Flow of polymeric melts in short tubes

In an attempt to further understand the flow of polymeric melts through gates in injection molding, the present investigation deals with measurement of pressure drops during isothermal extrusion of fiber-filled and unfilled polystyrene, polypropylene, and polycarbonate melts in short tubes with sudden contraction at high shear rates typical of injection molding. Flow curves for these materials have been determined over a wide range of shear rates at various temperatures by using a capillary rheometer and extruder. Measurements indicate that rheological properties of fiber-filled melts after injection molding differ from those of fresh samples. Moreover, it has been found that decreasing the tube length increases the slope of the curve for pressure drop vs. Volumetric flow rate. Extra pressure losses due to end effects have been determined which show that at high shear rates these losses can reach levels as high as 100 bar, with the effect being higher for the fiber-filled melts. By using a viscoelastic consitutive equation, the extra pressure losses have been separated into entrance and exit losses. Model parameters required for this calculation have been determined from viscosity-shear rate curves for the melts. For various polymers, master curves useful for industrial applications have been constructed for the extra pressure losses.     

Total applied shear in capillary extrusion

Viscoelastic properties of polymer fluids are single-valued functions of shear stress or shear rate only at high total applied shear. These parameters may vary with applied shear under milder shear histories. The mean total shear in capillary extrusion is shown to be a function of orifice geometry. Apparent flow curves can be measured at various total shear values by changing the length/radius ratio of the capillary. The true shear stress and true shear rate at the orifice wall correspond to infinite total shear conditions. The true flow curve and elastic parameters like die swell are not measured at equivalent total shear unless the capillary is extremely long.     

Shear viscosity of carbon black filled polypropylene at very low shear stresses

The shear viscosity of carbon black filled polypropylene with a range of different carbon blacks was investigated. This was accomplished using (a) a constant shear stress creep instrument, (b) a cone-plate rotational rheometer, (c) a capillary extrusion rheometer. It was found that stresses exist for these compounds below which there are only finite deformations and no steady flow, Much attention was given to measurements of creep at low stresses, especially in the neighborhood of yield values. The magnitudes of yield stresses obtained from such creep measurements are significantly lower than those obtained using standard extrapolation to zero shear rate of higher stress data from rotational instruments. The shear viscosity behavior near the yield value differs significantly depending upon the carbon black used. A high viscosity was observed (～10⁹ to 10¹⁰ Pa.s) plateau in some compounds.     

Rheological properties,flow visualization and extrudate swell of NR compound by rotating‐die rheometer

An experimental apparatus coupled with a rotating die system was especially designed and manufactured to study the rheological properties, flow patterns and swelling behavior of natural rubber (NR) compound for different shear rates and die rotating speeds at a test temperature of 110°C, the results being compared with those by the static capillary die. It was found that NR compound used exhibited psuedoplastic non‐Newtonian behavior. The rotation of the capillary die could reduce the extrusion load. The wall shear stress for any given shear rates increased with increasing die rotating speed. The fluctuation of the entrance pressure drop increased with increasing die rotating speed. The flow pattern development in the rotating‐die rheometer was different from that observed in the static die. The flow patterns in the rotating die were clearly unstable and contained two flow components which included axial flow along the barrel and circumferential flow at the die entrance. The size and shape of the axial and circumferential flows were more dependent on the piston displacement. It was found that the swelling ratio of the NR compound decreased with increasing die rotating speed. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Viscosity,modulus, and die swell of glass bead filled polystyrene-acrylonitrile copolymer

Flow curves were obtained at 190°C over the shear rate range 0.1 to 100 sec^?1 for polystyrene-acrylonitrile copolymer containing up to 36 percent by volume glass beads, using a capillary extrusion rheometer. The addition of glass beads always increased shear stress and viscosity at a given shear rate, with the increase being more pronounced at low shear rates. The addition of glass beads decreased die swell, which also depended on shear-stress and capillary length-to-radius ratio. At low shear rates a lower limiting value of die swell ratio of about 1.1 was achieved. Values of recoverable shear derived from end correction data by the technique of Philippoff and Gaskins and from die-swell data by the method of Bagley and Duffey are compared. A fairly good agreement was found for low concentration blends at low shear, However, the values differed by a factor of up to 3 at higher shear stresses. In all cases, recoverable shear was found to increase with shear stress at a fixed filler loading and to decrease with increased filler loading at a fixed shear stress. Values of shear modulus calculated from the recoverable shear measurements decreased rapidly with increasing shear stress.     

