Advances in Screw Processing of Polymeric Materials - In Memory of Professor James Lindsay White

A special issue of Polymers (ISSN 2073-4360). This special issue belongs to the section "Innovation of Polymer Science and Technology".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 140176

Special Issue Editors


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Guest Editor
Polymer Processing Department, Faculty of Production Engineering, Warsaw University of Technology, Narbutta 85, 02-524 Warsaw, Poland
Interests: rheology; polymer processing; morphology development; modeling, simulation and optimization; CAD/CAE software development

E-Mail
Guest Editor
Polymer Processing Department, Faculty of Production Engineering, Warsaw University of Technology, 02-524 Warsaw, Poland
Interests: polymer processing; designing extrusion dies and injection molds; optimization and scale-p; CAD/CAE software development; artificial intelligence

E-Mail
Guest Editor
Polymer Processing Department, Faculty of Production Engineering, Warsaw University of Technology, 02-524 Warsaw, Poland
Interests: polymer processing; rheology and rheometry; modeling of extrusion; FEM process modeling

E-Mail
Guest Editor
Polymer Processing Department, Faculty of Production Engineering, Warsaw University of Technology, 02-524 Warsaw, Poland
Interests: polymer processing; rheology and rheometry; modeling of extrusion; CAD/CAE for injection molding

Special Issue Information

Dear Colleagues,

Screw processing is fundamental for the polymer processing industry and includes many techniques of extrusion and injection molding, e.g., single screw extrusion and twin screw extrusion, both co-rotating and counter-rotating, injection molding and specialized injection techniques, as well as extrusion blow molding and injection blow molding. These techniques provide the conversion from a bulk polymeric material to a product of diverse specifications, and involve the interactions of a process thermomechanical field, material characteristics, and product properties. 

This Special Issue is dedicated to advances in screw processing, and a novelty is crucial for this issue. Invited and submitted articles may be devoted to material compounding and product manufacturing, novel designs and technology concepts, material aspects of processing, modeling and simulation, both for the process and molding tools (e.g., extrusion dies and injection molds), optimization and scale-up, artificial intelligence applications. The issue is not limited with respect to the type of polymeric materials, and studies on screw processing of polymer blends and composites are also expected. The goal of the issue is to present the latest achievements and the trends for future development in screw processing.

Special Statement: This Special Issue of Polymers is dedicated to the memory of Professor James Lindsay White  who passed away ten years ago (1938-2009) (website ). Prof. White was a pioneer in establishing Polymer Processing as an academic discipline. Various polymer institutions, societies and industries around the world have recognized his many fundamental research contributions in rheology and polymer processing. He published over 500 papers in international journals. He has also published eight books on the subjects of rheology, polymeric materials and polymer processing, and received numerous awards for his accomplishments, e.g. Bingham Medal of the Society of Rheology, Charles Goodyear Medal of the American Chemical Society. Yuko-Sho Award of the Japanese Society of Rheology, Heinz Herrmann Award of the Society of Plastics Engineers, and many others. Prof. White served The University of Tennessee as the Professor of Polymer Science and Engineering, and The University of Akron as the Harold A. Morton Professor of Polymer Engineering. Prof. White is the father of the International Polymer Processing Society which was founded to foster scientific understanding and technical innovation in polymer processing by providing a discussion forum for the worldwide community of engineers and scientists in the field. He also founded two scholarly journals: the Journal of Polymer Engineering and the International Polymer Processing Journal. Prof. White was a man of encyclopedic knowledge and great erudition. He had a great knowledge of world history, and he was an expert in the history of polymer engineering. The Guest Editor of this Special Issue had a chance to stay in The University of Akron as a Fulbright Scholar working with prof. White. Later, prof. White visited Warsaw University of Technology several times, showing his special consideration to our youth, students and PhD students. We remember prof. James Lindsay White with our highest respect for everything he did for the polymer processing community.

Prof. Dr. Krzysztof Wilczyński
Dr. Andrzej Nastaj
Dr. Adrian Lewandowski
Dr. Krzysztof J. Wilczyński
Guest Editors

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Keywords

  • extrusion and injection molding
  • design and technology concepts
  • material, process and product interactions
  • modeling, simulation and optimization
  • CAD/CAE for designing extrusion dies and injection molds
  • polymeric materials, polyblends, composites

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Published Papers (31 papers)

