Heat transfer to molten polymers flowing through tubes

A theoretical and experimental study of heat transfer to polymer melts flowing through circular tubes is presented. The mathematical model provides for shear heating and expansion cooling effects, and also heat of reaction during flow for various wall boundary conditions. Experimental results, obtained using low density polyethylene, show reproducible temperature and velocity profiles. The measured inlet melt temperature profile and the axial wall temperature profile provide the boundary conditions for the calculations. The experimental data confirm the predictions of the magnitude of the shear heating and expansion cooling effects during tube flow.     

Stress birefringence patterns in molten polymers during the mold-filling and cooling process

An experimental study has been carried out to better understand the phenomenon of stress buildup during the mold-filling process in the injection molding operation. For the study, a rectangular mold with two glass windows was constructed, so that stress birefringence patterns of molten polymers flowing into the mold could be photographed with the aid of a polariscope. As a feeding system, a 1-in. extruder was used attached to the mold with a 2-ft length of stainless steel tubing having a relief valve. In this way, the injection pressure (and injection velocity) was carefully controlled to ensure that the glass windows would not be damaged. The development of stress birefringence patterns during the mold-filling process was recorded on a movie film. It was observed that, in isothermal operation, when flow stopped after the mold was filled, stresses relaxed immediately because of the very slow cooling of the mold by ambient air. However, it was observed that, as cooling proceeded, stresses were gradually built up again in the mold. It was possible, therefore, to determine the residual stress in the mold, which originates from the cooling process alone.     

Experimental measurement of temperature profiles of molten flowing polymers in a heat exchanger

Molten polymer was pumped through an isothermal-wall heat exchanger and the temperature at four radial positions was measured with a hypodermic thermocouple. Temperature profiles were obtained for heating, cooling, and isothermal flow of polyethylene, polystyrene and polypropylene at Graetz numbers from 1.7 to 9.2. The results show large viscous heating effects, particularly for cooling.     

Residual stress determination with acoustic birefringence in slightly anisotropic polymers

The acoustic birefringence method has been used since a long time for metallic materials to detect residual stresses. This method is rarely used for polymers and composites due to the strong attenuation of the acoustic signal. Moreover, for thermoplastic polymer, with a slight anisotropy (known as texture for metals), coupling with applied stresses, extends the complexity of the residual stresses determination. The slight anisotropy of thermoplastic polymer should be studied with shear waves prior to the residual stress determination. If the material is perfectly isotropic, we are able to detect and quantify the residual stresses. If the material is slightly anisotropic, it is also possible to evaluate residual stresses by taking into account the directions of the principal axes of material anisotropy. POLYM. ENG. SCI., 55:2307–2312, 2015. © 2015 Society of Plastics Engineers     

Measuring of coalescence in polymer melt blends flowing through converging channels

Droplets of polymer blends flowing through convergent channels undergo collisions and coalescence because of the appropriate wineglass‐shaped flow paths with essential flow constriction at the entrance zone. Therefore, an attempt has been undertaken to use capillary flow for studying coalescence phenomena in polymer blends. When the initial drop diameters in a barrel (before extrusion), d_b, and in the extrudate, d_e, are measured, coalescence efficiency can be easily calculated as E_c = d/d, provided that no breakup of elongated domains occurs. Compared with methods employing simple shear flow, it has several advantages. For example, the convergent flow pattern combining both shear and extensional flows is directly related to industrial processing operations like extrusion, injection molding, blowing, etc. The method imposes minor limitations on processing parameters and materials used. Applicability of the technique proposed was verified by systematic studies of coalescence in PMMA/PS binary melts blends during capillary extrusion and by comparing these results to theoretical predictions and experimental data from literature. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Rheological behavior of zirconia feedstock flowing through various channels considering wall-slip

The existence of wall slip for ZrO₂ feedstock flow in micro powder injection molding was investigated based on capillary rheometer experiments using dies of three dimensions. A power law function was derived by data fitting to determine the wall slip velocity based on which numerical simulation was carried out to explore the influence of wall slip on micro injection molding. Experimental results indicate that the feedstock is less sensitive to temperature fluctuation at higher shear rates. Power-law model can provide higher accuracy than the modified Cross model to depict the rheological behavior of the feedstock in capillary flows with different channels. Numerical simulation results show that in case of steady flow higher dynamic viscosity of the feedstock and higher pressure losses of the flow appeared when the wall slip boundary was included as compared to no-slip assumption in micro powder injection molding. This is because that when the wall slip boundary was included the shear rate distribution of the feedstock was lower than that of the feedstock assuming no-slip boundary.     

