Numerical visualization of extensional flows in injection molding of polymer melts

Extensional flows generally take place in a channel with varied cross-sectional areas. During polymer processing with a variety of complex geometric features, it is difficult to separate extensional rates from shear rates in state-of-the-art predictive engineering tools of computational fluid dynamics. The recently proposed method of Tseng [Tseng, H.-C., “A Revisitation of Generalized Newtonian Fluids,” J Rheol 64 493–504 (2020)] decomposed the generalized strain rate as the characteristic shear and extensional rates via the rate-of-deformation tensor rotated along streamline coordinates. As validation for an isothermal center-gated disk flow, the predicted flow field profiles fairly matched the analytical solution for Newtonian fluid. Under injection molding simulations, an objective indicator is defined to visualize the colorful contours of extensional flows encountered in the gate-vicinity and the mid-plane of the cavity’s thickness direction, as well as contraction-expansion channels.

Hydrodynamics and mixing performance in a continuous miniature conical counter-rotating twin-screw extruder

The mixing performance in a miniature conical counter-rotating twin-screw extruder was investigated by means of experimental technique and computational fluid dynamics (CFD) simulation. An on-line experimental device based on the fluorescence detection was built to study the residence time distribution (RTD). Polypropylene was selected as the flow material and the blend of Polypropylene and anthracene was used as the tracer. This on-line detection device has good reproducibility. The hydrodynamics in the extruder was simulated by the finite element method (FEM) combined with the mesh superposition technique (MST). The particle tracking technique was carried out to evaluate the RTD and mixing efficiency. The effect of screw speed and feed rate on the hydrodynamics and mixing performance was investigated. The velocity magnitude and local shear rate tend to become smaller from inlet to outlet due to the decreasing diameters of screws. The mean length of stretch increases exponentially from inlet to outlet and the mean value of time averaged mixing efficiency remains positive along the axial direction.

ESTIMATION OF MECHANICAL LOAD ON RUBBER MIXING ROTORS BY USING A PARTIALLY FILLED FLOW SIMULATION IN CHAMBER

Mixing characteristics and mechanical loads of rubber-mixing rotors are considered to be the two most important factors in actual rotor design. For the design of highly reliable production mixers, there is a great need for a proper estimation method of mechanical load, such as radial force or rotation torque of the rotors. The mechanical load of tangential mixing rotors and surrounding flow are mainly discussed by using partially filled numerical flow simulation. Operational parameters of the mixing condition were set to be fill factor and rotor phase angle of two rotors rotating at an even speed. The Carreau model was applied to the shear rate dependence of viscosity. The volume-of-fluid method was used for free surface simulation. Both two-dimensional and three-dimensional simulations were carried out to discuss mechanical load and its fluctuation mechanisms. For the numerical results, radial force on rotors, pressure, and the velocity distribution around the rotors and their fluctuations are presented and discussed. It was found that the radial force of the rotors could be estimated using this kind of flow simulation, and the fluctuation phenomena could be explained by the movement of a high-pressure region between the front of the rotor wings and the chamber wall.

Nature of Carbon Black Reinforcement of Rubber: Perspective on the Original Polymer Nanocomposite

Adding carbon black (CB) particles to elastomeric polymers is essential to the successful industrial use of rubber in many applications, and the mechanical reinforcing effect of CB in rubber has been studied for nearly 100 years. Despite these many decades of investigations, the origin of stiffness enhancement of elastomers from incorporating nanometer-scale CB particles is still debated. It is not universally accepted whether the interactions between polymer chains and CB surfaces are purely physical adsorption or whether some polymer-particle chemical bonds are also introduced in the process of mixing and curing the CB-filled rubber compounds. We review key experimental observations of rubber reinforced with CB, including the finding that heat treatment of CB can greatly reduce the filler reinforcement effect in rubber. The details of the particle morphology and surface chemistry are described to give insights into the nature of the CB-elastomer interfaces. This is followed by a discussion of rubber processing effects, the influence of CB on crosslinking, and various chemical modification approaches that have been employed to improve polymer-filler interactions and reinforcement. Finally, we contrast various models that have been proposed for rationalizing the CB reinforcement of elastomers.

A Flow-Dependent Fiber Orientation Model

The mechanical performance of fiber reinforced polymers is dependent on the process-induced fiber orientation. In this work, we focus on the prediction of the fiber orientation in an injection-molded short fiber reinforced thermoplastic part using an original multi-scale modeling approach. A particle-based model developed for shear flows is extended to elongational flows. This mechanistic model for elongational flows is validated using an experiment, which was conducted for a long fiber reinforced polymer. The influence of several fiber descriptors and fluid viscosity on fiber orientation under elongational flow is studied at the micro-scale. Based on this sensitivity analysis, a common parameter set for a continuum-based fiber orientation macroscopic model is defined under elongational flow. We then develop a novel flow-dependent macroscopic fiber orientation, which takes into consideration the effect of both elongational and shear flow on the fiber orientation evolution during the filling of a mold cavity. The model is objective and shows better performance in comparison to state-of-the-art fiber orientation models when compared to μCT-based fiber orientation measurements for several industrial parts. The model is implemented using the simulation software Autodesk Moldflow Insight Scandium® 2019.