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23 pages, 4486 KiB  
Article
Estimation of the Shear Viscosity of Mixed-Polymer Materials for Screw Extrusion-Based Recycling Process Modeling
by Christian Kneidinger, Emil Wagner, Manuel Längauer and Gernot Zitzenbacher
Polymers 2024, 16(10), 1339; https://doi.org/10.3390/polym16101339 - 9 May 2024
Cited by 1 | Viewed by 1202
Abstract
The scope of this work is the development of a method to estimate the temperature and shear rate-dependent viscosity of mixtures composed of two polymers. The viscosity curve of polymer mixtures is crucial for the modeling and optimization of extrusion-based recycling, which is [...] Read more.
The scope of this work is the development of a method to estimate the temperature and shear rate-dependent viscosity of mixtures composed of two polymers. The viscosity curve of polymer mixtures is crucial for the modeling and optimization of extrusion-based recycling, which is the most efficient way to recycle polymeric materials. The modeling and simulation of screw extruders requires detailed knowledge of the properties of the processed material, such as the thermodynamic properties, the density, and the rheological behavior. These properties are widely known for pure materials; however, the incorporation of impurities, like other polymers in recycled materials, alters the properties. In this work, miscible, immiscible, and compatibilized immiscible polymer mixtures are considered. A new method based on shear stress is proposed and compared to the shear rate-based method. Several mixing rules are evaluated for their accuracy in predicting mixture viscosity. The developed methods allow the prediction of the viscosity of a compatibilized immiscible mixture with deviations below 5% and that of miscible polymer mixtures with deviations below 3.5%. Full article
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15 pages, 1889 KiB  
Article
Method Development for the Prediction of Melt Quality in the Extrusion Process
by Dorte Trienens, Volker Schöppner, Peter Krause, Thomas Bäck, Seraphin Tsi-Nda Lontsi and Finn Budde
Polymers 2024, 16(9), 1197; https://doi.org/10.3390/polym16091197 - 25 Apr 2024
Viewed by 999
Abstract
Simulation models are used to design extruders in the polymer processing industry. This eliminates the need for prototypes and reduces development time for extruders and, in particular, extrusion screws. These programs simulate, among other process parameters, the temperature and pressure curves in the [...] Read more.
Simulation models are used to design extruders in the polymer processing industry. This eliminates the need for prototypes and reduces development time for extruders and, in particular, extrusion screws. These programs simulate, among other process parameters, the temperature and pressure curves in the extruder. At present, it is not possible to predict the resulting melt quality from these results. This paper presents a simulation model for predicting the melt quality in the extrusion process. Previous work has shown correlations between material and thermal homogeneity and the screw performance index. As a result, the screw performance index can be used as a target value for the model to be developed. The results of the simulations were used as input variables, and with the help of artificial intelligence—more precisely, machine learning—a linear regression model was built. Finally, the correlation between the process parameters and the melt quality was determined, and the quality of the model was evaluated. Full article
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14 pages, 21443 KiB  
Article
Effect of Fiber Bundle Morphology on Fiber Dispersion for Long Fiber-Reinforced Thermoplastics
by Hector Sebastian Perez, Allen Jonathan Román, Abrahán Bechara Senior and Tim Osswald
Polymers 2023, 15(13), 2790; https://doi.org/10.3390/polym15132790 - 23 Jun 2023
Viewed by 1330
Abstract
Understanding the mechanics of fiber attrition during the extrusion process is highly important in predicting the strength of long fiber-reinforced thermoplastic composites. However, little work has been done to investigate the mechanics of fiber dispersion and its effects on fiber attrition. This study [...] Read more.
Understanding the mechanics of fiber attrition during the extrusion process is highly important in predicting the strength of long fiber-reinforced thermoplastic composites. However, little work has been done to investigate the mechanics of fiber dispersion and its effects on fiber attrition. This study aims at investigating fiber dispersion in simple shear flows for long fiber-reinforced thermoplastic pellets. Depending on the fabrication process, fiber bundles display distinct levels of compaction within the pellets. Studies have shown that morphological differences can lead to differences in dispersion mechanics; therefore, using a Couette rheometer and a sliding plate rheometer, coated and pultruded pellets were subjected to simple shear deformation, and the amount of dispersion was quantified. Additionally, a new image-based analysis method is presented in this study to measure fiber dispersion for a multi-pellet-filled system. Results from the single-pellet dispersion study showed a small amount of correlation between the dimensionless morphological parameter and the dispersion measurement. Pultruded and coated pellets were both found to have similar dispersion rates in a multi-pellet system. However, pultruded pellets were found to have a higher dispersion value at all levels when compared with coated pellets in both dispersion studies. Full article
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23 pages, 5244 KiB  
Article
Evolutionary Multi-Objective Optimization of Extrusion Barrier Screws: Data Mining and Decision Making
by António Gaspar-Cunha, Paulo Costa, Alexandre Delbem, Francisco Monaco, Maria José Ferreira and José Covas
Polymers 2023, 15(9), 2212; https://doi.org/10.3390/polym15092212 - 7 May 2023
Cited by 2 | Viewed by 2339
Abstract
Polymer single-screw extrusion is a major industrial processing technique used to obtain plastic products. To assure high outputs, tight dimensional tolerances, and excellent product performance, extruder screws may show different design characteristics. Barrier screws, which contain a second flight in the compression zone, [...] Read more.
Polymer single-screw extrusion is a major industrial processing technique used to obtain plastic products. To assure high outputs, tight dimensional tolerances, and excellent product performance, extruder screws may show different design characteristics. Barrier screws, which contain a second flight in the compression zone, have become quite popular as they promote and stabilize polymer melting. Therefore, it is important to design efficient extruder screws and decide whether a conventional screw will perform the job efficiently, or a barrier screw should be considered instead. This work uses multi-objective evolutionary algorithms to design conventional and barrier screws (Maillefer screws will be studied) with optimized geometry. The processing of two polymers, low-density polyethylene and polypropylene, is analyzed. A methodology based on the use of artificial intelligence (AI) techniques, namely, data mining, decision making, and evolutionary algorithms, is presented and utilized to obtain results with practical significance, based on relevant performance measures (objectives) used in the optimization. For the various case studies selected, Maillefer screws were generally advantageous for processing LDPE, while for PP, the use of both types of screws would be feasible. Full article