Shear viscosity of rubber modified thermoplastics: Dynamically vulcanized thermoplastic elastomers and ABS resins at very low stress

The shear viscosity of PP-EPDM dynamically vulcanized thermoplastic elastomers and ABS resins were investigated using (a) a constant shear stress creep instrument, (b) a rotational rheometer, and (c) a capillary extrusion rheometer. It was found that stresses exist for some of these materials below which they exhibit only finite deformations. This indicates they exhibit yield values. Much attention was given to measurements of creep at low stresses especially in the neighborhood of yield values. The magnitudes of the yield stresses obtained from these low stress measurements are significantly lower than those obtained using standard extrapolation to zero shear rate of higher stresses from rotational instruments. We also observed a high shear viscosity (～10⁹ PA s) plateau in the materials of high rubber content. We contrasted our results to those found in the literature.     

Superimposed effects in high‐shear‐rate capillary rheology of polystyrene melt

During micro‐injection molding, the polymer melt may undergo a shear rate up to 10⁶ s^?1, at which the rheological behaviors are obviously different from those in conventional molding process. Using both online and commercial rheometers, high‐shear‐rate capillary rheology of polystyrene (PS) melt is analyzed systematically in this work. The accurate end pressure drop and pressure coefficient of viscosity are determined via the enhanced exit pressure technique. Experimental and theoretical investigations are conducted on four significant effects, that is, the dissipative heating, end pressure loss, pressure dependence, and melt compressibility in capillary flow. For the PS melt, which exhibits distinct temperature and pressure dependence of viscosity, both dissipation and end effects become pronounced as the shear rate exceeds 2 × 10⁵ s^?1. From lower to higher shear rates (10³–10⁶ s^?1), the competition between dissipation and pressure effects results in the overestimation to underestimation of Bagley‐corrected pressure drop, and finally the comprehensively corrected viscosity becomes about half of the uncorrected one owing to the enhanced superimposed effects. Moreover, the compressibility shows a minor influence on the shear viscosity. Under the shear rate range investigated, the power‐law relationship is sufficient for describing the corrected viscosity curve of PS melt used. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Pumping characteristics of self-wiping twin-screw extruders—A theoretical and experimental study on biopolymer extrusion

The flow of Newtonian and non-Newtonian fluids which obeys a power law relationship between shear stress and shear rate has been modeled in the melt conveying section of a self-wiping co-rotating twin-screw extruder using a finite element analysis of an unwound channel section. Predictions of throughput against pressure gradient are compared with experimentally obtained results for maize grits which is represented as a power law material. Rheological data applicable to extrusion simulation were obtained from capillary rheometry. Comparisons are reasonable with predicted characteristic showing similar behavior.     

Melt Flow Properties During Capillary Extrusion of Linear Low-Density Polyethylene

Abstract

The melt flow properties of a linear low-density polyethylene (LLDPE) were measured by means of a capillary rheometer under the experimental conditions of temperatures from 220° to 260°C and apparent shear rates varying from 12 to 120 s^?1. The end pressure drop (ΔP _end) was determined by employing the Bagley's plotting method. The results showed that ΔP _end increased nonlinearly with increasing shear stress. The end pressure fluctuation phenomenon was observed at lower shear stress level, and several plateau regions were generated in the end pressure drop-shear stress curves, suggesting onset of the wall-slip phenomenon during die extrusion of the resin melt. The critical shear stress with onset end pressure fluctuation phenomenon increased with a rise of temperature. Furthermore, the melt shear flow did not strictly obey the power law. The melt shear viscosity decreased nonlinearly with increasing shear stress and with a rise of temperature, whereas the dependence of the melt shear viscosity on the test temperature accorded with a formula similar to the Arrhenius expression.     

