Polymer Melt Flow Research Articles

Hydrodynamic Structure of Secondary Polymer Melt Flows in Channels with Changing Geometry

Hydrodynamic Structure of Secondary Polymer Melt Flows in Channels with Changing Geometry

Inverse parameter estimation for the white–metzner equation using extrudate diameter measurements

Abstract This study presents a method to determine the elastic modulus of the White–Metzner (WM) viscoelastic model, which is used to describe polymer melt flow. In processes involving polymeric liquids, elastic effects are essential for accurate simulations. In particular, phenomena such as melt swelling after extrusion and upon gate passage in injection molding are critical to process simulation. However, systematic procedures for material characterization remain underdeveloped since implementation of an appropriate material model is challenging due difficulties inherent in parameter determination. In this work, to account for the shear thinning behavior, which is essential when handling polymeric liquids in current processes, while also incorporating elastic properties, the WM equation was employed. The method employs the post-extrusion swelling phenomenon where the diameter of the extruded material expands after exiting the capillary die. It integrates melt swell measurements with numerical simulations based on the WM equation and highlights the importance of considering gravity in the simulation. A laser scanning microscope is used to measure the extruded diameter while adaptive multi-objective optimization identifies unknown parameters in the model to align the simulation results with the measured diameter. This approach successfully determined the elastic modulus of the PET-PEN copolymer, establishing a system for determining the viscoelastic properties of polymer melts.

A multivariate piecewise interpolation model for viscosity representation and its application to the numerical simulation of non-isothermal polymer melt flow

In this study, a multivariate piecewise interpolation model is introduced to represent melt viscosity based on temperature and shear rate. The model does not require a predefined functional form for the entire data range, instead finding a suitable line between adjacent measured viscosity data points to obtain viscosity as a function of shear rate and temperature. To assess the effect of viscosity representation on polymer melt flow, a two-dimensional (2D) flow past a cylinder problem and a three-dimensional (3D) single screw extruder problem are numerically solved using different viscosity models. The pressure drop (ΔP) from the shift-factor model deviates by more than 10% at an average velocity (Uav) of 1 m/s due to overestimation of viscosity in the high shear rate region. The dimensionless thicknesses of the thermal boundary layer near the channel wall (δT/H) at wall temperature (Tw) of 210 °C are also misevaluated by more than 4% using both the shift-factor model and the Klein model, reflecting their poor viscosity evaluation. It is noteworthy that in all viscosity models, a high Tw leads to the formation of a thin thermal boundary layer, which adversely affects the heat transfer. In single screw extruder applications, viscosity misevaluation in high shear rate regions causes issues in pure drag flow cases, while misevaluation in low shear rate regions causes issues in pure back-pressure flow cases. These analyses highlight the accuracy and versatility of our multivariate piecewise interpolation model compared to existing viscosity models.

Multiphysics modeling and simulation of monolayer flow and die swelling in industrial tube extrusion process

AbstractIn a regular extrusion process for thermoplastic specimen, the material behavior in dies and its rheological properties have a major influence on the mechanical properties and the quality of the extruded product. This study outlines the multiphysical model, which has been adapted to address the specific issues associated with polyamide 12 polymer extrusion. A series of numerical simulations, based on the modeling of material behavior, have been conducted using the computational code Comsol Multiphysics®. These simulations have been applied to the study of polymer melt flows through an industrial extrusion die. The objective of this study is to analyze the influence of the imposed extrusion parameters on the physical field distribution and the material displacement within the die. The die swell at the exit of the extrusion die has been investigated as a function of the imposed pressure. The progression of the polymer flow front inside the extrusion tool and the swelling rates have been analyzed. In particular, the phenomenon of delayed swelling at high pressure has been highlighted at high pressure.Highlights Polymer swelling at industrial extrusion die exit is investigated. Polymer melt extrusion within industrial extrusion tool is numerically simulated. Flow front progression and extrudate swell are analyzed. Effect of extrusion pressure on instabilities and die swell is highlighted.

