Polymer Melt Flow Research Articles

Verification and Validation of openInjMoldSim, an Open-Source Solver to Model the Filling Stage of Thermoplastic Injection Molding

In the present study, the simulation of the three-dimensional (3D) non-isothermal, non-Newtonian fluid flow of polymer melts is investigated. In particular, the filling stage of thermoplastic injection molding is numerically studied with a solver implemented in the open-source computational library O p e n F O A M ® . The numerical method is based on a compressible two-phase flow model, developed following a cell-centered unstructured finite volume discretization scheme, combined with a volume-of-fluid (VOF) technique for the interface capturing. Additionally, the Cross-WLF (Williams–Landel–Ferry) model is used to characterize the rheological behavior of the polymer melts, and the modified Tait equation is used as the equation of state. To verify the numerical implementation, the code predictions are first compared with analytical solutions, for a Newtonian fluid flowing through a cylindrical channel. Subsequently, the melt filling process of a non-Newtonian fluid (Cross-WLF) in a rectangular cavity with a cylindrical insert and in a tensile test specimen are studied. The predicted melt flow front interface and fields (pressure, velocity, and temperature) contours are found to be in good agreement with the reference solutions, obtained with the proprietary software M o l d e x 3 D ® . Additionally, the computational effort, measured by the elapsed wall-time of the simulations, is analyzed for both the open-source and proprietary software, and both are found to be similar for the same level of accuracy, when the parallelization capabilities of O p e n F O A M ® are employed.

Hybrid Process Chain for the Integration of Direct Ink Writing and Polymer Injection Molding.

The integration of additive manufacturing direct-writing technologies with injection molding provides a novel method to combine functional features into plastic products, and could enable mass-manufacturing of custom-molded plastic parts. In this work, direct-write technology is used to deposit conductive ink traces on the surface of an injection mold. After curing on the mold surface, the printed trace is transferred into the plastic part by exploiting the high temperature and pressure of a thermoplastic polymer melt flow. The transfer of the traces is controlled by interlocking with the polymer system, which creates strong plastic/ink interfacial bonding. The hybrid process chain uses designed mold/ink surface interactions to manufacture stable ink/polymer interfaces. Here, the process chain is proposed and validated through systematic interfacial analysis including feature fidelity, mechanical properties, adhesion, mold topography, surface energy, and hot polymer contact angle.

Rotomolding and polyethylene composites with rotomolded lignocellulosic materials: A review

Rotomolding is a versatile process used in the manufacture of thermoplastic polymeric materials to produce large hollow plastic parts. The aim of this review article was to discuss the rotomolding process and show the properties of the polyethylene composite and rotomolded lignocellulosic fibers, which are processed for prolonged periods under temperature. The main process parameters studied are the shaft speed of the equipment, molding temperature, polymer particle size, polymer melt flow index, and amount of material, which must be well controlled to achieve a non-degraded product with homogeneous thickness and no porosity. Rotomolded composites containing sisal, pine, coir, banana, flax, and maple wood fibers, among others, have been evaluated primarily for their mechanical (impact, flexural, and tensile strength) and morphological properties. The type, content, and treatment of lignocellulosic fillers are the most widely studied variables in polyethylene-based rotomolded composites. Fiber content was the variable that most influenced mechanical properties, particularly impact strength and hardness due to the voids formed by the hydrodynamic volume between the polymer matrix and lignocellulosic filler. Chemical treatment of the fiber by mercerization with NaOH made it more hydrophobic and the addition of maleic anhydride-grafted polyethylene as a coupling agent improved the interfacial adhesion between the non-polar polymer matrix and polar filler. However, the best mechanical property results were obtained with the use of maleic anhydride-grafted polyethylene.

