液晶高分子-各向异性流体挤出拉伸分岔研究

应用共转导数型本构方程研究了液晶高分子纺丝挤出过程的拉伸黏度,应用计算机符号运算软件 Maple得出解析表达式,拉伸黏度与拉伸率之间关系(随剪切速率变化)表明存在分岔现象,得出拉伸黏度显著高于相应的剪切黏度,解释了液晶高分子熔体挤出时不发生挤出胀大的物理机制．     

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.     

Elongational and shear flow in polymer-clay nanocomposites measured by on-line extensional and off-line shear rheometry

Rheological behaviour of polymer nanocomposites has been usually characterized by rotational as well as capillary rheometry, which are both time and cost consuming. We have already published that reinforcement in polymer-clay nanocomposites can be estimated very fast using extensional rheometer in combination with a capillary rheometer. It has been proven that the magnitude of melt strength can be correlated with that of tensile strength, i.e. 3D physical network made of layered silicate and polymer matrix, which is responsible for material reinforcement, can be monitored directly using extensional rheometry. Therefore, additional time for samples preparation by press or injection moulding as well for long measurements by tensile testing is not required any more. In this contribution, results of extensional rheometry measured directly during compounding process are presented. In this manner, further reduction in time required for material characterization has been achieved. The samples have been prepared by advanced compounding using a melt pump and special screw geometries. With the use of on-line extensional rheometry and off-line rotational rheometry, different nanocomposites have been tested and the effect of processing conditions (screw speed and geometry in the twin-screw extruder) on elongational and viscoelastic properties has been investigated. It has been found that the level of melt strength measured by extensional rheometry correlates with a high accuracy with dynamic rheological data measured by rotational rheometry. It was hereby confirmed that the network structure made of silicate platelets in polymer melt is reflected in both elongational and shear flow in the same way.     

Determination of the elongational viscosity of polymer melts by melt spinning experiments. A comparison with different experimental techniques

In this work, melt spinning experiments were tentatively used for the determination of the elongational viscosity of polymer melts at different levels of tensile strain and strain rate. The materials examined were two high-density polyethylene grades for blow moulding with similar number-average molecular mass but different polydispersity index. The data from melt spinning tests were compared with transient extensional viscosity data obtained by uniform isothermal tensile tests, performed by means of an extensional rheometer, as well as with those produced by converging flow tests (Cogswell model). The results showed that for high strain and strain rate levels, the melt spinning experiments provide elongational viscosity data quite close to the transient extensional viscosity values obtained from the tensile tests.     

Effect of vinyl acetate content and silicate loading on EVA nanocomposites under shear and extensional flow

In this study, three EVAs (ethylene-vinyl acetate co-polymers) with different vinyl contents (VA) ranging from 9 wt% to 28 wt% (EVA9, EVA18 and EVA28) were melt blended with organo-clay to obtain polymer layered silicate nanocomposites. Filler intercalation and exfoliation were evidenced by X-ray diffraction. The melt state viscoelastic properties of EVA nanocomposites were studied to examine the influence of clay in altering the flow properties of these polymeric nanocomposites. The EVA18 and EVA28 nanocomposites exhibited remarkable difference in dynamic and steady shear properties compared to neat polymers. On the other hand, EVA9-5% nanocomposite did not exfoliate and exhibited rheological behaviour very similar to that of the neat polymer. Furthermore, the first normal stress difference was found to be dependent on the silicate loadings when measured at low shear stresses. The uniaxial extensional viscosity measurement indicated that the strain hardening was weaker in EVA nanocomposites compared to neat polymers. Environmental scanning electron (ESE)-microscopy elucidated a possible reason for reduced strain hardening in these systems.     

Influence of molecular structure on the extensional behaviour of polyethylene melts

The elongational behaviour of polyethylene samples having different molecular structure has been tested. Elongational viscosity measurements have been carried out using the isothermal melt spinning technique. The extensional behaviour of the different samples is analysed as a function of total strain. The effect of long-chain branching on elongational viscosities is described. A comparison is presented between elongational viscosity and melt strength data.Some of the results reported here were presented at the VIIIth International Congress on Rheology, Naples, September 1–5, 1980, cf. [16].     

Elongational flow and rheology of monodisperse polymers in solution

We describe the utilization of idealized stagnation point extensional flows, produced by opposed jets, for birefringence visualization of induced molecular strain and flow resistance measurements. We identify rheological changes associated with the coil---stretch transition which occurs beyond a critical strain-rate in elongational flow-fields. In dilute solutions of monodisperse atactic polystyrene, increases in extensional viscosity are observed as isolated molecules become stretched. The largest increases in extensional viscosity, however, are found only beyond a critical concentration and strain rate, and are associated with the stretching of transient networks of interacting molecules. These results parallel similar effects seen in porous media flow and capillary entrance experiments. We determine the molecular weight dependence of the critical concentration which scales as M^−0.55 in agreement with pairwise interaction of coils, but is much lower than conventional values of the critical polymer concentration, c^*. We believed that polydispersity may play an important role in the development of such transient networks, and in controlling the degradation behaviour during flow.     