Fill Factor Effects in Highly-Viscous Non-Isothermal Rubber Mixing Simulations

A finite volume technique in a commercial computational fluid dynamics (CFD) code is employed in this study to simulate transient, incompressible, non-Newtonian and non-isothermal rubber mixing. The simulation processes are conducted in a two-dimensional(2D) domain, where a mixing chamber partially-filled with rubber is equipped with a pair of two-wing non-intermeshing counter-rotating rotors. The main objective is to assess the effect of different fill factors of rubber on dispersive and distributive mixing characteristics by simulating 15 revolutions of the rotors rotating at 20 min−1. 50%, 60%, 70%, 75%, 80% and 90% are the six different fill factors chosen for the study. An Eulerian multiphase method has been applied to solve for the two different phases, rubber and air. The non-Newtonian property of rubber is handled using the shear rate dependent Carreau-Yasuda model, along with an Arrhenius function to include the temperature dependency. In addition to the governing equations related to the conservation of mass, momentum and energy, the volume of fluid (VOF) method is chosen to track the interface between air and rubber. With regard to the results, flow patterns, thermal distributions, viscosity behavior and volume fraction are analyzed for the different fill factors. In addition, dispersive and distributive mixing behavior is also assessed in detail using Lagrangian statistics, such as mixing index, cumulative distribution of maximum shear stress, cluster distribution index (CDI), scale of segregation (SOS) and length of stretch (LOS), calculated from massless particles. Both the Eulerian and Lagrangian results showed that fill factors between 70% and 80% presented the most reasonable and efficient mixing scenario, and also exhibited the best dispersive and distributive mixing characteristics combined.

Three-Dimensional, Non-Isothermal Simulations of the Effect of Speed Ratio in Partially-Filled Rubber Mixing

Three-dimensional, transient, non-isothermal calculations have been carried out using a commercial computational fluid dynamics (CFD) software in a two-wing rotor-equipped chamber partially-filled (75% fill factor) with rubber, to analyze the mixing efficiency for three different rotor speed ratios of 1, 1.125 and 1.5. The moving mesh technique has been used to incorporate the motion of the rotors. The Eulerian based volume of fluid (VOF) method has been used to track the interface between the two fluids, which are rubber and air. To assign the highly viscous and non-Newtonian properties of rubber, the Carreau-Yasuda model along with an exact Arrhenius formulation that accounts for the shear and temperature dependent viscosity, has been used here. Governing equations including the continuity, momentum and energy equations have been solved to characterize the flow field and various mixing parameters. Eulerian-based fields such as velocity magnitude, viscous heat generation, and average temperature and viscosity are compared between cases with different speed ratios. Dispersive and distributive mixing behaviour are assessed through a Lagrangian approach that tracks the paths of a set of massless particles. Statistical quantities such as cumulative distribution of maximum shear stress, cluster distribution index, and axial and inter-chamber particle transfer rates are calculated and presented as well. Results showed that the speed ratio of 1.5 displayed the best dispersive and distributive mixing characteristics in comparison to the other cases.

Numerical Investigation of Effect of Rotor Phase Angle in Partially-Filled Rubber Mixing

Among several operational parameters such as rotor speed, fill factor and ram pressure, the orientation of the mixing rotors with respect to each other plays a significant role in the mixing performance. An understanding of the flow field and mixing characteristics associated with the orientations of the rotors will help in obtaining a final product with a better quality. For that purpose three phase angle orientations: 45°, 90° and 180° are investigated here in a 75% filled chamber with two rotors counter-rotating at an even speed of 20 min–1. Two dimensional, transient, isothermal, incompressible simulations are carried out using a CFD code. While an Eulerian multiphase method was used to solve for the transport variables in the two phases: rubber and air, the volume of fluid (VOF) method was used to solve for the interface between the two phases. A non-Newtonian Carreau-Yasuda model was used to characterize rubber. Massless particles were injected in the domain to calculate statistical quantities in order to assess dispersive and distributive mixing characteristics associated with rotor orientations. The flow field is analyzed via pressure and velocity contours. Dispersive mixing was analyzed through histograms of mixing index and cumulative probability distribution functions of maximum shear stress experienced by the particles. Distributive mixing was quantified statistically using cluster distribution index and interchamber material transfer. The phase angle of 180° was found to perform the best in terms of both dispersive and distributive mixing characteristics.

Processing of Metallic Pigments in a Co-Rotating Twin-Screw Extruder Studied by Means of Dielectric Analysis and Terahertz Spectroscopy

When working with polymeric compounds containing metallic particles, it is essential to know the influence of the shear rate of different screw elements in a co-rotating twin-screw extruder (TSE) on particle size distribution and particle shape. Particle size and form are significant for various processing conditions. A large variety of TSE screw and mixing elements and a wide range of complex mixing geometries are available for processing polymeric compounds with metallic pigments. In this case study, we investigated the feasibility of extruding powder coatings containing metallic pigments as a replacement for the conventional bonding process. Further, we examined the influence of different screw elements on particle size by means of optical microscopy, scanning electron microscopy, dielectric analysis and terahertz spectroscopy.