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18 pages, 4437 KiB  
Article
Optimization for the Contrary-Rotating Double-Screw Extrusion of Plastics
by Andrzej Nastaj and Krzysztof Wilczyński
Polymers 2023, 15(6), 1489; https://doi.org/10.3390/polym15061489 - 16 Mar 2023
Cited by 4 | Viewed by 2131
Abstract
A novel computer optimization system for the contrary-rotating double-screw extrusion of plastics was developed in this study. The optimization was based on the process simulation performed with the use of the global contrary-rotating double-screw extrusion software TSEM. The process was optimized using the [...] Read more.
A novel computer optimization system for the contrary-rotating double-screw extrusion of plastics was developed in this study. The optimization was based on the process simulation performed with the use of the global contrary-rotating double-screw extrusion software TSEM. The process was optimized using the GASEOTWIN software developed for this purpose using genetic algorithms. Several examples of optimization of the contrary-rotating double screw extrusion process parameters, i.e., the extrusion throughput, and minimize the plastic melt temperature and the plastic melting length. Full article
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12 pages, 3864 KiB  
Article
Improving Layer Adhesion of Co-Extruded Polymer Sheets by Inducing Interfacial Flow Instabilities
by Raffael Rathner, Claudia Leimhofer, Wolfgang Roland, Alexander Hammer, Bernhard Löw-Baselli, Georg Steinbichler and Sabine Hild
Polymers 2022, 14(3), 587; https://doi.org/10.3390/polym14030587 - 31 Jan 2022
Cited by 3 | Viewed by 4117
Abstract
Co-extrusion is commonly used to produce polymer multilayer products with different materials tailoring the property profiles. Adhesion between the individual layers is crucial to the overall performance of the final structure. Layer adhesion is determined by the compatibility of the polymers at the [...] Read more.
Co-extrusion is commonly used to produce polymer multilayer products with different materials tailoring the property profiles. Adhesion between the individual layers is crucial to the overall performance of the final structure. Layer adhesion is determined by the compatibility of the polymers at the interface and their interaction forces, causing for example the formation of adhesive or chemical bonds or an interdiffusion layer. Additionally, the processing conditions, such as temperature, residence time, cooling rate, and interfacial shear stress, have a major influence on the interactions and hence resulting layer adhesion. Influences of temperature and residence time are already quite well studied, but influence of shear load on the formation of an adhesion layer is less explored and controversially discussed in existing literature. In this work, we investigated the influence of different processing conditions causing various shear loads on layer adhesion for a two-layer co-extruded polymer sheet using a polypropylene and polypropylene talc compound system. Therefore, we varied the flow rates and the flow geometry of the die. Under specific conditions interfacial flow instabilities are triggered that form micro layers in the transition regime between the two layers causing a major increase in layer adhesion. This structure was analyzed using confocal Raman microscopy. Making use of these interfacial flow instabilities in a controlled way enables completely new opportunities and potentials for multi-layer products. Full article
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20 pages, 2592 KiB  
Article
Computational Scale-Up for Flood Fed/Starve Fed Single Screw Extrusion of Polymers
by Andrzej Nastaj and Krzysztof Wilczyński
Polymers 2022, 14(2), 240; https://doi.org/10.3390/polym14020240 - 7 Jan 2022
Cited by 2 | Viewed by 2637
Abstract
A novel scaling-up computer system for single screw extrusion of polymers has been developed. This system makes it possible to scale-up extrusion process with both starve feeding and flood feeding. Each of the scale-up criteria can be an objective function to be minimized, [...] Read more.
A novel scaling-up computer system for single screw extrusion of polymers has been developed. This system makes it possible to scale-up extrusion process with both starve feeding and flood feeding. Each of the scale-up criteria can be an objective function to be minimized, represented by single values or functional dependencies over the screw length. The basis of scaling-up is process simulation made with the use of the GSEM program (Global Screw Extrusion Model). Scaling-up is performed using the GASES program (Genetic Algorithms Screw Extrusion Scaling) based on Genetic Algorithms. Scaling-up the extrusion process has been performed to increase extrusion output according to the scaling-up criteria defined by the single parameters of unit energy consumption, polymer plasticating rate and polymer temperature, as well as by the process parameters profiles of the temperature and plasticating. The global objective function reached the lowest value for the selected process parameters, and extrusion throughput was significantly increased. Full article
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17 pages, 50330 KiB  
Article
Design and Ductile Behavior of Torsion Configurations in Material Extrusion to Enhance Plasticizing and Melting
by Ranran Jian, Weimin Yang, Mohini Sain, Chuanwei Zhang and Lupeng Wu
Polymers 2021, 13(18), 3181; https://doi.org/10.3390/polym13183181 - 19 Sep 2021
Cited by 1 | Viewed by 2508
Abstract
In the present work, the ductile formation mechanism of a newly proposed torsion configuration has been investigated. One of the unique attributes of this paper is the first-time disclosure of the design and fabrication of a novel prototype screw with torsional flow character [...] Read more.
In the present work, the ductile formation mechanism of a newly proposed torsion configuration has been investigated. One of the unique attributes of this paper is the first-time disclosure of the design and fabrication of a novel prototype screw with torsional flow character validating the orthogonal test model experimentally. The torsional spiral flow patterns that occurred in the torsion channel cause a ductile deformation of polymer in the form of a spiral, which in turn enhances the radial convection, achieving an effective mass transfer of material from the top region to the bottom region and vice versa. Furthermore, the characteristic parameters of torsion configuration have a significant influence on the plasticizing and melting capability of polymer. By range analysis and weight matrix analysis, the best factor and level combination was obtained. Results indicated that the aspect ratio of the torsion channel is almost equal to 1, and the plasticizing and melting capability of polymer is optimal. This novel design innovation offers a paradigm shift in the energy-efficient plasticization of polymer compounds. Full article
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20 pages, 36941 KiB  
Article
Enhanced Processing of Regrind as Recycling Material in Single-Screw Extruders
by Philipp Thieleke and Christian Bonten
Polymers 2021, 13(10), 1540; https://doi.org/10.3390/polym13101540 - 11 May 2021
Cited by 6 | Viewed by 4284
Abstract
Regrind processing poses challenges for single-screw extruders due to the irregularly shaped particles. For grooved feed zones, the output is lessened by the reduction of bulk density in comparison to virgin material. Simultaneously, the melt temperature increases, reducing the extruder’s process window. Through [...] Read more.