The effect of rotationality on nonlinear shear flow of polymer melts and solutions

By considering the rotationality of shear flow, we distinguish between tube segments created by reptation before the inception of shear flow and those created during flow. Tube segments created before inception of shear flow experience both stretch and orientation, while tube segments created after inception of flow are not stretched, but are only aligned in the flow direction. Based on this idea, the Rotation Zero Stretch (RZS) model allows for a quantitative description of the start-up of shear flow and stress relaxation after step-shear strain experiments, in agreement with data of polystyrene long/short blends and corresponding polystyrene 3-arm star polymers investigated by Liu et al. (Polymer 2023, 281:126125), as well as the shear viscosity data of poly(propylene carbonate) melts reported by Yang et al. (Nihon Reoroji Gakkaishi 2022, 50:127–135). In the limit of steady-state shear flow, the RZS model converges to the Doi-Edwards IA model, which quantitatively describes the steady-state shear viscosity of linear polymer melts and long/short blends. The assumption of “non-stretching” of tube segments created during rotational flow is therefore in agreement with the available experimental evidence. Three-arm star polymers behave in a similar way as corresponding blends of long and short polymers confirming the solution effect of the short arm in asymmetric stars. The analysis of step-shear strain experiments reveals that stress relaxation is at first dominated by stretch relaxation, followed at times larger than the Rouse stretch relaxation time by relaxation of orientation as described by the damping function of the Doi-Edwards IA model. The RZS model does not require any nonlinear-viscoelastic parameter, but relies solely on the linear-viscoelastic relaxation modulus and the Rouse stretch relaxation time.Graphical

Thermorheological complexity in Nylon12‐Cork composites: Role of interfacial compatibilizer

AbstractHerein, we demonstrate how compatibilizers affect the thermorheological properties and morphology of engineering thermoplastic composites based on nylon and cork. Nylon12 was melt‐mixed with cork treated with four distinct compatibilizers with radically different chemical structures and compositions, respectively: (i) Octadecanamide (ODA), (ii) polyethylene‐graft‐maleic anhydride (PE‐g‐MA), (iii) polypropylene‐graft‐maleic anhydride (PP‐g‐MA), and (iv) (3‐aminopropyl)triethoxysilane (APTS). The rheological behavior was assessed using an oscillatory rheometer and the morphology was visualized using a scanning electron microscope. The rheological data were thoroughly analyzed using different formalisms based on empirical, phenomenological, and molecular origin, including the Carreau‐model, time–temperature superposition (TTS), Han plot, and van Gurp–Palmen (vGP) plot. It is observed that rheological data of neat nylon can be treated as themorheologically simple. However, the inclusion of cork makes the composite thermorheologically complex and increases the relaxation time (τ) by >50‐fold when compared to the neat polymer. As compatibilizers, ODA and PP‐g‐MA significantly lower τ, improve internal flow behavior, and demonstrate good cork distribution and dispersion. However, PE‐g‐MA does not affect the τ of composites significantly. The application of APTS as a compatibilizer enhances the interfacial interaction between Nylon12 and cork most significantly, which leads to a notable rise in τ, and the composite's elastic modulus surges by two orders in magnitude compared to neat Nylon. Additionally, the polymer melt flow becomes elastically dominant. Finally, it is observed that the Han plot offers a better insight into the correlation between changes in the thermorheological behavior and the microstructural modifications to the composites.Highlights Utilizing cork particles as a sustainable raw material for engineering thermoplastics. Quantifying compatibilizer's impact on rheological properties of polymer composite. Illustrating how interfacial interaction affects thermorheological complexity in composites. Visualizing morphological change in nylon‐cork composite with interfacial interaction. Producing lightweight engineering polymer composites using cork as a filler.

Unexpected Stress Overshoot in Extensional Flow of Star Polymer Melts.

