Simulation of polymer flow through a coat-hanger die: A comparison of two numerical approaches

Coat-hanger dies are commonly used for the extrusion of plastic sheets and films. To describe the flow of a molten polymer through a coat-hanger die, a two-dimensional approach is necessary. Moreover, the thermal effects, which play an important role in the flow distribution, have to be taken into account. In this paper, two numerical models for the simulation of coat-hanger dies are described and compared. These models differ mainly in the simplifying assumptions used and in the treatment of the thermal problem. The simulations obtained with the two models were compared with each other and with experimental data. The discrepancies between the two models can be explained by the different theoretical treatments.     

Three-dimensional modelling of Non-Newtonian fluid flow in a coat-hanger die

The three-dimensional model of isothermal flow of power-law fluid in a coat-hanger die has been developed using finite element method. The shape of coat-hanger die used in the present model was determined according to the previous analytical design equation which is based on one-dimensional flow model in the manifold and the slot. Because uniform flow rate across the die outlet is most important to achieve uniform thickness of extruded polymer sheet or film, flow rate distribution is mainly examined to determine the valid process condition for the design equation as the design parameters are changed. The effects of fluid property in terms of power-law index and process parameters not considered in one-dimensional design equation such as die inlet size and the presence of land were analyzed. Results show that the manifold angle is the most influencing design parameter on flow rate distribution. When the material of different power-law index from design value is processed, the change of power-law index affects the uniformity of flow rate appreciably.     

Analysis and simulation of non-Newtonian flow in the coat-hanger die of a meltblown process

Meltblown is one of the fastest growing processes for nonwoven production. The design of the coat-hanger geometry of a die is very important for meltblown technology. In this article, melt rheological properties were studied based on capillary rheometry, followed by analysis and simulation of the melt flow in the die and its experimental verification. It is essential for the optimal design of the die and helps to better understand the meltblown process as well. The result of this research showed that the rheological properties of melt flow in the die obey the power-law equation very well in the meltblown process. The coat-hanger die has a good operation feasibility for different resins and various operation conditions from the view of web uniformity. The pressure drop through the orifices is the major contribution to the pressure drop in the die. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67: 193–200, 1998     

Residence time distribution of polymer melts in the linearly tapered coat-hanger die

This article analyzes the average residence time distribution of polymer melt across the die width in a common linearly tapered coat-hanger die, which excells the T die but is a little inferior to the curvilinearly tapered coat-hanger die in residence time uniformity according to the approximated calculation of ten used. From another point of view, a linearly tapered coat-hanger die may be designed so that a desired ratio of the residence time through the die far end to that along the die center line may be imposed as one of the design constraints.     

Geometry design of a coat-hanger die with uniform flow rate and residence time across the die width

This article provides an approximate but sufficiently practical method of geometry design of a coat-hanger die having both uniform flow rate and residence time across the full width of the die. Such a die is often needed when a heat-sensitive resin such as poly(vinyl chloride) is sheeted, because different residence times across the die width are apt to cause a sheet defect in the transverse direction of the sheet. Although some assumptions were made facilitating mathematical analysis, an application of this method to a sheeting die 1 m wide gave good uniformity of flow rate and residence time.     

Two-dimensional multilayer coextrusion flow in a flat coat-hanger die. Part I: Modeling

The multilayer stratified flow of several polymers in a flat coat-hanger die was modeled using a finite element method. The problem was formulated using the lubrication approximation theory. A solution procedure in decoupling pressure and streamlines was developed. This new method is very powerful in comparison with more classical approaches, permitting the solution of flow problems involving a great number of layers in a complex industrial geometry. It allows us to obtain, among other things, pressure field, streamlines, residence times, and the values of the interface positions in the whole die.     

Design and analysis of a dual-cavity coat-hanger die

A method for the design and analysis of a dual-cavity coat-hanger die is presented in this paper. A macroscopic material balance and a microscopic flow analysis using the finite element method are combined to simulate polymeric fluid flow inside the die. Leonard's macroscopic procedure was adopted to include inertial, gravitational, and viscous effects, and the finite element method was then applied to estimate the contributions of inertial and viscous terms. In addition, the flow patterns in the outer cavity were computed by the finite element method so that the appearance of an undesirable vortex could be predicted. The residence time distributions for flow in the die were approximated by a simple, statistical approach. It was found through a case study that a dual-cavity coathanger die can effectively reduce the flow non-uniformities caused by fluid inertia and viscosity variations.     

