Elastic fracture of polystyrene solutions

Based on the assumption of a constant critical shear strain, an expression for the critical stress at the onset of entrance fracture as a function of polymer concentration has been developed. Experimental results with 10-25 percent narrow distribution, high molecular weight polystyrene-benzene solutions show the critical stress to be much lower than that for the polymer melt and in agreement with predicted values. This result is all the more impressive when the contrast in flow behavior at the capillary entrance for melts and solutions is observed. Instead of the rotating toroidal vortices surrounding a 90-deg material entrance cone observed with polystyrene melt, cine movies of the solution flow birefringence patterns in the capillary entrance region reveal only a stagnant zone surrounding a narrow cone less than 20 deg. At fracture, the cone axis moves in a rotary path circulating about the capillary axis without undergoing the flow discontinuities typical of melt behavior.     

Kinematics of the stick-slip capillary flow of high-density polyethylene

A study of the kinematics of the stick-slip capillary flow of high-density polyethylene has been carried out in this work by using particle image velocimetry (PIV). The experiments covered a wide range of shear rates and the velocity maps and profiles across the die were obtained for the different regimes of the discontinuous flow curve. In the low shear rate region, the melt exhibited shear thinning without slip. In the unstable stick-slip regime, an alternating behavior between full adhesion and slip was observed, whereas both, the maximum velocity and the slip velocity of the melt, changed continuously during pressure oscillations. In addition, non-homogenous slip, characterized by regions with and without slip at the die wall, was occasionally observed during the oscillations. In contrast to the general assumption, the flow in the high shear rate region was found to be unstable, and characterized by high frequency pressure oscillations. A steep rise of the slip velocity took place from the onset of the stick-slip regime and reached values higher than 70% of the maximum velocity for the profiles in the high shear rate branch. However, a true plug flow was never observed due to shear thinning of the melt. Finally, a direct proof of the Mooney hypothesis to account for slip in polymer melts is given on the basis of the comparison of velocity profiles measured in the low and high shear branch.     

ELASTIC FRACTURE OF POLYMERIC FLUIDS

The elastic fracture of polystyrene solutions and melts was investigated using a plunger driven viscometer. The polymeric extrudate emerging from a circular capillary was photographed to determine the onset of fracture, and an effort was made to relate this information to the shear stress at the capillary wall, the recoverable shear strain, the entanglement density and the geometrical parameters characterizing the system. It was found that narrow molecular weight distribution polystyrenes dissolved in benzene clearly fractured as reported in the literature, but the onset of fracture could not be predicted by available criteria. As opposed to this, highly concentrated (polymer volume fraction up to 0.57) and elastic solutions of a wide molecular weight distribution polystyrene in benzene showed no fracture when judged using similar criteria. Nonetheless, this latter polymer fractured as a melt at a value of the wall shear stress less than that achieved in the solution runs. From an examination of the polymer rheology, it is concluded that the recoverable shear strain is the key quantity influencing the onset of elastic fracture. Also, the recoverable shear-shear rate behavior is different for the melt and the solution and it depends not only on the polymer molecular weight and its distribution but also on the solvent used. The surprising absence of elastic fracture for highly viscoelastic solutions can be understood if one realizes that a critical value of the recoverable shear strain is needed for fracture to occur.     

Mixture Rules for Critical Shear Values of Extruded Linear PE/Branched PE Blends

Oscillatory flow and elastic turbulence belong to the types of flow instabilities frequently encountered during extrusion of polymer melts. The onset of these defects corresponds to the flow conditions when the critical shear stresses or the critical shear rates are attained. The critical values of shear stresses and shear rates were experimentally determined for linear polyethylene/branched polyethylene blends (IPE/bPE) that were prepared with various weight ratios. Consequently, mixture rules of the logarithmic type are proposed. These rules relate the critical value of shear stress (shear rate) of blend to the critical values of shear stresses (shear rates) of the individual pure components, weight fractions, and interaction parameters. There is a good agreement between the proposed mixture rules and experimentally determined critical values.     

The effct of asymmetries of die exit geometry on extrudate swell and melt fracture

Experimental investigations were performed to see how the die exit geometry and the extrusion velocity influence on extrudate swell and melt fracture for several polymer melts [low-density polyethylene, styrene-butadiene rubber (SBR) and SBR/HAF (carbon black) compound]. Four different types of die exit geometry were considered; 0° (symmetric. usual capillary die), and 30°, 45° and 60° (asymmetric dies) were chosen for the die exit angle. Extrudate diameters were measured without draw-down under isothermal condition. Polymer melts were extruded into an oil that has the same density and temperature as those of the extrudate. Extrudate swells from dies with different diameters were correlated with volumetric flow rates. It was observed that the extrudate swell increases with increasing volumetric flow rate and exhibits through a minimum value at about 45° die exit angle. As to the fracture phenomena, it was observed that the critical shear for the onset of melt fracture increases with the increasing die exit angle up to 45°. However, for 60° die exit angle, the onset of melt fracture is again similar to that of 0° exit angle.     