Solids behaviour in a dilute gas-solid two-phase mixture flowing through monolith channels

This paper reports, for the first time, the solids behaviour in a dilute gas-solid two-phase mixture flowing through monolith channels. The non-intrusive positron emission particle tracking (PEPT) technique was used in the work, which allowed investigation of three-dimensional solids motion at the single suspended particle level. Processing of the PEPT data gave solids velocity and occupancy in the monolith channels. The results showed a non-uniform radial distribution of both the solids velocity and concentration. The highest axial solids velocity occurred in monolith channels located in the central part of the column, whereas the highest solids concentration took place at a position approximately 0.7 times the column radius. The axial distribution of the axial solids velocity showed an entrance region with a length of approximately 33 times the hydrodynamic diameter of a monolith channel under the conditions of this work. Analysis of the PEPT data also gave distributions of particle residence time and tortuosity in terms of solids motion. The distributions were approximately Gaussian-type with the tortuosity distribution more skewed toward the right hand side. The peak residence time and tortuosity decreased with increasing superficial gas velocity and the distributions were broadened at lower superficial gas velocities. The results of this work also provided a possible explanation to our previously observed early laminar-to-turbulent flow transition in monolith channels.     

Measurement and prediction of diffusion coefficients of supercritical CO2 in molten polymers

The solubility and diffusivity of supercritical carbon dioxide (sc‐CO₂) in low‐density polyethylene (LDPE), high‐density polyethylene (HDPE), polypropylene (PP), ethylene‐ethylacrylate copolymer (EEA) and polystyrene (PS) were measured at temperatures from 150°C to 200°C and pressures up to 12 MPa by using the Magnetic Suspension Balance (MSB), a gravimetric technique for gas sorption measurements. The solubility of CO₂ in each polymer was expressed by Henry's constant. The interaction parameter between CO₂ and polymer could be obtained from the solubility data, and it was used to estimate the Pressure‐Volume‐Temperature relationship and the specific free volume of polymer/CO₂ mixtures. The diffusion coefficients were also measured by the MSB for each polymer. The resulting diffusion coefficients were correlated with the estimated free volume of polymer/CO₂ mixture. Combining Fujita's and Maeda and Paul's diffusion models, a model was newly developed in order to predict diffusion coefficients for the polymers studied. Polym. Eng. Sci. 44:1915–1924, 2004. © 2004 Society of Plastics Engineers.     

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.     

Transesterification reactions in molten polymers

The transesterification reaction of molten ethylene and vinyl alcohol copolymers (EVA), in presence of paraffinic alcohols and basic catalysts, leads to high conversion of the ester groups to secondary alcohol in both discontinuous and continuous processing equipment. Various kinds of alcohols and two different catalysts were used. Sodium methoxide is a powerful catalyst for the equilibrated transesterification reaction, but we also observed side reactions, such as cross-linking with low-molecular-weight alcohols and hydrolysis of the catalyst followed by partial saponification of the EVA. Kinetic studies were performed in the presence of dibutyltin dilaurate, an efficient catalyst without any side reactions. The solubility of the main alcohol reagents was verified by diffusion measurements. The general reaction scheme and the related kinetics, corresponding to a homogeneous system, lead to a fair evaluation of the rate constants.     

Development of stress birefringence and flow patterns during mold fillin and cooling

An experimental study was carried out to investigate the development of stress birefringence patterns of molten polymer during the mold filling and cooling operation. For this study, a rectangular mold cavity with glass windows on both sides was constructed, which permitted us to record on a movie film the changes in stress birefringence patterns in the mold cavity during the molding operation, using a circular polariscope. The mold was equipped with an automatic relay system which closes the shut-off valve when the pressure in the mold cavity reaches a predetermined value. The mold was also equipped with both heating and cooling devices, so that either isothermal or non-isothermal injection molding could be carried out. The mold temperature was controlled by thermistor regulated controllers. During the entire cycle of the molding operation, the mold cavity pressure was continuously recorded on a chart recorder, using a melt pressure transducer. The present study shows how molding conditions (namely, injection pressure, melt temperature, mold temperature) influence the distribution of stress birefringence patterns in a molten polymer while it is being injected into, and cooled in, a rectangular mold cavity.     

Pressure-volume-temperature behaviour of molten polymers

Summary The solubility parameter theory of Hildebrand and Scott extended for polymer blends originally has accounted for dissimilarities only between contact energies of the blend components, neglecting free volume effects which are predicted by the corresponding states theories. Biro et al., however, have shown that using expressions of the Prigogine-Flory corresponding state theories for energy and volume, effects of free volume will be implicity included in the solubility parameter approach too. The results are similar then to those derived by the corresponding state theories. In addition, it is shown that in this case the temperature and pressure dependencies of the solubility parameters are predicted qualitatively correct.We performed this procedure with the Sanchez- Lacombe EOS theory instead of the Prigogine-Flory approach, Formally, identical expressions result, and the calculated solubility parameters evaluated according to the two EOS theories are in good agreement. However, because Sanchez-Lacombe's approach is not a corresponding state theory, it is able to predict additionally qualitatively correct the dependence of the solubility parameters on chain length.     

Wall slip of molten polymers

There is considerable experimental evidence that the classical no-slip boundary condition of fluid mechanics is not always a valid assumption for the flow of high molecular weight molten polymers. In fact, molten polymers slip macroscopically at solid surfaces when the wall shear stress exceeds a critical value. Moreover, for linear polymers there exists a second critical wall shear stress value at which a transition from a weak to a strong slip occurs. These two modes of slip (weak and strong) are due to flow-induced chain detachment/desorption at the polymer/wall interface and to chain disentanglement of the polymer chains in the bulk from a monolayer of polymer chains adsorbed at the interface. In this review, the two physical mechanisms of slip are discussed and validated on the basis of published experimental data. The slip velocity of molten polymers is a complex function and has been reported to depend on wall shear and normal stresses, temperature, and molecular characteristics of polymers (molecular weight and its distribution). Proposed slip models, static and dynamic, are also reviewed and their significance on the rheology and flow simulations of molten polymers is discussed.     

