Volume 9, Issue 1

Distributive mixing in an internal mixer was studied numerically by means of tracking the evolution of the distance between pairs of particles in the mixing chamber. The distributions of these pairwise distances are reported in terms of the probability density function of a pairwise correlation function. In conjunction with this descriptive technique, a dynamic particle-tracking algorithm for two dimensions has been developed to study the dynamics of mixing in the mixer. We also propose a parameter e to monitor the extent of mixing. This general approach represents the first attempt of this kind to address directly the goodness of mixing. A total of five operating modes was considered. Three of them have even speed ratio of 60 rpm and rotors positioned at 90–90, 90–180, 90–270 relative to the horizontal axis, respectively. The remaining two have uneven speed of 60 rpm/40 rpm and rotors positioned at 90–90, 90–270 relative to the horizontal axis, respectively. For each operating mode, a complete period is represented as a sequence of snap shots (72 for even speed and 216 for uneven speed) and the flow field for each snap shot was calculated by means of FIDAP. Based on our proposed framework, we were able to demonstrate clearly that the anti-symmetric configuration (90–270) is the best operating mode among the three even speed cases and the configuration (90–180) is the worst. The performance of the uneven speed cases fell in between the even speed cases.

Composite models for the calculation of the filling level profiles, the pressure profiles, the melting profiles, the residence time distributions, the temperature profiles, the shear stress profiles, and the power consumption in modular tightly intermeshing co-rotating twin screw extruders (ZSK) are developed. A complex systematic design procedure was compiled, which is explained in part in this paper. The simulation of the intermeshing co-rotating machine involves both screw and kneading disc elements, including left- and right-handed sections. Kneading blocks were approximated by a screw of “equivalent pitch” with making allowance for the leakage flow across the flights from one channel to the adjacent channel. The mathematical treatment of co-rotating twin screw extruders has been based up according to the theory of single screw extruders. There was seen to be a good correlation between calculated and experimental results.

A simulator to emulate the working of a counter-rotating twin screw extruder was constructed for studying devolatilization (DV) of reactive polymer solutions. The rate of the release of the volatiles was measured by an in-line mass flow meter. The operating pressure and solution temperature were measured by a pressure transducer and a thermocouple. The vapor sample compositions were determined by UV spectrophotometer. The transesterification of ethylene-vinyl acetate copolymer with 3-phenyl 1-propanol in 1-nonane solution was chosen as a model reaction. The volumetric mass transfer coefficient K 1 A was determined at various temperatures, pressures, shaft speeds and sample sizes. The effect of the reaction on K 1 A was also examined. It was found that K 1 A of the solvent (1-nonane) increases significantly with a decrease in operating pressure, and that it also increases appreciably with shaft speed, whereas temperature and the initial sample size have little effect on it. The reaction shows undetectable effect on K 1 A of the inert solvent.

An experimental study is presented of the mixing of polyamide-6 and polyethylene in a Leistritz modular counter-rotating twin screw extruder. Seven different screw configurations were investigated and the material distributions and phase morphology developments along the axis of the screw were characterized. The behavior of different modular elements was determined including screw flights of varying thickness, Kiesskalt compression elements and shearing elements.

The Cavity Transfer Mixer (CTM) was primarily designed as a distributive mixing device to be used as an add-on unit to existing extruders. In determining the CTM overall mixing efficiency as well as its potential use for various applications, the flow patterns/characteristics within this mixer must be well understood. In this work, a fluid dynamics analysis package – FIDAP – using the finite element method was employed to simulate the flow patterns in a CTM with 3 rows and 6 cavities per row. A 3-D, isothermal flow analysis for a Newtonian fluid was carried out. The flow field was characterized in terms of velocity profiles, average shear stresses and a parameter λ quantifying the elongational flow components. The influence of processing variables on the flow characteristics was also discussed. The simulation results show good agreement with the experimental data.