Previous studies have shown that the nonlinear rheological behavior of 3-arm star polymer melts in fast extensional flow is identical to that of linear polymers with the same span molecular weight, because the star polymers are highly aligned and have a similar conformation as the corresponding linear polymers. However, with more arms, it would be more difficult for the stars to be aligned like linear chains, and the nonlinear extensional rheology of star polymers with more arms under large deformations has not been investigated yet. Here we show that the star polystyrene (8-10 arms) melts behave differently from the linear polystyrenes. A transient stress overshoot is observed in the fast extensional flow, probably due to the difference in entanglement density near and far away from the branch point.

A generalized method aiming at predicting the polymer melt flow field in the metering zone of large-scale single-screw extruders

Single-screw extruders (SSE) are commonly used in a wide variety of applications, ranging from polymer-extrusion to pellet additive manufacturing (PAM). Existing mathematical models focus on Newtonian and power-law rheologies to model melt flow in the last screw vanes. However, molten polymers usually follow more complex rheological patterns, and a generalized extrusion model is still lacking. Therefore, a semi-analytical model aiming at describing the flow of molten polymers in SSE is presented, to encompass a wide range of non-Newtonian fluids, including generalized non-Newtonian fluids (GNF). The aim is to evaluate the molten polymer flow field under the minimum set of dimensionless parameters. The effect of dimensionless extrusion temperature, flow rate, channel width, and height on the flow field has been investigated. A full factorial plane has been chosen, and it was found that the impact of dimensionless flow rate is the most prominent. The results were initially compared to numerical computations, revealing a strong agreement between the simulations and the proposed GNF method. However, significant deviations emerged when employing the traditional power-law model. This is particularly true at high values of flow rate and extrusion temperature: the mean error on overall flow speed is reduced from 12.91% (traditional power-law method) to 1.04% (proposed GNF method), while keeping a reasonable computational time (time reduction: 96.70%, if compared to fully numerical solutions). Then, the predicted pressure drop in the metering section was benchmarked against established literature data for industrial-scale extruders, to show the model’s accuracy and reliability. The relative errors of the traditional model range between 34.33 and 62%. The proposed method reduces this gap (errors ranging between 5.34% and 10.97%). The low computational time and high accuracy of the GNF method will pave the way for its integration in more complex mathematical models of large-scale additive manufacturing processes.

Numerical modelling of the viscoelastic polymer melt flow in material extrusion additive manufacturing

ABSTRACT In material extrusion (MEX), it is challenging to accurately predict the steady and transient feeding forces at various polymer extrusion rates when printing island and thin-walled structures involving rapid start/stop or acceleration/deceleration, especially for semi-crystalline polymers. This research presents a non-isothermal viscoelastic Computational Fluid Dynamics model to investigate the steady and transient feeding forces, as well as the phase transition process and viscoelastic behaviour of polylactic acid (PLA), a semi-crystalline polymer, during the extrusion process. The study establishes a relationship between polymer flow and viscoelastic stress, demonstrating that the elastic effect during extrusion is more significant than the viscous effect, particularly at higher feeding rates. Furthermore, the study uncovers critical aspects of PLA melt flow behaviour during the MEX process, laying the foundation for future research and optimisation of MEX printing processes.

Simulation of fiber-induced melt pressure fluctuations within large scale polymer composite deposition beads