Thermodynamics of gas solubilities in molten polymers

Perturbed-hard-chain theory is extended to mixtures of polymers and volatile fluids, including supercritical gases. This extension is used to derive an expression for Henry's constant for a solute in a molten polymer. Theoretical calculations and data reduction are reported for a variety of solutes in polyethylene, polyisobutylene, and poly(dimethyl siloxane) in the temperature region 25–300°C. Calculated Henry's constants and their temperature dependence are generally in good agreement with the limited experimental data now available.     

Compensation method for zero birefringence in oriented polymers

Optical birefringence is usually linked to molecular orientation in polymers. Birefringence in materials used for optical applications represents non-isotropic optical properties, and is therefore undesired, but cannot always be avoided. Molecular orientation was found to be possible without necessarily resulting in birefringence. This effect is achieved by combining suitable amounts of PMMA and poly(vinylidene fluoride) PVDF in the form of a compatible, amorphous blend. The observed drastic reduction in birefringence is the result of the compensation of positive and negative contributions to the overall birefringence.     

Dielectric rheological measurements of molten polymers

Rheological characterization of polymers above their melting points is performed with dielectric spectroscopy. A new in‐line interdigitated dielectric sensor as well as a commercial off‐line sensor were used to make the measurements. The dielectric dissipation or loss factor of a molten polymer was found to be directly proportional to independently measured rheological properties of the polymer. Time‐temperature superposition was used to translate dielectric and rheological curves to master curves where the curves are comparable in form, but the activation energy of a dielectrically‐induced relaxation was found to be lower than a rheological translational motion. The more localized and homogeneous effects imparted to the polymer during the dielectric measurement may cause the polymer to undergo a viscoelastic transition at a lower energy than the flow‐induced transition in rheological measurements. The dielectric methods detailed herein provide a new noninvasive technique to measure the viscoelastic properties of molten polymers.     

Stratified two-phase flow of molten polymers

A study has been made of stratified two-phase flow of molten polymers in a slit die. For the experimental study, measurements were taken of wall normal stresses along the longitudinal axis of a rectangular duct which had an aspect ratio of 10. Three pressure transducers were flush-mounted on each of the rectangle's long sides, directly opposite from each other. The measurements permitted one to determine the pressure gradients of each component (their viscous properties) and the exit pressures of each component (their elastic properties). For the theoretical study, the fully developed velocity distributions of two-phase flow were determined by solving the equations of motion by use of a power law model. The volumetric flow rates, calculated theoretically by use of a power law model, are compared with experimentally observed ones. Experimental evidence is presented which clearly shows that polystyrene and polypropylene form two incompatible phases in the molten state.     

Residual birefringence of amorphous polymers for optical-disk substrates

Based on the Mueller matrix approach, we have successfully designed and constructed a highly sensitive instrument for measuring optical birefringence (LB) by using a polarization modulation method and phase-sensitive technique. Our instrument can measure the retardation of a sample up to 10^?2 radian. Using this instrument, we have measured the residual birefringence of thermosetting resins, CR-39 resin and epoxy resin, for opticaldisk substrates. CR-39 resin results are summarized as follows: (1) Annealing is very effective in reducing LB of samples; (2) samples prepared from raw material 2 (monomer purity, 96%, oligomer, 4%) have smaller LB than those from raw material 1 (monomer purity, 99.9%); and (3) annealed samples prepared from 2 satisfy the requirement on LB to be used as optical-disk substrates. For epoxy resin: (1) “Second curing” largely reduces LB of samples; (2) “slow cooling” is more effective in reducing LB of samples than “fast cooling;” (3) after the second curing, cutting does not induce any residual stress birefringence in samples; and (4) slow-cooled samples have good optical properties to be used as optical disk substrates.     

Time-dependent birefringence in glassy polymers during stress-relaxation and recovery

The birefringence of polystyrene and polycarbonate have been measured during uniaxial stress relaxation tests. The birefringence of polystyrene shows an instantaneous positive increment on applying a tensile deformation; during stress relaxation the value showed a time-dependent change in the negative direction and the total birefringence eventually became more negative than the value measured prior to the deformation. On unloading, the overall trend was for the birefringence to change towards the level measured in the as-prepared sample prior to deformation but an initial departure in the opposite direction was observed. With polycarbonate, the birefringence changed instaneously on applying the deformation and remained steady during stress relaxation. On unloading the birefringence fell instaneously by an amount less than the increment observed on applying the deformation. Thereafter the birefringence continued to fall, approaching the original value with a time constant similar to that governing stress relaxation. These results are interpreted with reference to the molecular structures, in particular the location of the highly polarizable aromatic rings.