Measurements of residence time distribution for the peroxide degradation of polypropylene in a single-screw plasticating extruder

Measurements of the residence time distribution (RTD) in a single-screw plasticating extruder were carried out during experimental studies of the peroxide-initiated controlled chemical degradation of polypropylene (PP). A radioactive tracer method was employed, and the effect of screw speed, temperature, and reaction on the RTD was examined. An increase of the peroxide concentration resulted in a broader distribution whereas an increase of the extrusion temperature was found to result in a narrower distribution. Use of low screw speeds simply increased the time delay through the extruder without affecting considerably the breadth of distribution. Results obtained from the present experiments were compared with several theoretical models.     

Numerical simulation of fluid flow and heat transfer in a single-screw extruder with different dies

In a plasticating screw extruder, a polymer melt forms in the melting zone of the extruder. Pressurization of the molten polymer takes place in the melting and the metering sections so that the melt can flow through the restricted passage of the die and assume a desired shape. In a melt fed extruder, the throughput is governed by the pressure rise over the entire length of the extruder. The pressure developed in the screw channel may also be employed in rapid filling of molds, such as those in injection molding. When the geometry of the screw, the barrel temperature, and the die are selected, a unique set of operating parameters arise for a particular flow rate or screw speed. In the present study, numerical and analytical methods are used to calculate the transport in the extruder and the pressure drop in the die. An iterative numerical method based on solving the equations of motion and energy in the screw channel and a correction scheme to couple the die with the screw channel is discussed. The numerical algorithm is capable of handling an arbitrary variation of the viscosity of the polymeric fluid with the shear rate and temperature. The results obtained by simulating the fluid flow in the screw channel are compared with available numerical and experimental results in the literature, indicating good agreement. The performance characteristics of the extruder, for chosen thermal boundary conditions and screw geometry, are presented for different die geometries and different fluids. The important considerations that arise in the numerical simulation of the extrusion process are also discussed.     

Dynamic model of a plasticating extruder

A theoretical model for the simulation of dynamic operation of a plasticating extruder is proposed. The model can be recommended as a tool to study various dynamic situations of interest in the operation of an extruder. Several responses to changes in operating conditions are discussed. They indicate the occurrence of transient maximas and occasional oscillations. The controlling of flow rate by adjusting a valve at the die seems to cause temporary local high peaks in pressure, whereas its control through screw speed seems to be satisfactory.     

A plasticating model for single-screw extruders

By measuring the solid-bed transfer velocity, width and thickness under various conditions, die following results are obtained. As the result of melting, the solid bed decreases in width and thickness almost with the same rate, and the solid-bed transfer velocity is constant, while a melt layer exists between the solid bed and the screw root; also, when the phenomenon of dam-up occurs, caused by the combined effect of decreasing depth of the screw channel with tin insufficient decrease of solid-bed thickness, the transfer velocity increases proportional to the rate of decrease of channel depth. Consequently, the solid bed is considered to behave us loosely packed particles. A new plasticating model is developed by making the above results an assumption and adopting finite differential calculus with the Newton-Raphson method to obtain accurately the melting velocity, melt profile, and solid-bed temperature. Calculated values are in remarkably good agreement with the experimental values Solid-bed softening point, pressure, and screw torque are also successfully estimated.     

On the dynamics and control of a plasticating extruder

In recent years, there have been many papers published on the application of process control to plasticating extruders. Much of the literature concentrates on the more classical control techniques. However, recent research has studied the application of stochastic identification techniques for building transfer function models for the extruder. In particular, the relationship of screw speed to die pressure and temperature has been studied. In the present work, both step tests and pseudorandom binary sequence tests were used to study the process dynamics of a 38 mm Killion extruder having a Iength-to-diameter ratio of 24:1. This study concentrates on the regulation of the extruder pressure in the face of its inherent surging characteristics. Variations in the quality of the feed plastic were studied through pulse and step changes in input polymer composition. Significant control problems resulted from measurement noise, which appeared at the same frequency as the screw rotation speed. Various mathematical filters to reduce the effect of this noise on the control variables were studied.     

A dynamic melting model for a single-screw extruder

A new theoretical concept is given which provides an efficient and consistent method for predicting flow and heat transfer characteristics of the melting zone for a large single-screw extruder. In contradistinction to previous, theories, significant melt accumulation in the molten films as observed experimentally is considered, instead of postulating the melt accumulation in the “melt pool”. The mathematical model has been obtained by the simultaneous solution of the momentum and energy equation of the melt flow and. solid bed, allowing for the existence of the pressure gradient: The theory is supplemented by a numerical example which shows good agreement with experimental data obtained on a 90 mm extruder with polypropylene, where the down-channel pressure profile and me profile of the solid bed Were taken as yardsticks for the melting process. For exact determination of the area for applicability of this theory, more experimental information is required.     