Regrind processing poses challenges for single-screw extruders due to the irregularly shaped particles. For grooved feed zones, the output is lessened by the reduction of bulk density in comparison to virgin material. Simultaneously, the melt temperature increases, reducing the extruder’s process window. Through experimental investigations on a test stand, a novel feed zone geometry (nominal diameter 35 mm) is developed. It aligns the regrind’s specific throughput with that of virgin material. The regrind processing window is essentially increased. As the solids conveying in the novel feed zone cannot be simulated with existing methods, numerical simulations using the discrete element method are performed. Since plastic deformation occurs in the novel feed zone geometry, a new hysteresis contact model is developed. In addition to spheres, the regrind and virgin particles are modeled as superquadrics to better approximate the irregular shape. The new contact model’s simulation results show excellent agreement with experimental compression tests. The throughput of the extruder simulations is considerably underestimated when using spheres to represent the real particles than when using irregularly shaped superquadrics. Corresponding advantages can be seen especially for virgin material. Full article
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17 pages, 4728 KiB  
Article
A Computer Model of Starve Fed Single Screw Extrusion of Wood Plastic Composites
by Krzysztof J. Wilczyński and Kamila Buziak
Polymers 2021, 13(8), 1252; https://doi.org/10.3390/polym13081252 - 12 Apr 2021
Cited by 11 | Viewed by 3258
Abstract
In this study, we present a computer model of starve fed single screw extrusion of wood plastic composites (WPC). Experimental studies have been performed on the extrusion of the polypropylene (PP) based composites with various wood fiber contents (WF). The melting mechanisms of [...] Read more.
In this study, we present a computer model of starve fed single screw extrusion of wood plastic composites (WPC). Experimental studies have been performed on the extrusion of the polypropylene (PP) based composites with various wood fiber contents (WF). The melting mechanisms of the composites in the extruder have been observed, and melting models have been proposed for partially and fully filled sections of the screw. It was observed that in the partially filled section the material is melted by conduction, as in the case of extrusion of neat polymers. On the other hand, in the fully filled section, the Tadmor melting mechanism appears, which is different compared to the melting mechanism of neat polymers at starve fed extrusion, where dispersed melting is observed. Using the melting models, the global computer model of the process has been developed which makes it possible to predict the process flow, i.e., the polymer melt temperature and pressure, the polymer melting rate, and the degree of screw filling. To build the model, the specific forward/backward procedure was developed, which consists in determining “forward” the melting profile, and “backward” the pressure and screw filling profile. The temperature profile in the melting section is computed “forward”, while “backward” in the metering section. This procedure makes it possible to solve the crucial problem of modeling of the starve fed extrusion process, which is to find the location of the point where the screw is fully filled, and the pressure is developed. The model has been tested by pressure measurements in the extruder. Full article
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11 pages, 3515 KiB  
Article
Effect of the Process Parameters on the Adhesive Strength of Dissimilar Polymers Obtained by Multicomponent Injection Molding
by Luciano Pisanu, Leonardo Costa Santiago, Josiane Dantas Viana Barbosa, Valter Estevão Beal and Marcio Luis Ferreira Nascimento
Polymers 2021, 13(7), 1039; https://doi.org/10.3390/polym13071039 - 26 Mar 2021
Cited by 11 | Viewed by 2938
Abstract
The growing demand in the consumer market for products with sustainable technologies has motivated new applications using overmolded natural fiber composites. Therefore, studies have been conducted mainly to understand the adhesive properties of overmolded parts. In the present study, a polypropylene (PP) composite [...] Read more.
The growing demand in the consumer market for products with sustainable technologies has motivated new applications using overmolded natural fiber composites. Therefore, studies have been conducted mainly to understand the adhesive properties of overmolded parts. In the present study, a polypropylene (PP) composite with 30% coconut fibers without additives was developed with the aid of a corotating twin screw extruder. Subsequently, a multicomponent injection mold was developed based on the geometry of the ISO 527 type I specimen, in which samples overmolded with PP and PP–coconut-fiber composite, with the overlap in the central area, were obtained to evaluate the adhesive strength of dissimilar materials. The objective of this study was to evaluate the bond between PP and PP–coconut-fiber composite under different processing conditions using an adhesive strength testing device to perform a pure shear analysis. The experimental conditions followed a statistical design considering four factors in two levels and a significance level of 5%. The results indicated that adhesive strength increased significantly as the overlap area increased. It was observed that temperature and injection flow rate were the factors that most contributed to strengthening the bonds of dissimilar materials. Full article
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12 pages, 4181 KiB  
Article
The Role of Calender Gap in Barrel and Screw Wear in Counterrotating Twin Screw Extruders
by Abdullah Demirci, Ismail Teke, Nickolas D. Polychronopoulos and John Vlachopoulos
Polymers 2021, 13(7), 990; https://doi.org/10.3390/polym13070990 - 24 Mar 2021
Cited by 2 | Viewed by 3617
Abstract
It has been known in the industrial sector that in closely intermeshing counterrotating twin screw extruders, large separating forces develop in the calender gap, which push the screws towards the barrel wall. The result is significant wear in the region defined by 30°- [...] Read more.
It has been known in the industrial sector that in closely intermeshing counterrotating twin screw extruders, large separating forces develop in the calender gap, which push the screws towards the barrel wall. The result is significant wear in the region defined by 30°- and 60°-degree angles from the vertical. In the present investigation, pressures were measured around the barrel in extrusion of two rigid PVC resins in a laboratory extruder of 55 mm diameter and the forces on the screw core were determined. Numerical flow simulations were also carried out using the power-law viscosity parameters of the resins. From the experimental results, it was determined that the resultant forces are in the 30 degree angle direction, and from the computer simulations, the angle is between 18° and 25°. It is argued that the resultant force angle will be somewhat larger in large diameter extruders, due to the additional contribution of gravity. Full article
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17 pages, 3963 KiB  
Article
Properties of Starve-Fed Extrusion on a Material Containing a VHMWPE Fraction
by Raffael Rathner, Davide Tranchida, Wolfgang Roland, Franz Ruemer, Klaus Buchmann, Philipp Amsüss and Georg Steinbichler
Polymers 2021, 13(6), 944; https://doi.org/10.3390/polym13060944 - 19 Mar 2021
Cited by 3 | Viewed by 2374
Abstract