Extensional behavior influence on viscoelastic turbulent channel flow

In this work we use in the simulation of a viscoelastic turbulent channel flow a modification of the finitely extensible of non-linear elastic dumbbells with the Peterlin approximation (FENE-P) constitutive model for dilute polymer solutions, applicable to high extensional deformations. The new feature introduced by this modification is that the free energy of the polymer (since it is assumed to be entirely entropically driven) remains always bounded (FENE-PB). The characteristics of the model under steady shear flow, pure elongational flow and transient extensional behavior are presented. It is found that the FENE-PB model is more shear thinning than FENE-P. Most importantly, it also shows a higher extensional viscosity than the FENE-P model. Although the steady-state Trouton ratio asymptotically reaches at high extensional rates the same limit as the FENE-P model, the transition from the Newtonian value is sharper and faster. We use the FENE-PB model in direct numerical simulations (DNS) of viscoelastic turbulent channel flow using spectral approximations. The results for various statistics of the flow and the polymer conformation, when compared against those obtained with the original FENE-P model and the same rheological parameters, show an enhanced polymer-induced drag reduction effect and enhanced deformation of the polymer molecules. This indicates that it is not only the asymptotic but also details from the extensional rheological behavior that matter in quantitatively specifying turbulent viscoelastic flow behavior.     

Flow instability for binary blends of linear polyethylene and long-chain branched polyethylene

The rheological properties and flow instability are studied for binary blends composed of a long-chain branched polyethylene and a linear polyethylene. It is found that the blends containing a linear-polyethylene with high shear viscosity exhibit higher oscillatory moduli, drawdown force, and strain-hardening behavior. The blends showing the anomalous rheological phenomena show sharkskin failure in low shear rate region as compared with a pure linear polyethylene. Moreover, the blends exhibit severe gross melt fracture at low output rate. Enhanced strain-hardening in elongational viscosity and large entrance angle at a die entry will be responsible for the severe gross melt fracture for the blends.     

Linear and non-linear viscoelastic properties of ethylene vinyl acetate/nano-crystalline cellulose composites

This paper reports on the melt rheological properties of ethylene vinyl acetate containing between 0 and 10 wt.% of nano-crystalline cellulose (NCC). A complete set of rheological tests including frequency sweeps, shear transients, and uniaxial elongations was performed. Frequency sweeps showed that at low frequencies, a pseudo solid-like behavior was obtained for NCC concentrations higher than 5%. This behavior was related to hydrogen bonding between NCC particles and the creation of particle networks as the result of particle–particle interactions. For transient shear tests, all compositions presented a stress overshoot at high shear rates before reaching a steady state. It was found that the amplitude of this overshoot depends on both NCC content and shear rate. On the other hand, the time to reach the maximum was found to be highly shear rate dependent but concentration dependence was rather weak. For uniaxial extensional flow, higher extensional viscosity was observed with increasing NCC content. On the other hand, strain hardening was found to decrease with increasing NCC content.     

Rheological characterisation of a high-density polyethylene with a multi-mode differential viscoelastic model and numerical simulation of transient elongational recovery experiments

The rheological characterisation of a high-density polyethylene is performed by means of measurements of the storage and loss moduli, the shear viscosity and the transient uniaxial elongational viscosity, the latter being obtained with the Meissner extensional rheometer. The rheological behaviour of the polymeric material is described by means of a multi-mode Phan Thien-Tanner fluid model, the parameters of which are successively fitted on the basis of the linear and non-linear properties. By using a semi-analytical technique and the finite element method, numerical investigations are performed for the shape recovery of the sample, and the predictions are compared with their experimental counterparts. Surface tension effects are also explored. We discuss the agreement between the experiments and the simulation results. Received: 15 October 1998 Accepted: 22 December 1998     

Numerical simulation of entry flow of the IUPAC-LDPE melt

Numerical simulations have been undertaken for the creeping entry flow of a well-characterized polymer melt (IUPAC-LDPE) in a 4:1 axisymmetric and a 14:1 planar contraction. The fluid has been modeled using an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times (Papanastasiou–Scriven–Macosko or PSM model). Numerical values for the constants appearing in the equation have been obtained from fitting shear viscosity and normal stress data as measured in shear and elongational data from uniaxial elongation experiments. The numerical solutions show that in the axisymmetric contraction the vortex in the reservoir first increases with increasing flow rate (or apparent shear rate), goes through a maximum and then decreases following the behavior of the uniaxial elongational viscosity. For the planar contraction, the vortex diminishes monotonically with increasing flow rate following the planar extensional viscosity. This kinematic behavior is not in agreement with recent experiments. The PSM strain-memory function of the model is then modified to account for strain-hardening in planar extension. Then the vortex pattern shows an increase in both axisymmetric and planar flows. The results for planar flow are compared with recent experiments showing the correct trend.     