Rheology of polymer melts in high shear rate

Little is known of the rheology of polymer melts in the high shear rate up to 10⁶ s^?1 or more. A specially designed high-shear-rate rheometer was developed, by which the rheology of polymer melts for shear rates up to 10⁸ s^?1 can be investigated. Two non-Newtonian regions and a transition or the second Newtonian region were observed in the wide range of shear rates up to 10⁷ s^?1. The observed flow curves for various polymer melts are classified into three typical patterns. One is the flow curve typically shown of high-density polyethylene in which a clear second Newtonian region appears after the first non-Newtonian region. The second is the typical flow curve of polystyrene in which a “transition region” appears instead of the second non-Newtonian region. The third is the flow curve shown of acrylonitrile-styrene copolymer, which exhibits behavior between the two types. A generalized flow curve is proposed to explain the observed flow behaviors of various polymers over a wide range of shear rates. The flow behavior in high shear rate results from high orientation and scission of polymer molecules.     

A mechanism for extrusion instabilities in polymer melts

A mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non-monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time-dependent, incompressible, one-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady-state solutions to one-dimensional perturbations at fixed volumetric flow rateis analyzed by means of a linear stability analysis and finite element calculations. Self-sustained periodic oscillations of the pressure gradient are obtained when an unstable steady-state is perturbed, in direct analogy with experimental observations.     

A model viscoelastic fluid

Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Flow pattern observations in circular die entry flows in conjunction with independent shear and normal stress measurement strongly suggest that these fluids would make excellent model fluids for melt studies. Studies in which the influence of elasticity in the absence of shear thinning and fluid inertia can easily be made. Furthermore it is clearly shown that a realistic solution to the die entry flow problem is not obtained using second order flow theory. In the second order region the secondary cell is observed to be almost identical in size to the cell observed for an inelastic Newtonian fluid in creeping flow. Marked growth in the secondary cell as a function of elasticity is not observed until the shear rates exceed the region of second order behavior. This growth in cell size as a result of elasticity is followed at higher shear rates by a spiraling flow instability like that observed for some polymer melts.     

RHEOLOGICAL AND MIST IGNITION PROPERTIES OF DILUTE POLYMER SOLUTIONS

A spinning disc atomizer has been used to characterize the mist flammability of Jet A and diesel fuels that contain high molecular weight polymers. The critical disc velocity required to produce significant flame propagation was shown to depend on polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The viscoelastic properties of these same polymer solutions have been characterized by a maximum Darcy viscosity measured from flow in packed tubes. For the polymers discussed in this paper, the maximum Darcy viscosity was independent of the bead size or tube length; however, it was strongly affected by the same variables that affected mist flammability; i.e., polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The critical ignition velocity of dilute polymer solutions is shown to depend on the Darcy viscosity in a similar manner as observed for viscous oils. At low viscosities, the ignition velocity is only slightly affected, but the dependence grows stronger as the viscosity (both shear and Darcy) increases. A close correspondence was also shown to exist between the ignition velocity of a polymer solution with a high Darcy viscosity and the ignition velocity of a Newtonian oil with approximately the same high shear viscosity.

Numerous similarities are described between flow-induced birefringence of dilute polymer solutions with opposed capillary jets and viscoelastic resistance of dilute polymer solutions in packed tubes. These similarities suggest that the maximum Darcy viscosity is associated with a condition of almost complete extension and alignment of the polymer molecules.     

The influence of intermolecular hydrogen bonding on the flow behavior of polymer melts

The influence of hydrogen bonding on the flow behavior of polymer melts at high shear rate has been investigated using a capillary extrusion rheometer. The systems studied were copolymers of ethylene and acrylic or methacrylic acid. Hydrogen bonding was found to substantially enhance both flow activation energy and viscosity level, as well as the degree of dependence of viscosity on rate of shear. It was also found that hydrogen bonding does not influence the critical shear stress for onset of “melt fracture.” The data support the view that hydrogen bonds act effectively as temporary (quasi-) crosslinks during the short time scales of deformation involved in flow at high shear rates.     