Effects of convergent flow on in situ fibrillation of TLCP in PEN

A polymer melt entering a capillary die from a cylinder undergoes a convergent flow in which there is a complex combination of extensional and shear flows. The convergent flow plays an important role in controlling the in situ fibrillation of thermotropic liquid crystalline polymer (TLCP) in a thermoplastic matrix melt. This study examines effects of the convergent flow on development of TLCP fibrils in a TLCP/poly(ethylene naphthalate) (PEN) blend. A capillary rheometer was used and the extent of the convergent flow was varied by changing capillary dimension and shear rate. With a given capillary die, the TLCP fibrillation was found to increase with increasing shear rate because of the increased deformation of TLCP droplets. The establishment of a fully developed shear velocity profile by using a relatively long die is considered to be necessary to retain the TLCP fibrils initiated in the convergent flow region. At a given high shear rate, TLCP fibrillation improves with increasing capillary diameter (≤2 mm) because of the increased difference in velocity between the capillary and the cylinder. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1505–1513, 2004     

NR/SBR混炼胶挤出流动中自然收敛角的计算

考察了ＮＲ／ＳＢＲ共混胎面胶在毛细管挤出流动中的末端效应、基于以前的工作［１］提出了粘弹性流体自然收敛半角方程，并估算了试样在挤出条件下的人口自然收敛角（２α０）。结果表明，２α０值随着温度的升高而有所增大．随着剪切速率的增加而减小。     

Falling coaxial cylinder viscometry of polymer melts

This article considers possible erxors in experiment or analysis and alternative methods of data treatment for a falling coaxial cylinder viscometer. The viscometer uses a weighted rod falling into a polymer melt contained in a closed end concentric cylinder. Flow relations can be solved for non-Newtonian fluid response in steady, simple shearing flow. Although the rod fall is found not to be steady, as assumed, this produces negligible error in the computed flow curves. Consistent flow curves which were independent of apparatus geometry were obtained by a method in which instantaneous rod velocities were estimated graphically from raw data and an end correction was taken into account.     

高分子材料动态成型过程中熔体非线性行为的研究

借助流变测量和连续介质理论,不依赖已有的本构关系,对平行叠加正弦振动条件下高分子熔体经毛细管的动态挤出过程进行了理论分析。以低密度聚乙烯(LDPE)为原材料,实验测量LDPE熔体在一定振动频率和振幅下毛细管入口压力、体积流量和挤出胀大的瞬态值,即可得到动态成型过程中高分子熔体剪切应力、剪切速率和表观粘度的变化规律:随振幅和频率的变化,LDPE熔体的表观粘度呈非线性变化趋势;在不同的振幅和频率下动态挤出LDPE熔体,跟稳态挤出时一样,壁面剪切应力与壁面剪切速率也成非线性比例关系。     

Rheological properties of metallocene isotactic polypropylenes

Rheological properties of metallocene‐catalyzed isotactic polypropylenes (MET‐PP) were evaluated in comparison with those of Ziegler–Natta‐catalyzed isotactic polypropylenes (ZN‐PP) and MET‐PP was generally characterized in a rheological aspect. Based on the characterization, various flow processibilities and their effect on the higher order structure and product properties of the processed article were estimated. The capillary flow properties at various temperatures, elongational flow properties, and dynamic viscoelasticities of MET‐PPs and ZN‐PPs with various melt flow indexes (MFIs) were measured. Furthermore, as an example of application of rheological analysis, the selection of proper raw resin and processing conditions in the sheet‐extrusion of MET‐PP was studied. MET‐PP shows the following rheological features due mainly to the narrow molecular weight distribution in comparison with ZN‐PP with equivalent MFI to that of MET‐PP: while the viscosities at low shear rates are lower, those at high shear rates are higher. Although there is little difference in the loss modulus G″ (viscosity), the storage modulus G′ (elasticity) is very (about one decade) lower. The die swell is much smaller. The entrance pressure loss and end correction coefficient are lower. The critical shear rate at which a melt fracture begins to occur is lower. The melt tension, elongational viscosity, and melt flow index ratio are lower. The flow activation energy is slightly lower. The zero‐shear viscosity obeys the 3.4th‐power law independent of catalyst. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2157–2170, 2002     

A study of low shear viscosity of polymer melts

An inexpensive, accurate falling coaxial cylinder viscometer is described. Viscosities can be measured at shear stresses at least as low as 10³ dynes per cm² and flow curves can be obtained with shear thinning fluids. Data for a polystyrene and a polyethylene polymer coincide with those from other techniques and with corresponding literature values. The lower Newtonian viscosities pf both polymers were experimentally accessible, and it is shown that estimation of η_o by extrapolation from viscosities in the non-Newtonian region may be subject to errors of uncertain magnitude. Shear history of the sample affects the Newtonian and low shear viscosities of high molecular weight polymer melts.     