Single-screw extruders are usually operated with the screw fully filled (flood-fed mode) and not partially filled (starve-fed mode). These modes result in completely different processing characteristics, and although starve-fed mode has been shown to have significant advantages, such as improved mixing and melting [...] Read more.
Single-screw extruders are usually operated with the screw fully filled (flood-fed mode) and not partially filled (starve-fed mode). These modes result in completely different processing characteristics, and although starve-fed mode has been shown to have significant advantages, such as improved mixing and melting performance, it is rarely used, and experimental studies are scarce. Here, we present extensive experimental research into starve-fed extrusion at feeding rates as low as 25%. We compared various operating parameters (e.g., residence time, pressure build-up, and melting performance) at various feeding rates and screw speeds. The results show a first insight into the performance of starve-fed extruders compared to flood-fed extruders. We explored starve-fed extrusion of a polyethylene material which contains a Very High Molecular Weight Polyethylene fraction (VHMWPE). VHMWPE offers several advantages in terms of mechanical properties, but its high viscosity renders common continuous melt processes, such as compression molding, ram extrusion and sintering, ineffective. This work shows that operating single-screw extruders in extreme starve-fed mode significantly increases residence time, melt temperature, and improves melting and that-in combination—this results in significant elongation of VHMWPE particles. Full article
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12 pages, 2518 KiB  
Article
The Viscoelastic Swirled Flow in the Confusor
by Aidar Kadyirov, Rinat Zaripov, Julia Karaeva and Ekaterina Vachagina
Polymers 2021, 13(4), 630; https://doi.org/10.3390/polym13040630 - 20 Feb 2021
Cited by 3 | Viewed by 2244
Abstract
A two-dimensional mathematical model for a steady viscoelastic laminar flow in a confusor was developed under the condition of swirled flow imposed at the inlet. Low density polyethylene was considered as a working fluid. Its behavior was described by a two-mode Giesekus model. [...] Read more.
A two-dimensional mathematical model for a steady viscoelastic laminar flow in a confusor was developed under the condition of swirled flow imposed at the inlet. Low density polyethylene was considered as a working fluid. Its behavior was described by a two-mode Giesekus model. The proposed mathematical model was tested by comparing it with some special cases presented in the literature. Additionally, we propose a system of equations to find the nonlinear parameters of the multimode Giesekus model (mobility factor) based on experimental measurement. The obtained numerical results showed that in a confusor with the contraction rate of 4:1, an increase in the swirl intensity at Wi < 5.1 affects only the circumferential velocity, while the axial and radial velocities remain constant. The distribution pattern of the first normal stress difference in the confusor is qualitatively similar to the one in a channel with abrupt contraction, i.e., as the viscoelastic fluid flows in the confusor, the value of N1 increases and reaches a maximum at the end of the confusor. Dimensionless damping coefficients of swirl are used to estimate the swirl intensity. The results show that the swirl intensity decreases exponentially. Full article
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16 pages, 4977 KiB  
Article
Rheological Basics for Modeling of Extrusion Process of Wood Polymer Composites
by Krzysztof Wilczyński, Kamila Buziak, Adrian Lewandowski, Andrzej Nastaj and Krzysztof J. Wilczyński
Polymers 2021, 13(4), 622; https://doi.org/10.3390/polym13040622 - 19 Feb 2021
Cited by 21 | Viewed by 3901
Abstract
Wood polymer composites are materials with pseudoplastic and viscoelastic properties. They have yield stress and exhibit slip during flow. Studies on extrusion and rheology, as well as on process modeling of these highly filled materials are limited. Extensive rheological and extrusion modeling studies [...] Read more.
Wood polymer composites are materials with pseudoplastic and viscoelastic properties. They have yield stress and exhibit slip during flow. Studies on extrusion and rheology, as well as on process modeling of these highly filled materials are limited. Extensive rheological and extrusion modeling studies on the wood polymer composite based on the polypropylene matrix were performed. Viscous and slip flow properties were determined (with Rabinowitsch, Bagley, and Mooney corrections) at broad (extrusion) range of shear rate and temperature, using a high-pressure capillary rheometer. Rheological models of Klein and power-law were used for flow modeling, and Navier model was applied for slip modeling. A novel global computer model of WPC extrusion with slip effects has been developed, and process simulations were performed to compute the extrusion parameters (throughput, power consumption, pressure, temperature, etc.), and to study the effect of the material rheological characteristics on the process flow. Simulations were validated experimentally, and were discussed with respect to both rheological and process modeling aspects. It was concluded that the location of the operating point of extrusion process, which defines the thermo-mechanical process conditions, is fundamentally dependent on the rheological materials characteristics, including slip effects. Full article
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11 pages, 1829 KiB  
Article
Rheological Properties Related to Extrusion of Polyolefins
by Evan Mitsoulis and Savvas G. Hatzikiriakos
Polymers 2021, 13(4), 489; https://doi.org/10.3390/polym13040489 - 4 Feb 2021
Cited by 11 | Viewed by 4556
Abstract
Rheological properties related to the extrusion of polyolefins are the shear viscosity, the elongational viscosity, the slip velocity and their temperature- and pressure-dependencies. These properties are measured in the rheology lab mainly via a parallel-plate rheometer and a capillary rheometer. Then appropriate rheological [...] Read more.
Rheological properties related to the extrusion of polyolefins are the shear viscosity, the elongational viscosity, the slip velocity and their temperature- and pressure-dependencies. These properties are measured in the rheology lab mainly via a parallel-plate rheometer and a capillary rheometer. Then appropriate rheological models have to be used to account for all these properties. Such models are either viscous (e.g., the Cross model) or viscoelastic (e.g., the K-BKZ model). The latter gives the best fitting of the experimental data and offers excellent results in numerical simulations, especially in extrusion flows. Wall slip effects are also found and measured by rheometric flows. Modeling of extrusion flows should make use of appropriate slip models that take into effect the various slip parameters, including the effects of shear stress, molecular characteristics, temperature and pressure on the slip velocity. In this paper the importance of these properties in extrusion are discussed. Full article
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12 pages, 2173 KiB  
Communication
Average Shear Rates in the Screw Elements of a Corotating Twin-Screw Extruder
by Bruno Vergnes
Polymers 2021, 13(2), 304; https://doi.org/10.3390/polym13020304 - 19 Jan 2021
Cited by 17 | Viewed by 3539
Abstract
The rapid estimation of the average shear rate encountered by the material as it flows along the screw elements of a corotating twin-screw extruder is a key point for many applications. In this paper, two methods of evaluation are presented that allow the [...] Read more.