Degassing of molten polymers

Degassing is a key-step in polymer processing. Low-molecular-weight components are removed from a polymeric system. The transport of these components takes place by diffusion to the polymer-vapour interface. This interface can be formed by free surfaces of single-phase polymer melts or by bubbles. In this study, the transport with and without bubble nucleation is investigated independently from each other in a special designed apparatus similar to a degassing extruder.The mass transport in thin films and in rotating pools with surface renewal is measured. High surface renewal rates and thick films enhance the mass transfer for single phase flow and bubbly flow. Dimensionless mass transfer coefficients are given as a function of the surface renewal rate, the area of the free surface and the total mass of the polymer. The conditions for bubble nucleation and foam formation are investigated. The bubble nucleation is observed in the rotating pool in the area of high shear velocity.     

Wall Slip of Linear Polymer Melts During Ultrasonic‐assisted Micro‐injection Molding

The wall slip of linear polymer melts under ultrasonic vibration is investigated by correcting the slip mechanism, and melt flow behaviors in ultrasonic‐assisted micro‐injection molding (UμIM) method are discussed. Based on the effect mechanism of ultrasonic vibration on the melt, theoretical models of the critical shear stresses for the onset of weak and strong wall slip during UμIM are established, and the change in rheological properties due to the onset of wall slip under ultrasonic vibration is experimental investigated by a built measurement system. The results show that the onset of weak and strong wall slip of the melt in micro cavity are promoted by ultrasonic vibration, which agree with the built theoretical models, and the melt filling capability in micro cavity is enhanced by reducing apparent viscosity and releasing shear stress of the polymer melt, which improves the molding quality of micro polymer parts via UμIM method. POLYM. ENG. SCI., 59:E7–E13, 2019. © 2018 Society of Plastics Engineers     

STEADY SHEAR FLOW PROPERTIES OF HIGH SOLIDS SOFTWOOD KRAFT BLACK LIQUORS: EFFECTS OF TEMPERATURE, SOLIDS CONCENTRATIONS, LIGNIN MOLECULAR WEIGHT AND SHEAR RATE

The steady shear flow properties of several softwood kraft black liquors (slash pine) from a two level, four variable factorially designed pulping experiment were determined for solids concentrations from 50% to 85%, temperatures from 40°C to 140°C and shear rates up to 10,000 s-1 by using Instron capillary and Haake coaxial cylinder rheometers. It was shown that the slip velocity at the wall of the capillary is insignificant and that a two capillary method can be used to determine the viscosity of the samples. At high solids, black liquor can exhibit non-Newtonian behavior dependent upon temperature, solids concentrations, solids composition and shear rate. In general, the liquors behave as pseudoplastic fluids. The exact level of viscosity at any given condition is dependent upon the solids composition which will vary from liquor-to-liquor. The flow behavior of the liquors was described using power-law, Cross and Carreau-Yasuda models. Superposition principles developed for polymer melts and concentrated polymer solutions were applied to obtain reduced correlations for viscosity behavior of the liquors. By using a suitable reference temperature, related to the glass transition temperature of black liquors, a generalized WLF type shift factor was obtained for the liquors used in this study and can be used to obtain a reduced plot of viscosity behavior of other black liquors.     

ON THE SWELLING OF SUBMERGED JETS OF DILUTE AND SEMI-DILUTE POLYMER SOLUTIONS

Profound jet swelling is shown to exist when a dilute or semi-dilute solution of PEO (POLYOX WSR 301) is ejected from a capillary tube into a stagnant fluid. The jet swells up to ten times the diameter of the capillary tube depending on the shear rate in the tube and on the density difference between the ejected and the stagnant fluid. The diameter ratio (jet/tube) grows as the 1/3 power of the shear rate, regardless of the density difference, tube diameter and polymer concentration and provided the tube is long enough for the development of the flow profile. For SEPARAN AP 45 solutions, displaying a non-Newtonian behaviour in shear, it is shown that the 1/3 power law holds between the diameter ratio and the shear stress, instead of the shear rate. The analogy between the swelling behaviour of these dilute and semi-dilute polymer solutions and the one observed in concentrated solutions and melts is discussed. The possibility of utilizing the submerged jet technique to compute the polymer solution normal stresses is considered.     