Lattice Boltzmann simulation of power-law fluid flow in the mixing section of a single-screw extruder

The single-screw extruder is commonly used in polymer processing where the performance of the mixing section is significant in determining the quality of the final product. It is therefore of great interest to simulate the flow field in a single-screw extruder. In this paper simulations of non-Newtonian fluids in a single-screw extruder are performed using the lattice Boltzmann model.     

On the scale-up of plasticating extruder screws

In the most commonly used scale-up method of plasticating extruder screws, the screw channel depth is increased by the square root of the diameter ratio while the screw RPM is decreased by the square root of the diameter ratio such that the output rate increases proportionally to the square of the diameter ratio. This scale-up method, largely based on the pumping function of the screw, often leads to a higher melt temperature, a higher screw horsepower consumption per unit output rate and an inferior melt quality from the larger diameter screw. Analysis of the common scale-up method reveals that, although the shear rate in the melt is kept constant, the average residence time and the peripheral screw speed are increased for the larger diameter screw. Our recent study on the melting mechanism also reveals that the melting capacity increases less than the pumping capacity. A detailed examination of the common scale-up method in this paper shows that the pumping capacity and the solid conveying capacity increase more than necessary while the melting capacity increases insufficiently.     

On modeling the solids conveying zone of a plasticating extruder

A model for the solids conveying zone of a plasticating extruder is presented. The flow of solid granules is studied in the framework of thermomechanics of media with affine structure, and assimilated to plane steady flow of an incompressible viscous fluid with spherical indeformable structure. Simple constitutive equations are accepted, along with those kinematical assumptions which stem directly from the geometry of the system. The resulting balance equations are given a dimensionless form, and integrated so as to arrive at closed-form solutions for velocity, spin and temperature of granules. A discussion of the influence of the adimensional parameters relevant to the problem is presented; this discussion is supplemented with some examples. Finally, various developments and refinements of the present model are proposed.     

Mathematical modeling of melting of polymers in a single-screw extruder

This paper addresses the apparent controversy surrounding the role of the solid bed mechanics in the Maddock melting mechanism. It is demonstrated that the inability of the melting models based on the freely deformable solid bed concept to predict accurately the pressure gradients in the melting zone is not exclusively due to the highly simplified isothermal Newtonian treatment of the melt pool as presumed previously. This study has shown that when using a non isothermal non-Newtonian flow model for the melt pool, the freely deformable solid bed concept still results in unrealistically low pressure gradients while it may give good predictions of the melting rates. To the contrary, when a rigid solid bed is assumed, the pressure predictions tend to represent the experimental data more closely, whereas the theoretical melting rates seems to become less realistic. In view of the fact that both the freely deformable and the rigid solid bed concepts show such inconsistencies, it has been concluded that the mechanics governing the solids and melt transport in the melting zone require some additional examination, most notably, the influence of the constitutive behavior of the solid bed and of the cross-channel melt circulation around the solid bed, and possibly of the melting kinetics for semicrystalline polymers.     

Movement of powders in a single-screw extruder at high counterpressure

Mathematical models for the conveying of powder resins in single-screw extruders with smooth barrels are well known. It is the aim of this paper to define the range of operating conditions where these models can be adapted to single-screw extruders with grooved barrels. In order to calculate throughput and torque characteristics the relevant friction parameters and powder properties have been determined. Furthermore it has been clarified to what extent the friction forces in grooved barrels can be described by a coefficient of effective friction. The influence of dynamic bridge formations in grooved areas is discussed.     

Pressure development in the melting zone of a single-screw extruder

An analysis is given of the pressure generation mechanism in the tapered channel of a single-screw extruder. It is shown that when increasing the throughput the pressure build-up capacity of the melting zone tends to decrease. As a result, severe pressure drops may occur in the tapered sections. A relationship between the pressure profile and the melting mechanism (solid bed/melt pool configuration) is described in terms of the cross-channel melt circulation.     

A mathematical model for predicting dynamic behavior of a plasticating extruder

A mathematical model was developed to predict the dynamic behavior of flowrate and melt temperature in a plasticating extruder caused by changes in operating variables such as screw speed, back pressure and barrel temperature. The model has application for on-line computer control of an extrusion process or for simulation purposes off-line. Experimental data for developing the model was obtained from a 2½ in. diameter plasticating extruder producing high impact polystyrene sheet.     