The process-structure-property relationship in Large Area Additive Manufacturing (LAAM) technology is an ongoing area of research as the inherent microstructural properties (chiefly fibers and voids) affect the performance of printed parts. Unfortunately, we currently lack adequate understanding of micro void nucleation and evolution during the LAAM and fused deposition modelling (FDM) processes. Modeling of the polymer melt flow during the extrusion process is important in understanding the underlying microstructural formation and associated properties of the print, that determines the part performance in service conditions. In this paper we compute fiber-induced local pressure fluctuations which may promote void formation in the bead’s microstructure. On a macro-scale, we determine flow fields of a purely viscous, Newtonian planar polymer deposition flow through a LAAM nozzle which are utilized on a micro-scale model where we simulate the evolution of a single ellipsoidal fiber along streamlines obtained from the macro-model. On the micro-scale, we determine instantaneous values of the translational and rotational velocities of the rigid ellipsoidal fiber that satisfies a balance of hydrodynamic forces and couples on the fiber’s surface based on a Newton Raphson algorithm and we track the fiber’s motion along the flow path via an explicit numerical iterative algorithm. Model verification is achieved by benchmarking results with solutions from well-known Jeffery’s equation of motion of a particle in homogeneous simple shear flow. We account for rotary diffusivity due to short-range fiber-fiber interaction in the FEA simulation by determining an effective fluid domain size representative of the interaction coefficient of the melt flow through a correlation analysis that yields an equivalent steady state orientation based on the Advani-Tucker equation. We also consider different possible motions of the fiber along individual LAAM flow paths from a given set of random initial fiber conditions to determine pressure bounds on the fiber surface along each streamline. For improved computational efficiency, calculations are carried out with respect to the fiber’s local coordinate axes to overcome the rigor of adaptive remeshing during the quasi-transient analysis. Results show low pressure extremes near the fiber’s surface which varies across the printed bead as well as through its thickness. Discussion is provided to gain insight into the effect of low-pressure extremes on micro void formation, particularly at the nozzle exit and during die swell/expansion.

Разработка цифрового двойника экструдера для получения филамента из полиэтилена низкой плотности

On the basis of experimentally determined characteristics of low-density polyethylene, geometric dimensions of extruder parts and using COMSOL MULTIPHYSICS software, a digital model of the apparatus was created and hydrodynamic calculationof the polymer melt flow velocity from the extruder nozzle was performed. The agreement of the experimentally measured polymer melt flow velocity with the one calculated using the model is within the acceptable tolerance. This indicates the adequacyof the digital twin model, which can be used to predict the viscosity properties of composite materials based on low-density polyethylene and process conditions of their production by extruder blending.

Investigation of mechanical and frictional properties of ulexite and colemanite filled acrylonitrile-butadiene-styrene polymer composites for industrial use

Ulexite and colemanite filled acrylonitrile-butadiene-styrene parts are manufactured by injection molding method. Tensile and wear tests are applied to reveal specific properties of composite parts. Various characterization methods are used to confirm the filler-matrix interactions, polymer melt flow, friction mechanisms, and fracture modes. This study investigated the use of ulexite and colemanite as fillers in acrylonitrile-butadiene-styrene composite parts, focusing on their impact on mechanical and frictional properties. Results showed that the addition of ulexite and colemanite fillers significantly improved mechanical properties such as compared to pure ABS, however ulexite filler showed much better performance compared to colemanite. In terms of wear test, ulexite filled ABS specimen showed a smooth wear while pure and colemanite filled ABS provided severe wear characteristics. These findings have implications for the development of high-performance composite materials for use in industries such as automotive and aerospace.

60 years of the Kaye–Bernstein, Kearsley, Zapas rheological constitutive law for polymers

The K–BKZ (Kaye–Bernstein, Kearsley, Zapas) rheological constitutive model is now 60 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experimental evidence in polymer melt flow, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction, an historical perspective is given on developments in the last 60 years of the K–BKZ model. Then, a section on mathematical modeling of polymer flows follows, including the governing equations of flow, the rheological constitutive equations (with emphasis on the viscoelastic integral constitutive equations of the K–BKZ type), dimensionless numbers controlling the flow, and relevant boundary conditions. The “Method of Solution” section reviews the major developments of numerical techniques for particle tracking and integral evaluation for the viscoelastic stresses. Finally, selected examples of successful application of the K–BKZ model in polymer flows are presented including considerations of wall slip and non-isothermal flows.

Dimethylformamide Impurities as Propylene Polymerization Inhibitor.