ON THE SWELLING OF SUBMERGED JETS OF DILUTE AND SEMI-DILUTE POLYMER SOLUTIONS

Profound jet swelling is shown to exist when a dilute or semi-dilute solution of PEO (POLYOX WSR 301) is ejected from a capillary tube into a stagnant fluid. The jet swells up to ten times the diameter of the capillary tube depending on the shear rate in the tube and on the density difference between the ejected and the stagnant fluid. The diameter ratio (jet/tube) grows as the 1/3 power of the shear rate, regardless of the density difference, tube diameter and polymer concentration and provided the tube is long enough for the development of the flow profile. For SEPARAN AP 45 solutions, displaying a non-Newtonian behaviour in shear, it is shown that the 1/3 power law holds between the diameter ratio and the shear stress, instead of the shear rate. The analogy between the swelling behaviour of these dilute and semi-dilute polymer solutions and the one observed in concentrated solutions and melts is discussed. The possibility of utilizing the submerged jet technique to compute the polymer solution normal stresses is considered.     

Turbulent flow behaviour of dilute polymer solutions in an annulus

An experimental study has been carried out to investigate the turbulent flow behaviour of dilute polymer solutions in an annulus. The polymers used are two grades of Separan, AP30 and MG500, both are known to exhibit drag reduction characteristics in turbulent pipe flow. Similar drag reduction phenomena have been observed in annulus flow. At a given Reynolds number, the friction factor decreases with increase in polymer concentration and appears to reach a minimum (or maximum drag reduction) at certain optimum concentration. An estimate of the critical wall shear stress, which marks the onset of drag reduction, is consistent with pipe flow results, suggesting that the critical value is independent of flow geometry and size. A lower drag reduction, achieved in an annulus in comparison with circular pipes, is attributed mainly to a diameter effect.     

高密度聚乙烯的壁面滑移行为

用双筒毛细管流变仪和旋转流变仪研究了两种牌号的高密度聚乙烯(HDPE)熔体的壁滑行为,考察了发生壁滑的临界剪切应力。通过剪切速率扫描的方法发现两种牌号的HDPE熔体在较高的剪切速率下均发生粘滑转变,在150～230℃温度范围内,HDPE发生粘滑转变的临界剪切应力位于0.20～0.38 MPa范围内,与文献报道值一致;而且发生粘滑转变的临界剪切应力随温度线性增加,这与B rochard和de Gennes提出壁滑的解缠机理一致。用壁滑外推长度表征壁滑程度,发现两种牌号的HDPE熔体的壁滑外推长度均处于0.05～0.09 mm范围内。     

Velocity profiles of the exit region of molten polyethylene extrudates

The objective of the work described herein is the experimental investigation of the velocity field of polymer melts flowing through a capillary in the regons of flow prior to and after the capillary exit. The fluids studied are branched polyethylene melts in steady laminar isothermal flow. The technique employed for the determination of the Eulerian velocity profiles is one that utilizes phototomicrogroaphy of the reflected light from tracer particles dispersed in the flowing medium. Axial acceleration of the fluid elements just before the capillary exit was observed. It was found that this accelearation is more pronounced in melts of low bulk viscosity. This observation region, non-viscometric. The translation of the velocity profiles of the fluids studied, from one resembling a parabola to that of “plug” flow, involves inflection points with minima in the velocity vector v (r, z). These minima appear near the surface of the extrudates and can not be accounted for by an existing theory. It was also found that the density of the viscoelastic fluids studied is a function of the axial position, in the region of flow investigated. The density decreases before the exit and, before it reaches an equilibuiu value at an axial position downstream equal to one or two diameters, increases beyond that value upon exit. This phenomenon is attributed to an “overshoot” in the process fo elastic recoil of the high polymer melts fron a strained structure to a random one.     

Effect of process variables on melt velocity profiles in extrusion process using single screw plastics extruder

Abstract

Single screw extruders are used to generate a continuous flow of molten polymer in many industrial polymer processes. The melt velocity profile as extruded is important in determining the properties of the final product and influences process related phenomena such as die swell and the onset of sharkskin. The factors that influence the velocity profile would be expected to be the melt temperature (this affecting the viscosity of the melt), the screw and die geometry, and the output rate from the extruder. In the present work a thermocouple mesh sensor coupled with a cooled stainless tube has been used to determine velocity profiles in melts exiting from the screw of a single screw extruder. The results show that the technique can be used successfully to determine velocity profiles in the extrusion process.

It was found that the main influence on the magnitude of the melt velocity was the extruder screw speed. Melt temperature, and hence melt viscosity, were found to have little effect on the velocity profiles measured. The flow in the centre of the duct was retarded slightly owing to the flow across the screw tip and no rotational component of flow was observed. The velocity profiles measured seemed to be reasonably stable, only small changes being observed in the velocity profiles as the melt flowed along a duct of uniform cross-section, although these changes were limited in nature. Die diameter and length had a limited effect on the velocity profiles generated, although the die entry angle did have a significant effect on the shape of the velocity profile at higher screw speeds.