Analysis of the performance of plasticating single-screw extruders with a new concept of solid-bed deformation

The performance of plasticating single-screw extruders is analyzed by combining three functional sections: (a) solids-conveying section, (b) melting section, and (c) melt-conveying section. In the analysis of the melting section, we have incorporated a new concept of solid-bed deformation (i.e., the rheology of the solid bed) into Lindt-Elbirli's analysis and included convective heat transfer in the energy equation. Specifically, we have computed stresses on the surfaces of the solid bed, which is surrounded by thin melt films and a melt pool, and, also, computed the apparent modulus of the solid bed in the bulk state as a function of temperature and position within the solid bed, along the extruder axis. From this information, we were able to compute the extent of solid-bed deformation, by assuming a linear stress-strain relationship as the constitutive equation of the solid bed. In this approach, we do not assume a priori whether the solid bed is rigid or freely deformable. The solution of the system equations gives us the following information: (a) whether or not the solid bed deforms and if it does, then, how much; (b) the solid-bed velocity along the extruder axis; (c) pressure profiles along the extruder axis; (d) solid-bed profiles in the melting zone along the extruder axis; (e) temperature profiles along the extruder axis; (f) velocity and temperature distributions in the melt pool along the extruder axis; and (g) thicknesses of thin melt films surrounding the solid bed. Theoretically predicted solid bed and pressure profiles along the extruder axis are compared with experimental results reported in the literature. We have pointed out an urgent need for measurements of the apparent modulus of the solid bed in the bulk state as a function of temperature and pressure, under a combined shear/drag flow field.     

Experimental deep-channel velocity profiles and operating characteristics for a single-screw extruder

Data have been obtained on the operation of a deep-channel single-screw extruder, pumping a Newtonian liquid under isothermal, developed flow conditions. Flow rate, screw speed, and pressure gradient characteristics were measured, and a tracer particle technique was employed to determine channel velocity profiles. The data were required for the testing and development of a computer model for flow in the extruder, which takes into consideration channel curvature. Results confirm the correctness of the computer solutions previously reported.     

Mathematical modeling of melting of polymers in a single-screw extruder a critical review

Deterministic mathematical models of the Maddock melting mechanism based on analytical and finite-difference solution methods are surveyed and classified according to the key assumptions involved. It has been concluded that the rigid solid bed concept coupled with a consistent non-Newtonian analysis of the melt flow pattern, including cross-channel circulation, leads to superior results. It is suggested that the development of the melting theory for the Maddock mechanism as an engineering analytical tool is virtually complete.     

Dynamic behavior of a single screw plasticating extruder part II: Dynamic modeling

The dynamic response of a 2.5 inch plasticating extruder and the extrusion line are modeled using high density polyethylene and acrylics us extrudate. Screw speed, back pressure valve position, and material changes are used as forcing functions. Three fundamental transfer functions in the Laplace domain: a first order, a second order, and a lead-lag, are developed to simulate the short term and long term responses of temperatures, pressures, and extrudate thickness. A kinetic-elastic model which can predict rheological properties of non-Newtonian, viscoelastic materials is also applied to the pressure responses of the extrusion process. This model can fit the experimental data well but due to the complexity involved in its parameter setting, more modifications are required before it can be applied for the control of extrusion process.     

Dynamic behavior of a single screw plasticating extruder part I: Experimental study

The dynamic responses of a 2–1/2 inch single screw plasticating extruder and extrusion line were investigated. Step changes in screw speed, take-up speed, back pressure, and processing materials were used to determine the transient responses of barrel pressures, die pressure, melt temperature, and extrudate thickness. Dynamic responses of the entire extrusion line can be explained by the flow mechanism of the extruder and the logical properties of the polymer used. A capillary rheometer was also used to determine if it could simulate pressure responses in the extruder for screw speed changes. Results showed that capillary rheometer was helpful in estimating the short term pressure responses in the die.     

Extrusion of non-newtonian fluids in a single-screw extruder with pressure back flow

The transport phenomena underlying the extrusion of non-Newtonian fluids in single-screw extruders is investigated numerically and experimentally. The viscosity of the investigated fluids is a strong function of the temperature and, for the non-Newtonian case, of the shear rate. Therefore, the governing equations of motion are coupled to the energy equation through the viscosity. The velocity in the down channel direction of the screw extruder is a result of both shear and pressure driven transport. The pressure acts in a direction opposite to that of the drag flow, and comparatively high pressures arise at the die in typical extruders. When a narrow die is used in the screw extruder, the pressure gradient in the down-channel direction becomes so large that the down-channel velocity near the screw root becomes negative in terms of the coordinate system fixed to the screw. The conventional marching schemes fail to simulate the fluid flow when the down-channel velocity becomes negative, since the downstream conditions are not known. Two different numerical schemes used to simulate the fluid flow in a single-screw extruder for this circumstance, which often arises when dies with high flow resistance are used and which is termed as pressure back flow in the literature, have been discussed. One scheme is based on including the down-channel thermal diffusion, making the problem elliptic, and the other scheme uses a different coordinate system. Both formulations are found to yield results that are fairly close. Experiments were also carried out to measure the pressures at three different locations in a single-screw extruder. The computed results were found to be in good agreement with the experimental results. The pressures at the die obtained numerically by treating the flow as isothermal are found to be lower than those obtained when the flow is treated as nonisothermal, indicating the strong influence of thermal transport in this problem.