Molecular Dynamics Reveals a Dramatic Drop of the Friction Coefficient in Fast Flows of Polymer Melts

We here revisit existing results of Kremer–Grest molecular dynamics simulations of polymer melts that provide values of the friction coefficient ζ of the Kremer–Grest bead for the coarse-grained Fraenkel chain model, both at equilibrium, and in very fast uniaxial extensional flows. The Fraenkel chain model is chosen because it can guarantee chain inextensibility in the flow-induced fully aligned conformation. Since the value of ζaligned for the fully aligned conformation is found to be much smaller than the equilibrium value ζeq, a controversial issue of the nonlinear rheology of polymer melts is here resolved. Indeed, this finding confirms previous evidence emerging from the rheology of several polymers, where seemingly the friction coefficient decreases with increasing flow-induced molecular coalignment. Often, however, such evidence was indirect, and the friction coefficient reduction has not been accepted by a large fraction of the scientific community.

Flow and solidification of semi-crystalline polymer during micro-injection molding

This work investigates flow and solidification characteristics of semi-crystalline thermoplastic polymer melt during the micro injection molding process. When the melt flow enters micro-cavities and solidifies, it has been observed that micro-balls are formed on the flow front and coalesced with each other creating many micro-weld lines. Consequently, a characteristic pattern is observed by optical microscopy. This work has examined the mechanism of their creations experimentally as well as numerically. It has been hypothesized based on the experimental results that the onset of this phenomenon is initiated by nucleation in the micro-cavities. For the same micro-cavity, both injection molding and imprinting have been conducted and the shape and the morphologies of the molded parts have been analyzed. Based on observation of the morphologies, this work concludes that nucleation is due to high shear rate while entering the micro-cavity and the balls are formed by the growth of the spherulites. Moreover, the validity of the hypothesis has been verified by the numerical simulation of the ball formation process. The numerical simulation has reproduced the geometric shape found in the experiments. This result supports the proposed hypothesis.

Effects of chain length and polydispersity on shear banding in simple shear flow of polymeric melts.

The characteristics of shear banding were investigated in entangled, polydisperse, linear polymer melts under steady-state and startup conditions of simple shear flow. This virtual experimentation was conducted using course-grained nonequilibrium dissipative particle dynamics simulations expressed in terms of a force-field representation that faithfully models the atomistic system dynamics. We examined melts with two mean molecular bead numbers of Nn = 2 50 and 400 and polydispersity indexes of 1.0, 1.025, and 1.05. The wide range of relaxation timescales in the polydisperse melts decreased the nonmonotonic character of the steady-state shear stress vs. shear rate profile compared to a monodisperse linear melt. The polydispersity level required to observe a stress plateau in the shear stress profile at intermediate shear rates was correlated with the nominal entanglement density. Startup of shear flow simulations revealed the development of spatial inhomogeneities and dynamic instabilities in polydisperse fluids containing both monotonic and nonmonotonic shear stress flow curves. Although the shape and duration of instabilities were found to be correlated with the monotonicity of the shear stress profile, the onset and underlying mechanism leading to the formation of shear bands were generally universal. The simulations revealed that perturbations arose soon after the occurrence of a large stress overshoot under startup conditions, and that banded structures stemmed from local reorientation and subsequent deconstruction of the entanglement network. Furthermore, data indicated that the inception of strain localization occurred at shear rates near the reciprocal of the Rouse characteristic timescale, [small gamma, Greek, dot above] > τR-1. Transient shear banding was observed in shorter chain melts undergoing startup of shear flow in which instabilities arose after the appearance of a stress overshoot. These instabilities eventually decayed, but only long after the stresses had attained their steady-state values. The longer chain melt exhibited a shear band structure that remained indefinitely after the stresses had attained steady state.

