Solids conveying in screw extruders part II: Non isothermal model

Isothermal solids conveying theories have been developed in the past. However, due to friction, the surface temperature of the solid plug does increase. This change in temperature will strongly affect the temperature sensitive coefficients of friction and consequently also the pressure that develops. The surface temperature of the solid plug is also an important variable on its own because, when it reaches the melting point, the solids conveying zone is terminated. A mathematical model has been developed to calculate the temperature profile in the solid plug together with the strongly interacting pressure profile. Calculations indicate that high pressure in the solids conveying zone can practically be obtained only by very efficient cooling of the barrel in this zone.     

Solids conveying in screw extruders part I: A modified isothermal model

An improved theoretical model was derived for the solids conveying zone of a plasticating extruder. The model makes possible calculations in variable channel depth section. It also allows for a bulk density which is a function of pressure and for the non-isotropic pressure distribution in the solid plug. An expression for maximum flow rate was also derived. Results simulated by the model on a computer indicate the effect of variables on extruder performance. The power consumption terms in the solids conveying zone of a plasticating extruder were also derived. Total power consumption is the sum of power consumptions on the barrel surface, screw surfaces and those due to pressure rise. Their relative importance was analyzed by computations. The effect of operating conditions and coefficients of friction on the various power terms was also analyzed.     

Dependence of solids conveying on screw axial vibration in single screw extruders

In the single‐screw extruder, the vibration force field is applied to the solids conveying process by the axial vibration of the screw and the novel concept on the solids conveying process being strengthened with the vibration force field has been brought forward in this study. We establish the mathematical model that describes the solids conveying process with the vibration force field and obtain the approximative analytical solutions of the pressure and velocity of the solids conveying in the down‐channel. In the new theory, if the screw has no axial vibration the solids conveying pressure is the same as that of the Darnell and Mol theory, but the density and velocity of solids conveying along the screw channel is variable, which has modified the Darnell and Mol theory in which the density and velocity of the solids conveying along the screw channel was considered invariable. The results reveal that the axial vibration of the screw can increase the average pressure of solids conveying, decrease the channel length of the solids conveying section and increase the solids conveying angle. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 2998–3007, 2006     

Maximum pressure developed by solid conveying force in screw extruders

There are two distinct solid conveying theories that can be applied to plasticating screw extruders. One is Darnell and Mol's theory based on a solid-to-solid friction model and the other is Chung's theory based on a viscous shearing model. The two theories predict very different solid conveying performances for a same set of conditions. In this paper, the maximum pressures that can be developed inside plasticating screw extruders by the solid conveying force are calculated using each of the two theories. Comparison of the results may shed some light on the applicability of each theory for a particular extrusion operation.     

Modeling of the conveying of solid polymer in the feeding zone of intermeshing co-rotating twin screw extruders

In this paper, a model for the conveying of solid polymer in the feeding zone of intermeshing co-rotating twin screw extruders is proposed. The theoretical model uses an approach that is similar to that commonly used in single screw extruders; however, it takes into account the particular geometry of the screw channel, the partially filled channel, and the special configuration of the two self-wiping screws. The model thus considers two conveying mechanisms: the first one in the channel, which is analyzed in terms of polymer-metal friction, and the second one, which is mainly an axial transport in the intermeshing zone. The theoretical predictions of the model are compared with the experimental results obtained on a laboratory extruder with a polymer in powder form, and satisfactory agreement is observed. The model enables the prediction of the evolution of the filling of the screws towards the geometry and the operating conditions. This is an important key to analyzing the thermal aspects in this zone, which can lead to a prediction of the melting capacity of the extruder. Indeed, the filling of the feeding zone defines the heat transport that occurs between the hot barrel and the solid polymer.     

The torque in the metering zone of single screw extruders

To study the energy dissipation in the different zones of an extruder, a special barrel has been designed where local torques T_q can be measured at the beginning of the conveying, the transition, and the metering zone. Experiments carried out for a commercial polyethylene and poly(vinyl chloride) at different processing conditions show that in some cases negative T_q in the metering zone may occur. A very basic analytical treatment of the flow situation in the metering zone shows that for a given drag flow T_q is dependent on the pressure gradient and particularly on its sign. T_q decreases with decreasing positive pressure gradient until there is pure drag flow. It further decreases with increasing negative pressure gradient until it becomes zero and even negative. A comparison of theoretical and experimental results for the metering zone shows good quantitative agreement though the main aim of the paper is to provide a better general understanding of the complex situations inside an extruder.     