The rapid estimation of the average shear rate encountered by the material as it flows along the screw elements of a corotating twin-screw extruder is a key point for many applications. In this paper, two methods of evaluation are presented that allow the calculation of the average shear rate as a function of the screw geometry, feed rate, and screw speed. A comparison is made between the approximate and exact methods. It is shown that it is crucial to take into account the shear component due to the pressure flow, especially in the left-handed screw elements. Full article
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19 pages, 14073 KiB  
Article
Manufacturing Polypropylene (PP)/Waste EPDM Thermoplastic Elastomers Using Ultrasonically Aided Twin-Screw Extrusion
by Hui Dong, Jing Zhong and Avraam I. Isayev
Polymers 2021, 13(2), 259; https://doi.org/10.3390/polym13020259 - 14 Jan 2021
Cited by 8 | Viewed by 4039
Abstract
The compounding of waste EPDM from postindustrial scrap with polypropylene (PP) is a possible way to manufacture thermoplastic elastomers to solve a significant environmental problem. Accordingly, the present study considers the one-step (OS), two-step (TS), and dynamic revulcanization (DR) compounding methods for the [...] Read more.
The compounding of waste EPDM from postindustrial scrap with polypropylene (PP) is a possible way to manufacture thermoplastic elastomers to solve a significant environmental problem. Accordingly, the present study considers the one-step (OS), two-step (TS), and dynamic revulcanization (DR) compounding methods for the manufacturing of PP/EPDM blends at different ratios of components with the aid of an ultrasonic twin-screw extruder (TSE) at various ultrasonic amplitudes. In the OS method, PP and waste EPDM particles were directly compounded using TSE with and without ultrasonic treatment. In the TS and DR methods, the waste EPDM particles were fed into the TSE and devulcanized without and with ultrasonic treatment. Then, in the TS method the devulcanized EPDM was compounded with PP using TSE without the imposition of ultrasound. In the DR method, the devulcanized EPDM after compounding with curatives was mixed with PP and dynamically revulcanized without the imposition of ultrasound in TSE. The die pressure during compounding was recorded and correlated with the rheological properties of compounds. The mechanical properties of the PP/EPDM blends obtained in the OS and TS methods did not show any improvement with ultrasonic treatment. In the DR method, all the PP/EPDM blends showed a significant increase in the tensile strength and elongation with ultrasonic amplitude and a slight decrease in the Young’s modulus. In particular, a tensile strength of 30 MPa and an elongation at break of 400% were achieved at an ultrasonic amplitude of 13 μm for the PP/EPDM blend at a ratio of 75/25. The complex viscosity, storage, and loss moduli of dynamically revulcanized PP/EPDM blends increased with the ultrasonic amplitude while the loss tangent decreased. At the same time, the results for the blends obtained by the OS and TS methods showed an opposite trend in the dynamic property behavior with the ultrasonic amplitude. Optical micrographs indicated that the blends obtained by the DR method at an ultrasonic treatment at 13 μm showed the lowest sizes of dispersed revulcanized EPDM particles in the PP matrix, leading to the excellent performance of these thermoplastic elastomers. Full article
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18 pages, 2165 KiB  
Article
A Novel Modeling Approach for Plastics Melting within a CFD-DEM Framework
by Alptekin Celik, Christian Bonten, Riccardo Togni, Christoph Kloss and Christoph Goniva
Polymers 2021, 13(2), 227; https://doi.org/10.3390/polym13020227 - 11 Jan 2021
Cited by 9 | Viewed by 4230
Abstract
Existing three-dimensional modeling approaches to single-screw extrusion can be classified according to the process sections. The discrete element method (DEM) allows describing solids transport in the feed section. The melt flow in the melt section can be calculated by means of computational fluid [...] Read more.
Existing three-dimensional modeling approaches to single-screw extrusion can be classified according to the process sections. The discrete element method (DEM) allows describing solids transport in the feed section. The melt flow in the melt section can be calculated by means of computational fluid dynamics (CFD). However, the current state of the art only allows a separate consideration of the respective sections. A joint examination of the process sections still remains challenging. In this study, a novel modeling approach is presented, allowing a joint consideration of solids and melt transport and, beyond that, the formation of melt. For this purpose, the phase transition from the solid to liquid states is modeled for the first time within the framework CFDEMCoupling®, combining CFD and DEM by a novel melting model implemented in this study. In addition, a melting apparatus for the validation of the novel melting model is set up and put into operation. CFD-DEM simulations are carried out in order to calculate the melting rate and are compared to experimental results. A good agreement between the simulation and experimental results is found. From the findings, it can be assumed that the CFD-DEM simulation of single-screw extruder with a joint consideration of the feed and melt section is feasible. Full article
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27 pages, 13256 KiB  
Article
Melting Behavior of Heterogeneous Polymer Bulk Solids Related to Flood Fed Single Screw Extruders
by Christian Kneidinger, Erik Schroecker, Gernot Zitzenbacher and Jürgen Miethlinger
Polymers 2020, 12(12), 2893; https://doi.org/10.3390/polym12122893 - 2 Dec 2020
Cited by 4 | Viewed by 3057
Abstract
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 [...] Read more.
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. Full article
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26 pages, 10162 KiB  
Article
A Method for the Validation of Simulated Mixing Characteristics of Two Dynamic Mixers in Single-Screw Extrusion
by Christian Hopmann, Malte Schön, Maximilian Mathias Reul and Martin Facklam
Polymers 2020, 12(10), 2234; https://doi.org/10.3390/polym12102234 - 28 Sep 2020
Cited by 9 | Viewed by 4751
Abstract
The field of simulation and optimisation of dynamic mixing elements (‘mixers’) is lacking good methods for spatially resolved validation and flow visualisation. For this reason, the authors present an experimental setup that gives better insight into the thermal, distributive and dispersive mixing process [...] Read more.
The field of simulation and optimisation of dynamic mixing elements (‘mixers’) is lacking good methods for spatially resolved validation and flow visualisation. For this reason, the authors present an experimental setup that gives better insight into the thermal, distributive and dispersive mixing process by measuring melt temperatures upstream of the mixer and injecting a secondary, visually distinguishable stream of melt upstream. Running extrusion trials for a polyethylene on both a rhomboidal and a Maddock mixer, temperatures, gray scale distribution of images of extrudates and size of dispersed domains in incompatible polystyrene were measured. It was found that temperatures upstream and downstream of the mixer can be quantified. This was used to validate a simulation of thermal mixing. In distributive mixing, good agreement with simulation and an excellent spatial resolution were observed, thereby identifying an area of the rhomboidal mixer in need of geometric improvement. For dispersive mixing, a trend coherent with extrusion theory was found. Full article
