Increase Of Elongational Viscosity Research Articles

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.

EXPERIMENTAL AND THEORETICAL ANALYSES OF FILM CASTING PROCESS

A film casting process of polymer melts was discussed in this report and, in particular, the experimental measurement for rheological properties in film casting was carried out using with polypropylene and low density polyethylene. As a result, no remarkable difference in the viscoelastic properties was observed between two polymers except for the elongational ones. Low density polyethylene showed a remarkable increase in the elongational viscosity at high strain. Serious differences in the elongational properties were observed in the behavior of the necking phenomenon in the experimental film casting process. The necking width at the film edge of polypropylene was increased under the condition of higher draw ratio. However, in the case of low density polyethylene it was nearly constant and independent of the draw ratio. From these experiments, we concluded that the necking phenomenon in film casting depends on the elongational properties. Furthermore, to clarify the behavior in film casting, the flow simulation was carried out using three rheological models (the Newtonian, the Bird-Carreau and the Giesekus models) and their applicability was evaluated respectively. The simulation results on the necking phenomenon and film thickness distribution calculated with the Giesekus model was quantitatively agreed with the experimental ones for two polymers used in this study. For low density polyethylene with the remarkable increase of elongational viscosity at high strain, in particular, we clarified that the Giesekus model is suitable for the simulation of the film casting process, but other ones (the Newtonian and the Bird-Carreau models) are not applicable owing to the inaccurate expression in elongational viscosity.

Direct numerical simulations of hard particle suspensions in planar elongational flow

We present a new direct simulation technique of inertialess particle suspensions in planar elongational flow of a Newtonian fluid. The extensional bi-periodic domain concept is introduced such that a single cell problem with a small number of particles may represent a large number of repeated structures of such a cell in planar elongational flow. For implicit treatment of the hydrodynamic interaction between particles and fluid, we employ a finite-element/fictitious-domain method similar to the distributed Lagrangian multipliers (DLM) method together with a rigid-ring description of the particle. The extensional bi-periodic frame is incorporated by constraint equations with Lagrangian multipliers and is implemented by the mortar element method. In our formulation, the bulk stress is evaluated by simple boundary integrals. Concentrating on 2D circular disk particles, we present numerical examples of single-particle, two-particle and 100-particle problems in the extensional bi-periodic frame. We discuss effects of solid fraction and particle configuration on the elongational viscosity of the suspension, in comparison with simple shear flow. We found that, at zero strain, the relative elongational viscosity is almost the same as the relative shear viscosity in simple shear for moderately concentrated suspensions. There is a small increase in elongational viscosity for large strains, which is related to an anisotropic distribution of the particles.

Elongational Viscosity as a Tool to Predict the Foamability of Polyolefins

The foaming of polyolefins (POs) by direct gas injection is a delicate balance between the melt strength of the expanding polymer and the pressure of the blowing gas in the growing cells. Important parameters in this process are: melting and crystallization temperature of the polyolefin grade, viscosity in the crystallization temperature range and elongational viscosity in the crystallization temperature range. In particular, the increase in elongational viscosity or so-called strain hardening is vital for a successful foam structure. This study shows how the elongational viscosity is measured according to the rheological melt extension (RME) method. The experimental conditions for LDPE, LLDPE, HDPE, mPE plastomers, and PP are defined and used for a series of 25 PO grades. These experiments show that the strain hardening ratio (SHR) is influenced by the average molecular length, molecular weight distribution (MWD) and the long chain branching (LCB).

Analysis of the Effect of Incorporation of a Small Amount of PMMA on Fiber Structure Formation of PET

The presence of a small amount of finely dispersed polymer, which has higher Tg than the matrix poly(ethylene terephthalate) (PET) and is immiscible with PET, such as polymethylmethacrylate (PMMA), suppresses orientated crystallization of PET under high-speed fiber spinning. To examine the mechanism of the reduced degree of oriented crystallization in the fibers, experimental data were compared with the results from computational calculations in terms of diameter or strain rate profile along the spin line. The computational simulation for the diameter and the strain rate profiles, assuming an increase of solidification temperature and an increase of elongational viscosity under higher strain rate, was qualitatively in good agreement with the experimental results. On the other hand, the measured birefringence of PET/PMMA fiber was substantially lower than the calculated one, which requires further improvement considering the skin‐core structure and stress distribution in both PET and PMMA as a future research item.

Recycling of poly(ethylene terephthalate) into closed‐cell foams

AbstractThe increase of the elongational viscosity of recycled poly(ethylene terephthalate) (PET) is investigated with the aim of producing closed‐cell foams by means of a cost‐effective reactive extrusion technique. A recycled PET grade containing controlled contamination levels of polyvinyl chloride (PVC) and poylethylene (PE) is selected, and compared with virgin bottle‐grade PET as a reference. Reactive processing with a tetrafunctional epoxy additive induces randomly branched molecules with a lower degree of branching in recycled PET than in virgin PET, as shown by a molecular structure analysis. The corresponding increase in elongational viscosity is related to foaming experiments performed using supercritical CO2 in a pressurized vessel. Observations of foam microstructures reveal that modified virgin PET forms closed‐cell structures under a large variety of foaming conditions, as opposed to unmodified virgin and recycled PET, which collapse as a result of insufficient elongational resistance. Closed‐cell foams are also obtained using modified recycled PET, providing that the temperature at which the pressure is released is lowered to 260°. Recycling of PET into closed‐cell foams is thus achieved, although the processing window is slightly reduced compared to virgin PET.