A calculation of fiber orientation of reinforced thermoplastics in two tube die geometries is presented. The flow field and fiber motion are calculated using coupled anisotropic constitutive equation and equation of change for fiber orientation. A finite element method is used for the flow field computation, and a simplified characteristic method for the fiber orientation. Results show that fibers orient parallel to the tube axis in a classical die of constant radius in the final land whereas fibers have a more isotropic orientation in a die with a final divergent land. Experimental observations and quantification of fiber orientation in reinforced thermoplastic tubes extruded with the two dies are presented. Results of the calculation agree well with the experimental data for the classical die. For the diverging die, the agreement is good at the tube surface, but the calculation underestimates the degree of orientation perpendicular to the tube axis in the core of the tube.

Solid-state extrusion experiments were carried out through constant area convergent-divergent dies using two crystalline polymers, i.e. ultra high molecular weight polyethylene (UHMWPE) and polytetrafluorethylene (PTFE), with the aim of producing extrudates exhibiting biaxial orientation. The evolution of orientation was examined along the extrusion axis by measuring the off-plane birefringence values at various distances from the entry on specimens removed from the dies. Simple analytical expressions relating orientation factor to draw ratio in the three mutually perpendicular directions were derived for crystalline polymers. These generalised relationships were found applicable for all types of deformations, i.e. monoaxial, biaxial and pure shear. On the basis of the data obtained and the predictions from the theoretical analysis, the deformations taking place in dies with small converging angles, known as fish-tail dies, were found to be close to a state of pure shear deformations, while dies with high converging angles initially, then changing to high divergencies in the second section, known as dual-taper dies, were found to give rise to a state of unbalanced biaxial deformations.

This paper deals with the flow behavior and the resulting fiber orientation during compression molding of semi-concentrated fiber suspensions. The suspension is characterized using the Dinh and Armstrong integral constitutive relations, expressed in terms of the finite deformation tensors. The equations of motion are expressed in a convenient Generalized Eulerian-Lagrangian reference frame. The resulting nonlinear system of equations is solved using full Newton-Raphson iteration procedure. An integral boundary condition has been applied at the press wall to represent the constant force condition at that boundary. Results are presented for the isothermal filling of a two-dimensional rectangular cavity for the flow field and the associated fiber orientation. The influence of different parameters such as molding force, fiber concentration, fiber aspect ratio etc. on the compression rate is also presented.

A theoretical equation of state (EOS) for chain molecule fluids is presented based on an improved hole and cell model in which the geometries of both the cells and the mers are defined as the dodecahedrons and reasonably related with the Lennard-Jones potential. Furthermore the number of configurations is treated to contribute to the EOS by means of minimizing the Helmholtz free energy to determine the cell size. This study may be regarded as the improved theories about the hole and cell model proposed by Simha et al. and the hole model by Sanchez and Lacombe. The present EOS has three characteristic parameters per pure fluid, which can lead to a corresponding-state principle for pure polymeric fluids. The validity and applicability of the equation were investigated by correlating the experimental PVT data for some common polymers and predicting the thermal expansion coefficient and isothermal compressibility of PVAc.

The differences between residual stress formation mechanisms are studied for several important polymer processes. The most important cases are free quenching (e.g. in extrusion), constrained quenching and constrained quenching with varying applied pressure (injection moulding). A simple, but physically relevant, elastic solid model is assumed (viscous melt and purely elastic solid) yielding Struik's cooling stress model for the free quenching case. In the constrained quenching case, however, the residual stresses are found to vanish. This allowed us to derive a simple analytical expression for the residual stresses in injection moulded products. These stresses were found to be proportional to the maximum melt pressure and are tensile near the surfaces. The predictions compared well with the measured stress distribution. Finally the effects of residual stresses with respect to warpage and environmental stress cracking are discussed.

A new method is presented for analyzing fiber orientation distribution in fiber reinforced composites. A fiber orientation state in fiber reinforced composites is first obtained from soft X-ray image by making contract micro-radiograph (CMR). The distribution of the fiber orientation is measured by a fiber orientation index G(θ) as proposed in this paper. Furthermore, a computer simulation for the fiber orientation distribution is carried out in order to evaluate the fiber orientation index G(θ). It has been found that the value of the fiber orientation G(θ) decreases with an increase in the scatter of the fiber orientation distribution. Not only the direction but also the degree of the fiber orientation can be shown from the curve of the fiber orientation index G(θ). The result shows that this method is easy and useful to evaluate the fiber orientation distribution in fiber reinforced composites.