Computer-aided analysis of a linearly tapered coat-hanger die

We describe the computer-aided engineering analysis of a linearly tapered coat-hanger die in this paper. The general governing equation for flow distribution inside the die was derived first. On the basis of this equation, we have developed the design formula for a die to deliver uniform flow. In addition, we have also examined the variations of lateral flow uniformities and residence time distributions of polymeric liquids under several different design and operating conditions: (1) using manifolds with non-circular cross-sections, (2) adjusting production widths, (3) delivering fluids with different viscosities, and (4) enlarging manifolds for practical production considerations.     

Shear flow of molten polymer in melt blowing

Besides the air flow field, the flow field of molten polymer plays a key role in fiber formation in the melt‐blowing (MB) process. In this article, the flow field of molten polymer was discussed, and its effects on the fiber microstructures were studied through theory and experiments. First, this field was supposed to be a kind of shear flow field. Two equations were introduced and solved. Then, analyzing the solutions combining with the actual melt‐blown practice, we concluded that the distribution profile of this flow field was a series of inverse parabolic in the course of the polymer stream attenuating. Further inferring from this flow pattern, we could also assume that there could have been a novel cross‐sectional microstructures in the melt‐blown fibers. Finally, the comparison experiments concerning the MB and its fibers were designed and carried out. The results indicated that the shear flow field could be qualitatively described by the equations, and the assumptions about the microstructures are basically in agreement with the experimental results. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Two-dimensional multilayer coextrusion flow in a flat coat-hanger die. Part 2: Experiments and theoretical validation

In a previous paper (1), a two-dimensional computation model for multilayer flows in coat-hanger dies was proposed. It was based on lubrication approximation theory and enabled us to obtain the pressure field, the streamlines, and the interface positions in the whole die. The present paper is aimed to present experimental results obtained on an industrial line for a three-layer configuration and to compare the results to the theoretical computation. The order of magnitude of pressure drops, flow rates, and interface positions were correctly predicted by the model. Some remaining discrepancies may be explained by the isothermal assumption and the lack of encapsulation mechanism in the computation.     

Heat transfer to molten polymer flow in tubes

This article presents the results of a numerical study (finite differences) of the heat transfer problem in flowing polymer melts. The tube wall is assumed to be at a constant temperature. The rheological behavior of the melt is described by a power law temperature-dependent model. A convective and a viscous dissipation term are included in the energy equation. Temperature profiles, bulk temperatures, and Nusselt numbers are presented for a variety of flow entry temperatures.     

Investigation of the flow of molten tellurite glass in a double-crucible die

The viscoplastic flow of molten tellurite glass realized during the process of the drawing of an optical fiber through a double-crucible die was numerically investigated. The procedure for the computational experiment and the results of the simulation, including those obtained under local temperature disturbances, regarding the interactions between the melts in the die outlet part during the starting and stationary flow stages were described. The computational investigations were performed with the use of the ANSYS CFX software.     

A unified lubrication approach for the design of a coat-hanger die

A simple unified lubrication approach has been proposed to design a coat-hanger die that can deliver wide and uniform liquid sheets. This approach requires that the wall stress in the manifold be constant. With this constraint, any inelastic non-Newtonian fluid model can be used to describe the liquid motion inside the die. Fluid models that can represent the pseudoplastic or viscoplastic behavior of polymeric liquids have been selected for illustration. A general equation that can be solved to determine the effect of production variations on flow uniformity inside the die has also been derived.     

Theoretical and experimental study of the flow of a molten polymer in a micro-compounder

Micro-compounders are more and more used to characterize and optimize the formulations and the flow conditions of complex materials, with very low quantities, around a few grams. These machines are composed of a small-size conical twin-screw extruder, coupled with a recirculating channel, in which the material can be processed during a fixed time and a certain number of cycles, before being purged. However, the precise flow conditions inside these machines are not well known, what makes an optimal interpretation of the results difficult. Therefore, in this paper, a theoretical model based on continuum mechanics is proposed to calculate the flow in the recirculating mode. An experimental study on a well-chosen polymer is carried out to define the influences of the main processing parameters (screw speed, mass of material, barrel temperature) and to validate the model. Despite the simplicity of the theoretical approach, the calculated results are in satisfactory agreement with the experiments.     