In Ukrainian

There were highly-filled composites, based on (polypropylene) PP and containing 5 – 50 % mass. of calcite concentrate (CC), consisting in highly-dispersed calite powder, modified with organic compounds. It is established, that value for organic part content in CC was 24 % mass. CC and highly-flowing PP was used for process of concentrate granulation process. It is shown, that, when at increase of CC’s contents values, those ones of viscosity for compositions melts decreases simultaneously, dissonating with traditional laws for polymer melt flows, when those are intrisically and typically increasing. It is established, that melt flow index values, when at increase of CC contents for those ones, increasing also – from 3.1 g/10 min for pure PP, to 6,6 g/10 min for composition of 50 % mass. CC. It is discovered, that CC is having influence on melt and crystallization processes of PP. When at low (5 % mass.) and middle (10 – 20 % mass.) of CC contents values, there are meling and crystallization temperatures increasing – from 168 °C to 169 – 170 °C and from 115 °C to 117 – 118 °C, accordingly, and melting temperature range is narrowing – from 42 °C pure PP) to 38 – 34 °C, for composites of CC contents values of 30 – 50 % mass., accordingly, and crystallization temperature range – from 18 °C (pure PP, 0 % CC), to 16 – 15 °C, for composites of high CC contents values, accordingly also. There are increasing of phase transitions temperatures exists, pointing on formation of more large and perfect crystallites, however, narrowing in those ones range points on creation of more dimensionally uniform such of supermolecular structures. Such influence for CC on rheological behavior and temperature characteristics of phase transitons phenomena links with plastyfying effect of modifier‘s chains on CC surfaces of particles, and, simultaneously, at presence of highly-flowing PP as base polymer in. CC injection making some decrease here, namely for activation energy values for oxidative thermodestruction, this phenomen is expaining with more decrease of bounding degree in system, causing with presence of modifier additions in system, and one have influence on.

Experimental and analytical study of the polymer melt flow through the hot-end in material extrusion additive manufacturing

Material extrusion additive manufacturing utilizes a thermoplastic polymer in the form of a solid filament as a built material. The polymer melts inside the hot-end channel and flows under the pressure generated by the filament feeding force. The flow of polymer through the hot-end is not fully understood yet, as it involves many complex phenomena, such as phase transition, shear rate and temperature dependent viscosity, as well as viscoelastic effects. In this paper, we investigate experimentally the filament feeding force, as a function of the feeding rate, for different materials (PLA and ABS), liquefier temperatures, nozzle diameters, and lengths of the liquefier. Two extrusion regimes are identified: a linear regime with a stable flow, and a non-linear regime with fluctuations in the feeding force, which are concomitant to unstable extrusion. Increasing the liquefier length and liquefier temperature are found to extend the linear extrusion regime. It is shown that the filament feeding force predicted by the analytical models available in the literature deviates from the measurements, especially at high feeding rates. A model solely based on heat transfer considerations is proposed to estimate the maximum feeding rate before the extrusion becomes unstable. The modelling results agree well with the measurements. The model can be used to select the hot-end design as well as appropriate printing parameters.

Modelling contraction flows of bi-disperse polymer blends using the Rolie-Poly and Rolie-Double-Poly equations

The flow of a bi-disperse polymer melt through a hyperbolic contraction is simulated using the recently proposed Rolie-Double-Poly constitutive model (Boudara et al., 2019). This simplified tube model takes account of the nonlinear coupling between the dynamics of the long and short-chains in a bi-disperse blend, in particular it reproduces the enhancement of the stretch relaxation time that arises from the coupling between constraint release and chain retraction. Flow calculations are performed by implementing both the Rolie-Double-Poly and multimode Rolie-Poly models in OpenFOAM using the RheolTool library. While both models predict very similar flow patterns, the enhanced stretch relaxation of the Rolie-Double-Pol models results in an increase in the molecular stretch of the long chain component in the pure extensional flow along the centre-line of the contraction, but a decrease in the stretch in shear-flow near the channel walls.