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30 pages, 7646 KiB  
Article
Development of an Analytical Model to Describe the Disperse Melting in Wave-Dispersion Screws
by Marius Dörner, Christian Marschik, Volker Schöppner and Georg Steinbichler
Polymers 2020, 12(4), 946; https://doi.org/10.3390/polym12040946 - 18 Apr 2020
Cited by 4 | Viewed by 3436
Abstract
The progressive development of new screw concepts in single screw extrusion also makes it necessary to develop new models for the correct process description. When looking at wave-dispersion screws, the disperse melting behavior should be mentioned in particular, which has so far been [...] Read more.
The progressive development of new screw concepts in single screw extrusion also makes it necessary to develop new models for the correct process description. When looking at wave-dispersion screws, the disperse melting behavior should be mentioned in particular, which has so far been less researched and modeled than the conventional melting behavior, as it occurs in standard screws. Therefore, an analytical model is presented in this paper, which considers the disperse melting under consideration of the melt and solid temperature. The basic assumption is Fourier heat conduction from the melt surrounding the particles into the particles. Furthermore, the melt temperature development by dissipation and the cooling effects were modeled analytically. Additionally, the solid bed temperature was modeled by a 2D-FDM method. By dividing the screw into several calculation sections with constant boundary conditions, it was subsequently possible to calculate the melting process over the screw length. The model developed shows comprehensible results in verification and successfully reproduces the solids content over the screw length with a mean deviation of absolute 11% in validation tests using cooling/pulling-out experiments. Full article
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20 pages, 7100 KiB  
Article
A Strategy for Problem Solving of Filling Imbalance in Geometrically Balanced Injection Molds
by Krzysztof Wilczyński and Przemysław Narowski
Polymers 2020, 12(4), 805; https://doi.org/10.3390/polym12040805 - 3 Apr 2020
Cited by 16 | Viewed by 3913
Abstract
Simulation and experimental studies were performed on filling imbalance in geometrically balanced injection molds. An original strategy for problem solving was developed to optimize the imbalance phenomenon. The phenomenon was studied both by simulation and experimentation using several different runner systems at various [...] Read more.
Simulation and experimental studies were performed on filling imbalance in geometrically balanced injection molds. An original strategy for problem solving was developed to optimize the imbalance phenomenon. The phenomenon was studied both by simulation and experimentation using several different runner systems at various thermo-rheological material parameters and process operating conditions. Three optimization procedures were applied, Response Surface Methodology (RSM), Taguchi method, and Artificial Neural Networks (ANN). Operating process parameters: the injection rate, melt temperature, and mold temperature, as well as the geometry of the runner system were optimized. The imbalance of mold filling as well as the process parameters: the injection pressure, injection time, and molding temperature were optimization criteria. It was concluded that all the optimization procedures improved filling imbalance. However, the Artificial Neural Networks approach seems to be the most efficient optimization procedure, and the Brain Construction Algorithm (BSM) is proposed for problem solving of the imbalance phenomenon. Full article
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14 pages, 8117 KiB  
Article
Enhancing Mixing and Thermal Management of Recycled Carbon Composite Systems by Torsion-Induced Phase-to-Phase Thermal and Molecular Mobility
by Ranran Jian, Zhonghe Shi, Haichao Liu, Weimin Yang and Mohini Sain
Polymers 2020, 12(4), 771; https://doi.org/10.3390/polym12040771 - 1 Apr 2020
Cited by 4 | Viewed by 3024
Abstract
A novel torsion screw has been proposed to resolve the inadequate control of mass transfer and the thermal management of two component polymer blends and their carbon fiber composites. The novel torsional screw distinctly introduced radial flow in the torsion screw channel, which [...] Read more.
A novel torsion screw has been proposed to resolve the inadequate control of mass transfer and the thermal management of two component polymer blends and their carbon fiber composites. The novel torsional screw distinctly introduced radial flow in the torsion screw channel, which is a significant improvement over the flow pattern developed by the conventional screw. The heat transfer and mixing behavior of melt mixtures are enhanced by adapting screws with torsion elements compared with the traditional screw elements. Heat transfer efficacy in the polypropylene–polystyrene bi-phasic extrusion process improved with the increase in torsion element numbers. An increased number of newly designed torsional elements also improved the dispersion of minor phase in bi-phase polypropylene–polystyrene composition and their carbon fiber composites. The unique flow pattern induced by the torsion elements shows a synergistic effect on the melt-phase mass flow and the thermal flow field facilitating phase-to-phase thermal and molecular mobility and enhanced fiber orientation, crystallinity and mechanical properties of composite made from recycled carbon fiber/polypropylene. Microtomographs of recycled carbon fiber demonstrated the extraordinary ability of a torsion screw element to orient carbon fiber in both axial and radial directions. Full article
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17 pages, 4302 KiB  
Article
Optimization for Starve Fed/Flood Fed Single Screw Extrusion of Polymeric Materials
by Andrzej Nastaj and Krzysztof Wilczyński
Polymers 2020, 12(1), 149; https://doi.org/10.3390/polym12010149 - 7 Jan 2020
Cited by 18 | Viewed by 7001
Abstract
A novel computer optimization system for flood fed/starve fed single screw extrusion of polymeric materials has been developed. This coupled system allows us to optimize single screw extrusion both flood fed and starve fed. Optimization is based on process simulation which is performed [...] Read more.
A novel computer optimization system for flood fed/starve fed single screw extrusion of polymeric materials has been developed. This coupled system allows us to optimize single screw extrusion both flood fed and starve fed. Optimization is based on process simulation which is performed using global extrusion model GSEM (Global Screw Extrusion Model). The process is optimized with the use of GASEO (Genetic Algorithms Screw Extrusion Optimization) procedures which were developed using Genetic Algorithms. An example of optimization of extrusion process parameters has been presented to maximize extrusion output and minimize specific energy consumption. Optimization has been performed in a unique and original way in a coupled manner when both modes of feeding were allowed. The studies have shown that the optimal process is extrusion with starving. In this case, the global objective function reached the highest value, and extrusion throughput was relatively high and specific energy consumption was minimal. Full article
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Review

