first pass through the high strain rate region.     

Mass and heat transfer from or to a single sphere in simple extensional creeping flow

The first detailed numerical investigation on the mass and heat transfer both outside and inside a solid or liquid sphere immersed in a simple extensional flow for a larger range of Peclet numbers (1–100,000) is presented. By making use of the known Stokes velocity field at small Reynolds numbers, a finite difference method with the control volume formulation is adopted to solve the convection‐diffusion transport equation. Simulation results show that the transport rate, which is represented by Sherwood number, is significantly affected by Peclet number and viscosity ratio. The flow direction, no matter a uniaxial extensional flow or a biaxial extensional flow, has no effect on the total transport rate but affects the concentration distribution a lot. Some comparisons between present simulations and previous studies are made to validate each other and confirm the reliability and applicable scopes of reported correlations. A few new correlations are put forward to predict the transfer rate at finite Peclet numbers for various values of viscosity ratios. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3214–3223, 2012     

The influence of non-Newtonian flow on effective viscosity and channel efficiency in screw pumps

A method is given for selecting the “effective viscosity” for isothermal flow of non-Newtonian liquids in screw pumps or melt extruders. Effective viscosity is the Newtonian viscosity that would give the same screw-pump performance with non-Newtonian liquids at the same flow rate and speed. When effective viscosity is known, it can be inserted in performance equations for simple Newtonian flow. The analysis is restricted to shallow screw-pump channels with large aspect ratios and to shear stress/shear rate curves with modest curvatures when shown in a double logarithmic plot. The shear stress/shear rate curve is replaced by a power-law tangent to that curve in the domain of prevailing shear rates, but the analysis could be extended to more complex behavior. Curves are also included for calculating the efficiency of the screw-pump channel, which can be used to estimate the energy dissipated in screw-pumps. It is shown that efficiency decreases with decreasing power-law exponent.