Variational multi-scale finite element method for the two-phase flow of polymer melt filling process

PurposeThe purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface.Design/methodology/approachThe algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time.FindingsThe numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems.Originality/valueFor the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

Low density polyethylene tubular reactor control using state space model predictive control

One of the conventional commodity polymers in the world is Low density polyethylene (LDPE). LDPE is mostly produced from free radical polymerization of ethylene gas under high pressure and temperature environment. However, the control of LDPE polymerization reactor is challenging due to the complexity of the polymerization process and the nature of the reactor itself. Thus, this study explores the application statespace model predictive control (SS-MPC) in controlling LDPE polymerization tubular reactor process. SS-MPC is a type of model predictive control (MPC) scheme which utilizes state space model as its process model. In general, MPC control scheme has a wide application in the industry due to its ability to handle multivariable control and optimize process performance. In order to implement the control scheme, a dynamic model of the reactor was developed using Aspen Dynamic. The dynamic model is then linked with MATLAB Simulink for online control implementation. The LDPE polymerization process was controlled by regulating the initiator and chain transfer agent (CTA) flowrate to control reactor temperature and polymer Melt Flow Index (MFI) grade. The state space model was identified using identification technique through two approaches; MIMO model and augmented SISO model. In order to evaluate the controller performance, MFI grade transition and disturbance rejection tests are conducted along with PID controller, as a comparison. Based on the tests, MPC had presented a notable performance in handling polymer grade transition (Integral squared error, ISE = 4530) and disturbance rejection (ISE = 99.03) in MFI profile compared to PID controller respond (ISE = 7003 for set point tracking and ISE = 12.66 for disturbance rejection). Nonetheless, PID controller had also presented a comparable performance in controlling maximum reactor temperature.

Viscoelastic modeling and simulation for polymer melt flow in injection/compression molding

To describe the characteristics of compressing flow, we propose a new constitutive equation based on the Phan–Thien–Tanner (PTT) model to account for the additional stresses induced by rapid shear rate change. Analytical stress solutions are derived for shear and extensional flows to make this model describe shear thinning and strain hardening of polymers. We establish the uniform viscoelastic flow problem for injection/compression in terms of a non-isothermal compressible fluid, and construct the corresponding variational equations using the finite element method. In order to make the numerical scheme stable and efficient, a pseudo Poisson equation for pressure in weak form is founded. In addition, a two-fold iterative scheme is proposed to decouple velocity, pressure, temperature and stress. We simulate the benchmark 4:1 contraction flow to validate the proposed method and compare with the published results. Furthermore, real injection/compression molding experiments are conducted. The agreements with published and measured data shows that the proposed constitutive model accurately describes compressing flow.

Integral transform method solution for heat transfer in polymer melt flow in a parallel plate single screw channel with periodic inlet temperature

This work investigates the capacity of a particular class of flows, namely drag and pressure driven flows, to propagate and distorts a transient sinusoidal temperature disturbance occurring at the inlet of the metering zone of a polymer processing screw channel. The integral transform method is applied to the forced convection heat transfer problem in a parallel plate channel with a general drag and pressure driven flow velocity profile for a Newtonian fluid, with the pressure gradient as an adjustable flow parameter. We follow closely the procedure outlined by Cotta and Özişik in their seminal paper [5]. We found that the knowledge of the lowest eigenvalue in the solution is sufficient to characterise the dampening efficiency of an inlet temperature fluctuation by the flow and that a higher level of positive pressure difference is indeed improving the thermal homogeneity in the flow. Moreover, we found that for any given flow, the higher frequency disturbances are dispersed more efficiently than the lower frequency disturbances.

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

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

Three-dimensional flow simulations for polymer extrudate swell out of slit dies from low to high aspect ratios

The impact of the slit die geometry and the polymer melt flow characteristics on the extrudate swell behavior, which is a key extrusion operating parameter, is highlighted. Three-dimensional (3D) numerical simulations based on the finite element method are compared with their conventional two-dimensional (2D) counterparts at the same apparent shear rates using ANSYS Polyflow software. The rheological behavior is described by the differential multimode Phan-Thien-Tanner constitutive model, with polypropylene as a reference. It is shown that increasing the aspect ratio of the die geometry (width/height ratio variation from 1 to 20) contributes to a significant change in the 3D extrudate deformation (relative changes of 10% in several directions; absolute changes up to 30%) and delays the equilibrium axial position (up to a factor 10). High aspect ratios induce a switch to contract flow (swell ratio <1) for the edge height swell. The 3D extrudate swell strongly deviates from the 2D simplified case due to the die effect near the wall, even for higher aspect ratios. Also a different relation with the material parameters is recorded. The initially large swell behavior is followed by a small shrinkage flow in the middle height direction which cannot be captured by the 2D counterpart. The findings are supported by a comprehensive analysis of the velocity and stress fields in and out of the slit dies.