This research study examined how the use of dimethylformamide (DMF) as an inhibitor affects the propylene polymerization process when using a Ziegler-Natta catalyst. Several experiments were carried out using TiCl4/MgCl2 as a catalyst, aluminum trialkyl as a cocatalyst, and different amounts of DMF. Then, we analyzed how DMF influences other aspects of the process, such as catalyst activity, molecular weight, and the number of branches in the polymer chains obtained, using experimental and computational methods. The results revealed that as the DMF/Ti ratio increases, the catalyst activity decreases. From a concentration of 5.11 ppm of DMF, a decrease in catalyst activity was observed, ranging from 45 TM/Kg to 44 TM/Kg. When the DMF concentration was increased to 40.23 ppm, the catalyst activity decreased to 43 TM/Kg, and with 75.32 ppm, it dropped even further to 39 TM/Kg. The highest concentration of DMF evaluated, 89.92 ppm, resulted in a catalyst productivity of 36.5 TM/Kg and lost productivity of 22%. In addition, significant changes in the polymer's melt flow index (MFI) were noted as the DMF concentration increased. When 89.92 ppm of DMF was added, the MFI loss was 75%, indicating a higher flowability of the polymer. In this study, it was found that dimethylformamide (DMF) exhibits a strong affinity for the titanium center of a Ziegler-Natta (ZN) catalyst, with an adsorption energy (Ead) of approximately -46.157 kcal/mol, indicating a robust interaction. This affinity is significantly higher compared to propylene, which has an Ead of approximately -5.2 kcal/mol. The study also revealed that the energy gap between the highest occupied molecular orbital (HOMO) of DMF and the lowest unoccupied molecular orbital (SOMO) of the Ziegler-Natta (ZN) catalyst is energetically favorable, with a value of approximately 0.311 eV.

Multiphysics modelling of powder bed fusion for polymers

ABSTRACT Polymeric materials for powder bed fusion additive manufacturing have been attracting extensive research interest due to their vast potential for fabricating end-use functional parts. Here, a high-fidelity multiphysics approach combining the discrete element model with the computational fluid dynamics model has been developed to simulate the printing process of polymers in powder bed fusion, involving powder recoating, melting, and coalescence. The developed approach considers particle flow dynamics, the reflection, absorption, and transmission of infrared laser radiation, and the viscous flow of polymer melt. The pore formation mechanisms due to lack of fusion and gas entrapment in polyamide 12 parts printed via selective laser sintering are studied. The simulation results reveal that lower polymer viscosity would be beneficial to the densification rate of the printed parts. Excessively small powder particles would degrade powder bed quality due to the agglomeration of polymer powder, thus leading to high porosity in the printed parts.

The importance of extensional viscosity on a peculiar ear-flow front for injection molding simulations of fiber-reinforced composites

An ear-flow front is discovered in the industrial practice of injection molding, especially for fiber-reinforced composites; the advance of the flow front in the center of the cavity is obviously slower than at the edges. To date, such a peculiar flow has not yet been predicted theoretically or computationally and is beyond the predictive capabilities of existing commercial computer aid design (CAE) packages for the injection molding process. Recently, the GNF-X (Generalized Newtonian Fluid eXtended) model of weighted shear/extensional viscosity has been incorporated availably in state-of-the-art predictive engineering software of the 3D-CFD (three-dimensional computational fluid dynamics) framework to show the extension-induced vortex growth in contraction flows of polymer melts. Through 3D-CFD coupled with GNF-X in injection molding simulations, it is significant to demonstrate the importance of extensional viscosity on the ear-flow formation in relation to the weighted viscosity and extension fraction for long-branched and fiber-filled polymer materials. In addition, one can point out that the ear-flow front probably occurs in fast filling conditions for anisotropic fluids.

Effects of Friction Stir Welding on the Mechanical Behaviors of Extrusion-Based Additive Manufactured Polymer Parts.

The friction stir welding (FSW) of thermoplastic polymers is gradually receiving attention because of its advantages including high efficiency and pollution-free manufacturing. The extrusion-based additive manufacturing (EAM) of polymers has also become one of the main processing methods for thermoplastic parts. In this paper, a hybrid manufacturing method for the FSW process and EAM technology is proposed and explored. The effects of the FSW process using two different welding tools on the mechanical behaviors of 3D printing polymer parts were compared and investigated and the corresponding mechanism was analyzed. The results show that the appropriate welding tool is beneficial for eliminating the anisotropy and decreasing the porosity of 3D-printed parts. Therefore, the improving effects of the FSW process on the mechanical behaviors of the EAM parts are verified. The mechanism was attributed to the high-speed rotation of the welding tool with the appropriate shape, which can promote the flow of polymer melt in the welding region, leading to the formation of dense structures caused by the entanglement of the molecular chains. This study may provide some assistance in modern industrial manufacturing for the processing of large custom components.