Mechanism of fibrillation in the flow of molten polymer mixtures

Experiments on the flow of melts of mixtures of thermodynamically incompatible polymers show that ultra-fine fibrils of one of the polymers form in the matrix of the other in the entrance to the extrusion orifice.     

3-D Non-isothermal die flow of power-law fluids with viscous heating

The nonisothermal flow of incompressible viscous non-Newtonian fiuids is analyzed numerically. A three-dimensional finite element code is developed for the flow simulation purpose. The energy equation is decoupled from the equations of motion and both the flow field and the thermal field are solved iteratively. Two dimesionless groups, the Peclet number and the Brinkman number, are introduced to represent the characteristics of the thermal field. Results are presented for velocity, pressure and temperature distributions in the entrance region, and comparisons made with various mesh layouts. The results provide new insight into the temperature regulation in the extrusion process.     

Non-isothermal laminar channel flow

This article deals with the non-isothermal, laminar flow of a power-law fluid between parallel plates with a constant plate temperature. The fluids are assumed to be incompressible and to have constant physical properties except for the consistency-index, which latter quantity is assumed to vary exponentially with temperature. Calculations are performed on the “non-isoviscous” hydrodynamics and heat transfer rate. The results are presented as logarithmic mean Nusselt-numbers and dimensionless velocity distributions and pressure drops as a function of the dimensionless axial length in the channel and as a function of a quantity Q which measures the deviation of “isoviscous” fluid behaviour.The heat transfer rate appears to be a unique function of the velocity gradient at the wall, independent of the fluid rheology.All results have been summarized in a few practical approximations and are verified experimentally with pressure drop and heat transfer measurements of laminar, newtonian channel flow. It turns out that the results may be applied to flow between rectangular ducts up to aspect ratios H/B = 0·25.     

Theoretical and experimental study of the molten polymer flow in the calender bank

The flow of molten polymers in the calender bank has been computed using a finite-element method with stream function and vorticity. Two nonsymmetrical-recirculating regions have been obtained fully in agreement with the experimental observations on poly(vinyl chloride) melt banks. The pressure distribution along the flow axis is very close to the one obtained using the classical-lubrication approximation.     

A study of bubble nucleation in a mixture of molten polymer and volatile liquid in a shear flow field

Bubble nucleation in a mixture of volatile liquid and polymer melt under shear flow conditions was investigated, using a light scattering technique. In the study, a mixture of polystyrene and trichlorofluoromethane was extruded through a slit die having glass windows and bubble nucleation in the flow channel was observed optically. A He-Ne laser was used to illuminate the nucleating and growing bubbles. The light flux scattered by the growing bubbles at a fixed angle was detected by a photomultiplier with the aid of a high-voltage power supply. The bubble nucleating site in the flow channel was located using a computer controlled tracking system, which was designed to move the entire optical system automatically in the three dimensional space, and also had the ability to follow the software control command and cooperate with the data acquisition system. When the site of bubble nucleation was located, the coordinates of this site in the flow channel and the experimental conditions were automatically recorded on a floppy diskette by entering a software command. The pressure profile along the flow channel was measured by pressure transducers, with the aid of a microprocessor-based pressure reading system. It has been found that the site of bubble nucleation varies with the position in the direction perpendicular to the flow direction, which is attributed to the nonuniform velocity and stress distributions in the slit flow channel. The present investigation suggests that bubble nucleation can be induced either by flow and/or shear stress; specifically, flow-induced bubble nucleation is the dominant mechanism at positions near the center of the die opening, and shear-induced bubble nucleation is the dominant mechanism at positions near the die wall. It should be mentioned that the bubble near the die wall may also be generated by cavitation brought about by the surface roughness of the wall and also by thermal fluctuations due to the heat transfer between the metal (die wall) and the mixture of polymer and volatile component. The present study indicates that bubble nucleation in a shear flow field can occur at an unsaturated condition. This is in contrast to bubble nucleation under static conditions, where supersaturation is necessary.     

Non-isothermal phenomena in polymer engineering and science: A review. Part II: Non-isothermal phenomena in polymer deformation

Thermal phenomena in deformation of solids and flows are reviewed. Regularities common to all these phenomena as well as their characteristic features and consequences important for science and engineering are reported. The analogy between thermal phenomena in polymer mechanics and in chemical reaction is noted.