Effects of stick–slip transition on polymer melt apparent shear viscosity measurement

ABSTRACTA twin‐bore capillary rheometer is used for the apparent shear viscosity measurement of commercial polyolefin melts based on Ostwald‐de Waele model. The effects of stick–slip transition of linear low‐density polyethylene (LLDPE) and high‐density polyethylene (HDPE) are investigated. The maximum error of apparent shear viscosity calculated by corrected shear rate is 23% when the stick–slip transition occurs. Based on the entanglement‑disentanglement theory, a schematic diagram for shear stress curve containing stick–slip transition is presented to illustrate polymer melt flow in capillary. In this study, the critical stress at the beginning of stick–slip transition at 220 °C is 23.01 kPa higher than that at 190 °C, and why it increases with increasing temperature is discussed with a molecular mechanism in combination with entropy elasticity and entanglement‑disentanglement theory. Through the analysis of ULDPE, PS, EVA, and K‐Resin, it can be found that short branches or side groups are helpful to avoid the stick–slip transition. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 48230.

Numerical solution of polymer melt flow problem in a single screw extruder

Numerical solution of polymer melt flow problem in a single screw extruder

Effect of cavity surface roughness and wettability on the filling flow in micro injection molding

The surface to volume ratio in micro injection molding is quite large and this makes interfacial phenomena particularly crucial for the effectiveness of the process. This criticality is more evident for thin parts molding, where the influence of roughness on the thermal boundary conditions is not negligible. In this case, the contact between polymer and mold significantly affects the heat transfer at the interface and consequently it strongly influences the polymer melt flow behavior. In this paper, the effects of the polymer-mold interface on polymer flow were experimentally investigated. In particular, the filling of a representative micro part with a thickness of 100 μm was studied in relation to surface roughness and mold wettability. The results showed that the state of the polymer-mold interface plays a fundamental role in the filling of thin-wall micro injection molding. In particular, the flow length increases with both the mold roughness and the contact angle between the molten polymers and the cavity surface.

The Numerical Prediction of Flow of Branched Polymer Melts Through Planar Contraction Channel by Finite Element Method

In this work we present an investigation of a complex viscoelastic flow through an abrupt expansion with expansion ratio D/d = 4, where the Oldroyd-B model was consider as a constitutive equation. The governing equations are solved using the Finite Element Method. The polymer is modeled as a monodisperse suspension of “Oldroyd-B” molecules, which provides a direct link the molecular topology and the flow properties of the melt. The branching produces an enhancement in the size of upstream vortex in creeping flows. Also was found that including inertia forces will give the intensity of lip vortex increases, while the size of corner vortex will initially decreased with growth of Weissenberg number but with more increase (We>4), the size of corner vortex will begin to increase in size. The effect arises from the differing responses in shear and extensional flows of polymer melts.

Global Modeling of Single Screw Extrusion with Slip Effects

Abstract An extensive study is presented on the polymer melt flow with slip effects in a single screw extrusion process. Fully three-dimensional non-Newtonian FEM computations are performed to design the screw pumping characteristics and the die characteristics which may be implemented into the composite model of the process. ANSYS Polyflow software is applied to model the melt flow in the extruder. An analysis is performed for the flow of polymers with slip effects both in the screw (on the screw and barrel surfaces) and in the die. Screw pumping characteristics and die characteristics are calculated and modeled for various power law indices, and various slipping parameters. The effect of slipping on extruder operation is discussed.