Jump to: Research, Other

19 pages, 7926 KiB  
Review
Modeling and Experimental Studies on Polymer Melting and Flow in Injection Molding
by Krzysztof Wilczyński, Krzysztof J. Wilczyński and Kamila Buziak
Polymers 2022, 14(10), 2106; https://doi.org/10.3390/polym14102106 - 21 May 2022
Cited by 17 | Viewed by 5092
Abstract
Injection molding, in addition to extrusion, is the most important technology in the polymer processing industry. When modeling injection molding, the global approach is necessary to take into account the solid polymer transport, polymer melting and the polymer melt flow. The model of [...] Read more.
Injection molding, in addition to extrusion, is the most important technology in the polymer processing industry. When modeling injection molding, the global approach is necessary to take into account the solid polymer transport, polymer melting and the polymer melt flow. The model of polymer melting is fundamental for the development of such a global injection molding model. In the paper, the state-of-the-art of modeling and experimentation of the flow and melting in injection molding machines has been presented and discussed. It has been concluded that the existing mathematical models have no strong experimental basis. Therefore, experimentation of the polymer flow and melting in the injection molding machine has been performed, and the effect of processing conditions: the screw speed, the plasticating stroke and the back pressure on the process course has been investigated. Starving in the beginning sections of the screw has been observed, which was not presented in the literature so far. The novel concepts of injection molding modeling have been discussed. Full article
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29 pages, 10244 KiB  
Review
Investigation of the Polymer Coextrusion Process: A Review
by Jean-François Agassant and Yves Demay
Polymers 2022, 14(7), 1309; https://doi.org/10.3390/polym14071309 - 24 Mar 2022
Cited by 9 | Viewed by 4343
Abstract
A review of the different coextrusion processes and the related processing problems is presented. A one-dimensional bilayer coextrusion Poiseuille flow model is first developed with Newtonian and shear-thinning rheological behaviors. A transitory computation at the convergence between the two independent polymer layers shows [...] Read more.
A review of the different coextrusion processes and the related processing problems is presented. A one-dimensional bilayer coextrusion Poiseuille flow model is first developed with Newtonian and shear-thinning rheological behaviors. A transitory computation at the convergence between the two independent polymer layers shows that stationary interface position and velocity profile are established after a short distance of the order of the die gap which justifies the validity of the 1D stationary model. This model is then applied to multilayer temperature dependent coextrusion flows which correspond to realistic industrial coextrusion conditions. Marked interface instabilities may be observed depending on the rheology of the coextruded polymers and of their flow rate ratios. Experiments point clearly out that these instabilities may be amplified along the die land. Convective stability analysis as well as direct numerical computation discriminate flow situations which amplify or damp down instabilities. These 1D models are unable to account for the complex feedblock coat-hanger die geometries. A thin layer coextrusion model is then developed, based on the Hele-Shaw lubrication approximations already used for single layer extrusion problems. It allows to predict the location of the interfaces between the different layers in the whole die, and especially at die exit. This represents a major issue in feedblock die coextrusion. These thin layer approaches are unable to address the encapsulation of one polymer by the other in these complex die geometries with important gap thicknesses. Experiments conducted in dies of square section allow identifying the dynamics of encapsulation. 3D models are required to account for this phenomenon but the management of the sticking contact at the die wall poses difficult numerical problems. Full article
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28 pages, 7525 KiB  
Review
Modeling of Twin Screw Extrusion of Polymeric Materials
by Adrian Lewandowski and Krzysztof Wilczyński
Polymers 2022, 14(2), 274; https://doi.org/10.3390/polym14020274 - 10 Jan 2022
Cited by 37 | Viewed by 15803
Abstract
An issue of modeling of twin-screw extrusion of polymeric materials is reviewed. The paper is written in honor of Prof. James L. White who was a pioneer in studying this issue. A global approach to process modeling is presented which includes solid polymer [...] Read more.
An issue of modeling of twin-screw extrusion of polymeric materials is reviewed. The paper is written in honor of Prof. James L. White who was a pioneer in studying this issue. A global approach to process modeling is presented which includes solid polymer transport, polymer plasticating, and the flow of molten polymer. The methodology of CFD modeling of twin-screw extrusion is presented as well as the examples of this modeling which show the details of the process. Optimization and scaling of twin-screw extrusion are also covered. And finally, the future prospects of developments and research of twin screw extrusion is discussed. Full article
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22 pages, 2775 KiB  
Review
Optimization and Scale-Up for Polymer Extrusion
by Andrzej Nastaj and Krzysztof Wilczyński
Polymers 2021, 13(10), 1547; https://doi.org/10.3390/polym13101547 - 12 May 2021
Cited by 24 | Viewed by 5617
Abstract
A review paper is presented on optimization and scale-up for polymer extrusion, both single screw and twin screw extrusion. Optimization consists in obtaining a multidimensional space of process output variables (response surface) on the basis of an appropriate set of input data and [...] Read more.
A review paper is presented on optimization and scale-up for polymer extrusion, both single screw and twin screw extrusion. Optimization consists in obtaining a multidimensional space of process output variables (response surface) on the basis of an appropriate set of input data and searching for extreme values in this space. Scaling consists in changing the scale of the process according to specific criteria, that is, changing the process while maintaining the scaling parameters at a level that is as close to the reference process parameters as possible. It consists in minimizing the differences between the parameters characterizing the reference process and the resulting process. This may be obtained by using optimization techniques leading to the minimization of discrepancies between the parameters of scaled processes. In the paper, it was stated that optimization and scale-up based on process simulation are more effective than those based on experimentation which is time consuming and expensive. The state-of-the-art on extrusion process modeling which is the basis of optimization and scale-up has been presented. Various optimization techniques have been discussed, and the Genetic Algorithms have been identified as powerful and very efficient. Optimization and scale-up based on the process simulation using Genetic Algorithms have been broadly reviewed and discussed. It was concluded that, up to date, there is a lack of optimization studies on the counter-rotating twin screw extrusion, although the global models of this process are known. There is also a lack of process simulation-based scaling-up studies, both on the counter-rotating twin screw extrusion and on the starve fed single screw extrusion. Finally, development perspectives in this field have been discussed. Full article
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31 pages, 7630 KiB  
Review
Fundamentals of Global Modeling for Polymer Extrusion
by Krzysztof Wilczyński, Andrzej Nastaj, Adrian Lewandowski, Krzysztof J. Wilczyński and Kamila Buziak
Polymers 2019, 11(12), 2106; https://doi.org/10.3390/polym11122106 - 15 Dec 2019
Cited by 55 | Viewed by 20236
Abstract
A review paper is presented on modeling for polymer extrusion for both single screw and twin-screw extrusion. An issue of global modeling is discussed, which includes modeling for solid conveying, melting, melt flow, and co-operation of the screw/die system. The classical approach to [...] Read more.
A review paper is presented on modeling for polymer extrusion for both single screw and twin-screw extrusion. An issue of global modeling is discussed, which includes modeling for solid conveying, melting, melt flow, and co-operation of the screw/die system. The classical approach to global modeling of the extrusion process, which is based on separate models for each section of the screw, i.e., solid transport section, melting and pre-melting sections, and the melt flow section is presented. In this case, the global model consists of the elementary models. A novel continuous concept of global modeling based on CFD (Computational Fluids Dynamics) computations is also presented, and a concept of using the DEM (Discrete Element Method) computation coupled with CFD computations is discussed. Full article
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Other

Jump to: Research, Review

2 pages, 148 KiB  
Book Review
Rheology in Polymer Processing: Modeling and Simulation, Krzysztof Wilczyński, Hanser Publishers, 1st Edition. 2020, ebook ISBN: 978-1-56990-661-3; Print ISBN: 978-1-56990-660-6; 390 Pages
by John Vlachopoulos
Polymers 2021, 13(12), 1981; https://doi.org/10.3390/polym13121981 - 17 Jun 2021
Viewed by 2214
Abstract
In 1945, about one million tons of polymer resins were produced globally, and due to rapid growth, 400 million tons were produced in 2020 [...] Full article
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