Die‐swell behavior during the short‐tube flow of rubber compounds

In this study, the flow properties and die‐swell ratios (B's) of two kinds of rubber compounds (SI was a calcium carbonate filled natural rubber compound, and SII was a carbon‐black‐filled natural rubber/butadiene–styrene rubber/cis‐1,4‐butadiene rubber compound) in a short‐tube extrusion flow were measured by means of a capillary rheometer under test conditions with a temperature of 90°C and an apparent shear rate varying from 10 to 4000 s^?1 to identify the effects of extrusion conditions on the rheological behavior of the materials and to estimate B. The shear flow roughly obeyed the power law, whereas B increased nonlinearly with increasing extrusion rate. Under the same shear rates, the viscosity of SII was higher than that of SI, whereas the values of B of SI were higher than those of SII. Furthermore, B of the rubber compounds was estimated by means of an extrudate swell equation published in a previous work. The results show that the predictions of B were close to the measured data from the experiments. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Determination of capillary entrance pressure losses and first normal stress difference in polystyrene and high impact polystyrene melts

In industrial polymer processing, polymeric melts give rise to shear stresses above 10⁵ dynes/cm². For the determination of rheological properties and particularly melt elasticity, only the capillary type instrument is applicable to this range. In this paper, a comparative experimental study of the first normal stress difference, obtained from end pressure losses, entrance pressure losses and die swell is reported for polystyrene and high impact polystyrene. Good agreement between results from the three methods of measurement was obtained. The results are in accordance with literature data obtained using a capillary rheometer. It is seen that the values of first normal stress difference are greater in polystyrene than in high impact polystyrene.     

Rheological equation for polymer melt under the action of vibration

Abstract

The entire extrusion process of a polymer melt within a capillary was analyzed thoroughly when a sinusoidal vibration of small amplitude was superimposed in parallel on the flow direction of the polymer melt. On the basis of rheological measurement, an equation for a polymer melt under parallel vibration, i.e. the apparent viscosity, was obtained. Calculation of the apparent viscosity was established by making use of novel experimental equipment. After collecting and analyzing the instantaneous data of capillary entry pressure, capillary volume flux and their phase difference in a superimposed vibration, the apparent viscosity of low-density polyethylene (LDPE) within a capillary was calculated. Meanwhile, the relationship of shear stress vs. shear rate for a LDPE melt with and without imposed vibration was presented.     

STEAM DRYING OF SINTERED SPHERES OF GLASS BEADS

ABSTRACT

Superheated steam drying of sintered spheres of glass beads with different diameters is investigated to reveal the effects of the gravitational force on drying rates. In a previous study, the drying rate curves of small samples with coarse glass beads in which the frictional resistance to flow of water and the effect of the gravitational force are negligible, were predicted by an evaporation zone model.In the present investigation, the drying rate curves of sintered spheres of glass beads with diameters ranging from 1.53×10^-2m to 4.99×lO^-2m are experimentally and theoretically obtained, and also the capillary pressure curves are measured by use of Haines' apparatus. The drying rate curves of large samples in which the effect of the gravitational force can not be negligible, are compared with those for small samples and the difference among these curves is discussed in terms of the moisture distributions which are estimated from the evaporation zone model with the observed capillary pressure curves.     

Capillary extrusion behavior of phenolphthalein poly(ether-ether-sulphone) (PES-C)

The capillary extrusion flow properties of novel engineering thermoplastic phenolphthalein poly(ether-ether-sulphone) (PES-C) have been investigated using capillary rheometer. The dependence of viscosity on the wall shear rate and temperatures were obtained. The flow activation energy was found to decrease with shear rate but to be constant with shear stress. The entrance effect was calculated and from which the extensional behavior was estimated using Cogswell's method. From the extrudate swell ratio the principal normal stress was evaluated and a temperature-independent correlation was observed when they were plotted against shear stress. The melt fracture phenomena were checked and discussed also. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:951–958, 1997