The influence of pre-shearing on the elongational behaviour of dilute polymer and surfactant solutions

Experimental results are presented which provide information about the elongational behaviour of pre-sheared dilute polymer and surfactant solutions. The viscosity behaviour of these pre-sheared solutions is explained on the basis of molecular data and by flow visualization. A rotational viscometer was modified in such a way that the sheared test fluid left the gap of the viscometer through an orifice in the outer cylinder. The flow-rate at a constant pressure drop through the orifice is related to the elongational viscosity of the fluid. The elongational viscosity of dilute polymer solutions increases when a critical shear gradient is exceeded. The critical shear gradient was found to be independent of the polymer concentration. It could be lowered by increasing the molecular weight of the polymer. Visualization of the orifice flows were done in a rectangular channel. A sudden increase of the apparent elongational viscosity, which is found for poly(isobutene) solutions when a certain Deborah number is exceeded, and an increase of the elongational viscosity, which for poly(acrylamide) solutions is independent of the pre-shearing deformation, can both be related to entrance vortices and instabilities of the entrance flow in the orifice. This was confirmed by flow visualization. The surfactant solutions which were used exhibit a sudden increase of the shear viscosity due to the formation of a shear-induced state (SIS) when a critical shear rate is exceeded. In the SIS their elongational viscosity is also increased. However, the Trouton ratio remains at a value of three which is characteristic for Newtonian fluids.

Birefringence of polyethylene melt in transient elongational flow at constant strain rate

AbstractSimultaneous birefringence and elongational viscosity measurements were carried out on molten commercial grade, low‐density polyethylenes during simple elongational flow at constant strain rate and constant temperature. The birefringence increased with time during constant strain rate elongation. The increase in birefringence was a linear function of elongational stress throughout whole elongation, but the elongational viscosity increased in two stages. The increase in elongational viscosity can be divided into linear viscoelastic and nonlnear viscoelastic regions. The linear region appeared at small strain and the nonlinear region appeared at strain greater than 0.7. The elongational viscosity in the nonlinear region increased much more rapidly than that in the linear region. The Gaussian approximation, which is commonly used in molecular models, could be used for the transient elongational flow. A constant stress‐optical coefficient C = 1.3 × 10−10 cm2/dyn was obtained for all the elongational experiments, independent of strain rate (0.002‐0.2s−1). The stress‐optical coefficients were weakly dependent on temperature, as predicted by the theory of rubber elasticity.

Elongational Flow of Solution Treated Ultra-high Molecular Weight Polyethylene

The experimental study of elongational flow for solution treated ultra-high molecular weight polyethylene (polyethylene gel) was carried out using an elongational rheometer. Three different molecular weight polyethylenes, Mw=1.0×10n, 2.0×106, 2.5×106 were used. Solutions were prepared by dissolving 10wt% of the polyethylenes in decalin. The solution treated ultra-high molecular weight polyethylenes were uniformly elongated in constant strain rate elongation experiments. The elongational viscosity-time relation at 140°C shows the same behavior as polymer melts except at high viscosity. The elongational strain (draw ratio) at high temperature are much smaller than that in lower temperature experiments. A rapid increase in elongational viscosity appears at ca. 200sec for strain rate of 0.008sec-1. The degree of the viscosity increase of the solution treated polyethylene is much steeper than that of polymer melts. The steep increase in the viscosity was discussed in terms of the structure development of the solution treated polyethylene.

Elongational viscosity in the isothermal melt spinning of polypropylene

The elongational viscosity of polypropylene has been investigated by isothermal melt spinning, carried out over a range of experimental conditions. The filament diameter and the elongational force were measured for running filaments and the relationship between elongational viscosity and elongational strain rate reported. The elongational viscosity was observed to decrease in the vicinity of the spinneret and then remained constant before increasing along the thread line. An increase in elongational viscosity did not occur within the isothermal zone until the elongational flow was fully developed. The onset of an increase in elongational viscosity was determined from the constant total elongational strain. The degree of molecular orientation was also studied by birefringence measurements and was investigated as a function of elongational stress. At a high elongational stress, the relation between birefringence and elongational stress departed from linearity and exhibited a rapid increase which can be related to the increase in elongational viscosity.

Elongational Viscosity and Secondary Instability of Laminar Boundary Layer

Drag reduction phenomena of liquid flows due to an addition of polymer molecules are caused by an interaction of the elongational viscosity of the polymer solution and the elongational-type secondary flow of the base flow. In transition form laminar to turbulent flow on a flat plate boundary layer the elongational viscosity acts on the secondary vortices appearing by amplification of Tollmien-Schlichting waves and extends the stable region of Tollmien-Schlichting waves. At the same time the wave number corresponding to the critical state of neutral stability for the waves becomes larger with an increase in elongational viscosity. By this analysis it is suggested that the addition of polymer can delay the turbulent transition of boundary layer flow.

A study of fiber extrusion in wet spinning. II. Effects of spinning conditions on fiber formation

AbstractA study is carried out to investigate the effects of spinning conditions on fiber formation in the wet‐spinning process. The spinning conditions studied are free velocity (and hence free diameter), throughput rate, maximum take‐up velocity, jet stretch (the ratio of take‐up velocity to free velocity), and filament tension. The coagulating bath temperature and concentration are varied, and three spinnerette diameters are used. The spinning dope is an aqueous solution of polyacrylonitrile in sodium thiocyanate. The present study shows that the coagulating bath concentration influences the spinning tension and maximum take‐up velocity. Two thread breakage mechanisms are postulated which take into account the rate of coagulation, spinning tension, and thread velocity. An attempt is made to predict the concentration profile of solvent in the moving filament by simultaneously solving the mass and force balance equations, in which the increase in elongational viscosity along the spinning way is assumed to be mainly due to the hardening process.