Modeling of Non-Isothermal Polymer Melt Flow in a Conical Annular Channel of a Disk Extruder

Purpose. The homogenization zone consists of various channels with different configurations, for each of which it is necessary to determine the passage of the melt flow process, and on its basis - the velocity fields, which determine the quality of mixing and distribution of components in the melt. To ensure a flexible and controllable homogenization process with the possibility of improving the quality of the melt, it is necessary to study the flow processes in the channels of a disk extruder. Therefore, the main objective of this work is to perform hydrodynamic modeling of processes during melt flow in a conical channel. Methodology. To achieve this goal, we propose a methodology for determining the flow processes in a conical channel, and find out which zones are convenient to consider in a special conical orthogonal coordinate system. For this purpose, the change in the radial coordinate , which has the same meaning in both the straight and the conical gap, was described - it is a coordinate along the width of the gap. This makes it possible to further apply this coordinate for the width of the disk gap - between the moving and stationary disks. Findings. A method has been proposed that describes the flow processes in the conical channel of the homogenization zone of a disk extruder. The calculation procedure is presented in an analytical form, and graphical dependences of the distribution of tangential and longitudinal velocities and shear velocities of the melt flow along the width of the annular channel at the nominal and maximum disk speeds and at the nominal and maximum disk gap are also given. Originality. For the first time, a methodology for calculating the conical channel of the homogenization zone of a disk extruder is presented, which describes the flow processes in a conical orthogonal coordinate system, which allows taking into account the common coordinate for the entire homogenization zone. The general procedure for calculating the channels of the homogenization zone has been supplemented. Practical value. The procedure for calculating the channels of the homogenization zone, which was started earlier, was extended and applied to the flow in a conical annular channel. This coordinate allows us to describe the flow processes along the width of the channel for all channels of the homogenization zone of a disk extruder, which greatly simplifies the calculations. Important results of hydrodynamic and thermal processes were obtained for the annular channel, which makes it possible to design disk extruders with greater accuracy and calculate their optimal operating modes.

Statistical research on the mixing properties of wave based screws by numerical simulations

Abstract Research based on numerical simulation with the CFD software ANSYS POLYFLOW is conducted on the mixing properties for the wave screw elements, as well as barrier screw elements, by using statistical tools. Then, the investigation is conducted in detail on the relationship between pressure, maximum shear rate, mixing index and other flow field characteristics of the two above screws under the same simulation conditions. It is found that polymer melt flow in the wave screw possesses various advantages compared with the normal barrier screw, such as acquiring larger pressure, stronger shearing and stretching action, better mixing and efficiency, which mainly result from the periodic depth change design in the screw groove. On the other hand, the increased wave bulge in the wave screw lessens the space for the polymer melt to be conveyed forward, which can greatly reduce the original function of the secondary flight. Also, the convergent and divergent zones in the wave screw groove produce a much stronger stress favoring the shear and elongation rates, and also lead to a sharp increase of the axial force load on the wave screw. Consequently, for the optimization of the wave screw configuration it is suggested to reduce the axial force without decreasing the effect of the excellent distributive and dispersive mixing.

Numerical study of nonisothermal flow of polymer melt with undermelted granules in an annular channel of a disk extruder

A computational experiment was carried out on the basis of the created model of melt flow with undermelted granules in a straight annular channel, which takes into account the design characteristics of a pilot-industrial disk extruder. A polymer composition based on high-pressure polyethylene (PE 15803-020) was chosen as a model object. The calculation procedure is presented in an analytical form at disk speeds of minimum value – 120, nominal value – 150, and maximum value – 180 rpm.