Extracting extensional properties through excess pressure drop estimation in axisymmetric contraction and expansion flows for constant shear viscosity,extension strain-hardening fluids

In this study, hyperbolic contraction–expansion flow (HCF) devices have been investigated with the specific aim of devising new experimental measuring systems for extensional rheological properties. To this end, a hyperbolic contraction–expansion configuration has been designed to minimize the influence of shear in the flow. Experiments have been conducted using well-characterized model fluids, alongside simulations using a viscoelastic White–Metzner/FENE-CR model and finite element/finite volume analysis. Here, the application of appropriate rheological models to reproduce quantitative pressure drop predictions for constant shear viscosity fluids has been investigated, in order to extract the relevant extensional properties for the various test fluids in question. Accordingly, experimental evaluation of the hyperbolic contraction–expansion configuration has shown rising corrected pressure drops with increasing elastic behaviour (De=0～16), evidence which has been corroborated through numerical prediction. Moreover, theoretical to predicted solution correspondence has been established between extensional viscosity and first normal stress difference. This leads to a practical means to measure extensional viscosity for elastic fluids, obtained through the derived pressure drop data in these HCF devices.     

Elongational flow behavior of polymeric fluids according to the Leonov model

The viscoelastic behavior of polymeric systems based upon the Leonov model has been examined for (i) the stress growth at constant strain rate, (ii) the stress growth at constant speed and (iii) the elastic recovery in elongational flow. The model parameters have been determined from the available rheological data obtained either in steady shear flow (shear viscosity and first normal-stress difference as a function of shear rate) or oscillatory flow (storage and loss moduli as a function of frequency in the linear region) or from extensional flow at very small strain rates (time-dependent elongation viscosity in the linear viscoelastic limit). In addition, the effect of the parameter characterizing the strain-hardening of the material during elongation has also been studied. The estimation of this parameter has been based upon the structural characteristics of the polymer chain which include the critical molecular weight and molecular weight of an independent segment. Five different polymer melts have been considered with varying number of modes (maximum four modes). Resulting predictions are in fair agreement with corresponding experimental data in the literature.     

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.     

Shear and elongational flow behavior of acrylic thickener solutions. Part II: effect of gel content

We have investigated the effect of crosslink density on shear and elongational flow properties of alkali-swellable acrylic thickener solutions using a mixing series of the two commercial thickeners Sterocoll FD and Sterocoll D as model system. Linear viscoelastic moduli show a smooth transition from weakly elastic to gel-like behavior. Steady shear data are very well described by a single mode Giesekus model at all mixing ratios. Extensional flow behavior has been characterized using the CaBER technique. Corresponding decay of filament diameter is also well fitted by the Giesekus model, except for the highest crosslink densities, when filament deformation is highly non-uniform, but the non-linearity parameter α, which is independent of the mixing ratio, is two orders of magnitude higher in shear compared to elongational flow. Shear relaxation times increase by orders of magnitude, but the characteristic elongational relaxation time decreases weakly, as gel content increases. Accordingly, variation of gel content is a valuable tool to adjust the low shear viscosity in a wide range while keeping extensional flow resistance essentially constant.     

Molecular theory for moderately concentrated polymer solutions in shear flow

A molecular theory for the rheological properties of moderately concentrated polymer solutions is developed on the basis of a model of interacting dumbbells. The interaction is treated in a mean field approximation, leading to an effective one-particle potential and a Gaussian stationary distribution function. Various rheological functions such as birefringence, shear viscosity and first normal-stress coefficient for simple shear flow and the Trouton viscosity for simple extensional flow are calculated. Good qualitative agreement with experimental observations is found, especially at intermediate flow rates. It is predicted, for example, that the birefringence increases approximately linearly with shear rate at intermediate shear rates and that the concentration dependence of the gradient varies asc ^1/2. The typical non-Newtonian behaviour is obtained for the shear viscosity. For small concentrations the onset of shear rate dependence decreases asc ^–1/2. At intermediate shear rates an apparent power law is obtained with an exponent between – 0.5 and – 1.0, decreasing with concentration.     

An unsymmetric constitutive equation for anisotropic viscoelastic fluid

A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid–liquid crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie–Ericksen theory is described by the first Rivlin–Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion–extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extrudate of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a series of new anisotropic non-Newtonian fluid problems can be addressed. The project supported by the National Natural Science Foundation of China (10372100, 19832050) (Key project). The English text was polished by Yunming Chen.     

Rheological characterization of commercial highly viscous alginate solutions in shear and extensional flows

The rheological properties of sodium alginate in salt-free solutions were studied by steady shear, dynamic oscillatory and extensional measurements. This biopolymer consists of mannuronic and guluronic acid residues that give a polyelectrolyte character. We applied the scaling theories and checked their accordance with polyelectrolyte behaviour for low concentrations with a shift to neutral polymer behaviour at larger concentrations. This nature was supported by the effect of the concentration on the specific viscosity, the relaxation times from steady shear and the longest relaxation times from small amplitude oscillatory shear (SAOS) measurements. To analyze the extensional behaviour of the samples, we conducted a study of dimensionless numbers and time scales where filament thinning driven by viscous, capillary or elastic forces is at play. We conclude that an exponential filament thinning followed by breakup results in the best regimes that describe the experimental data. Besides, the data pointed out that alginate in salt-free concentrated solutions shows strain thinning of the extensional viscosity and chain rigidity, behaviours that cannot be inferred from the shear rheometry.