Applicability of the Cox-Merz Rule to High-Density Polyethylene Materials with Various Molecular Masses.

The Cox-Merz rule is an empirical relationship that is commonly used in science and industry to determine shear viscosity on the basis of an oscillatory rheometry test. However, it does not apply to all polymer melts. Rheological data are of major importance in the design and dimensioning of polymer-processing equipment. In this work, we investigated whether the Cox-Merz rule is suitable for determining the shear-rate-dependent viscosity of several commercially available high-density polyethylene (HDPE) pipe grades with various molecular masses. We compared the results of parallel-plate oscillatory shear rheometry using the Cox-Merz empirical relation with those of high-pressure capillary and extrusion rheometry. To assess the validity of these techniques, we used the shear viscosities obtained by these methods to numerically simulate the pressure drop of a pipe head and compared the results to experimental measurements. We found that, for the HDPE grades tested, the viscosity data based on capillary pressure flow of the high molecular weight HDPE describes the pressure drop inside the pipe head significantly better than do data based on parallel-plate rheometry applying the Cox-Merz rule. For the lower molecular weight HDPE, both measurement techniques are in good accordance. Hence, we conclude that, while the Cox-Merz relationship is applicable to lower-molecular HDPE grades, it does not apply to certain HDPE grades with high molecular weight.

Melting Behavior of Heterogeneous Polymer Bulk Solids Related to Flood Fed Single Screw Extruders.

Melting models for flood fed single screw extruders, like the Tadmor model, describe the melting of pure thermoplastic polymers. However, the melting behavior of heterogenous polymer systems is of great interest for recycling issues, for example. In this work, the melting of polymer mixtures and that of pure bulk polymers by the drag induced melt removal principle is examined both theoretically and experimentally. The applied model experiments represent the melting of the solid bed at the barrel in single screw extruders. As polymer pellet mixtures, polypropylene-homopolymer mixed with polypropylene-block-copolymer, high density polyethylene, polyamide 6, and polymethylmethacrylate were studied using different mixing ratios. The melting rate and the shear stress in the melt film were evaluated dependent on the mixing ratio. The results show that when processing unfavorable material combinations, both shear stress and melting rate can be far below that of pure materials, which was also confirmed by screw extrusion and screw pull-out experiments. Furthermore, approaches predicting the achievable melting rate and the achievable shear stress of polymer mixtures based on the corresponding values of the pure materials are presented.

Application of Network Analysis to Flow Systems with Alternating Wave Channels: Part A (Pressure Flows).

Wave-dispersion screws have been used industrially in many types of extrusion processes, injection molding, and blow molding. These high-performance screws are constructed by replacing the metering section of a conventional screw with a melt-conveying zone consisting of two or more parallel flow channels that oscillate periodically in-depth over multiple cycles. With the barrier flight between the screw channels being selectively undercut, the molten resin is strategically forced to flow across the secondary flight, assuring repeated cross-channel mixing of the polymer melt. Despite the industrial relevance, very few scientific studies have investigated the flow in wave-dispersion sections in detail. As a result, current screw designs are often based on traditional trial-and-error procedures rather than on the principles of extrusion theory. This study, which was split into two parts, was carried out to systematically address this issue. The research reported here (Part A) was designed to reduce the complexity of the problem, exclusively analyzing the pressure-induced flows of polymer melts in wave sections. Ignoring the influence of the screw rotation on the conveying characteristics of the wave section, the results could be clearly assigned to the governing type of flow mechanism, thereby providing a better understanding of the underlying physics. Experimental studies were performed on a novel extrusion die equipped with a dual wave-channel system with alternating channel depth profiles. A seminumerical modeling approach based on network theory is proposed that locally describes the downchannel and cross-channel flows along the wave channels and accurately predicts the pressure distributions in the flow domain. The solutions of our seminumerical approach were, moreover, compared to the results of three-dimensional non-Newtonian CFD simulations. The results of this study will be extended to real screw designs in Part B, which will include the influence of the screw rotation in the flow analysis.

Extended Regression Models for Predicting the Pumping Capability and Viscous Dissipation of Two-Dimensional Flows in Single-Screw Extrusion.

Generally, numerical methods are required to model the non-Newtonian flow of polymer melts in single-screw extruders. Existing approximation equations for modeling the throughput⁻pressure relationship and viscous dissipation are limited in their scope of application, particularly when it comes to special screw designs. Maximum dimensionless throughputs of Π V < 2.0 , implying minimum dimensionless pressure gradients Π p , z ≥ - 0.5 for low power-law exponents are captured. We present analytical approximation models for predicting the pumping capability and viscous dissipation of metering channels for an extended range of influencing parameters ( Π p , z ≥ - 1.0 , and t / D b ≤ 2.4 ) required to model wave- and energy-transfer screws. We first rewrote the governing equations in dimensionless form, identifying three independent influencing parameters: (i) the dimensionless down-channel pressure gradient Π p , z , (ii) the power-law exponent n , and (iii) the screw-pitch ratio t / D b . We then carried out a parametric design study covering an extended range of the dimensionless influencing parameters. Based on this data set, we developed regression models for predicting the dimensionless throughput-pressure relationship and the viscous dissipation. Finally, the accuracy of all three models was proven using an independent data set for evaluation. We demonstrate that our approach provides excellent approximation. Our models allow fast, stable, and accurate prediction of both throughput-pressure behavior and viscous dissipation.

A Network-Theory-Based Comparative Study of Melt-Conveying Models in Single-Screw Extrusion: A. Isothermal Flow.

In many extrusion processes, the metering section is the rate-controlling part of the screw. In this functional zone, the polymer melt is pressurized and readied to be pumped through the die. We have recently proposed a set of heuristic models for predicting the flow behavior of power-law fluids in two- and three-dimensional metering channels. These novel theories remove the need for numerical simulations and can be implemented easily in practice. Here we present a comparative study designed to validate these new methods against experimental data. Extensive experiments were performed on a well-instrumented laboratory single-screw extruder, using various materials, screw designs, and processing conditions. A network-theory-based simulation routine was written in MATLAB to replicate the flow in the metering zones in silico. The predictions of the three-dimensional heuristic melt-conveying model for the axial pressure profile along the screw are in excellent agreement with the experimental extrusion data. To demonstrate the usefulness of the novel melt-flow theories, we additionally compared the models to a modified Newtonian pumping model known from the literature.