Solids conveying in the solids compaction zone of vane extruder

On the basis of the forces on the differential element in the solids bed, a function between bulk density and pressure, and the nonisotropic pressure distribution in the element, an expression of pressure in the circumferential direction is derived. And the total power introduced through the positive conveying and the friction dragging conveying is also deduced. Experimental data are obtained using a self‐developed and simplified vane extruder with an adjustable rotor eccentricity. The solids conveying mechanism in the solids compaction zone of a vane extruder is theoretically and semiempirically confirmed. Besides, the various portions of total power consumption including the power dissipated on the surfaces of the stator and baffles, the power used to build pressure and the power converted into rotational kinetic energy are derived. The effects of the eccentricity on the solids conveying are also discussed theoretically and semiempirically. POLYM. ENG. SCI., 55:719–728, 2015. © 2014 Society of Plastics Engineers     

Twin screw extruders: The latest developments

This month's Plastics Additives & Compounding discusses some of the latest developments in twin screw extrusion technology for the compounding and masterbatch industries.     

Surging in screw extruders

Output uniformity is one of the main factors limiting the maximum output obtainable from a single screw plasticating extruder, and is adversely affected by surging. Several causes of surging have been identified, perhaps the most important being instabilities in the melting process. These are caused by periodic break-up of the bed of compacted solid polymer formed in the screw channel. Solid bed break-up is shown, both experimentally and theoretically, to be associated with rapid acceleration of the bed in the downstream direction parallel to the screw flight. A novel method of measuring solid bed velocity and hence acceleration is described. The theoretical model of the melting process is shown to be capable of predicting this acceleration reliably, and therefore the tendency for a particular combination of screw design, material and operating conditions to cause surging.     

Melting performance of single screw extruders with a grooved melting zone

A novel melting model for single screw extruders with a grooved melting zone was established. The whole solid plug, which came from the grooved feed zone, was ruptured and melted mainly by continuously changing the volume of the barrel grooves and the screw channel in the grooved melting zone. A new single screw extruder platform with hydraulic clamshell barrels was constructed to investigate the melting of solid polymer with different combinations of barrels and screws. The melting model was verified by experiments. The results showed that the melting started earlier and finished in a shorter length for single screw extruders with a grooved melting zone than that for conventional single screw extruders and the melting efficiency was improved by introducing a grooved melting zone to a single screw extruder. The theoretical values are consistent with experimental results. The novel single screw extruder with grooved melting zone can dramatically increase the plasticizing efficiency and the throughput.     

Melting in single screw extruders

A model for the melting of granules in a single screw extruder is presented in Part I. It is consistent with observations of earlier workers and retains some of the ideas introduced by Tadmor in his model; however, it assumes that the solid bed of granules cannot stand large differences of principal stresses and so account has to be taken explicitly of the downstream force balance on the solid bed and in the melt pool. Detailed quasi-analytic results are given for a Newtonian (constant viscosity) fluid in Part II. These illustrate the model for a particularly simple case and have relevance for some materials. A more elaborate numerical scheme is described in Part III for a non-Newtonian model and results are presented for comparison with the predictions of other theories and with experiments.     

Melting in single screw extruders

A model for the melting of granules in a single screw extruder is presented in Part I. It is consistent with observations of earlier workers and retains some of the ideas introduced by Tadmor in his model; however, it assumes that the solid bed of granules cannot stand large differences of principal stresses and so account has to be taken explicitly of the downstream force balance on the solid bed and in the melt pool. Detailed quasi-analytic results are given for a Newtonian (constant viscosity) fluid in Part II. These illustrate the model for a particularly simple case and have relevance for some materials. A more elaborate numerical scheme is described in Part III for a non-Newtonian model and results are presented for comparison with the predictions of other theories and with experiments.     

The operating characteristics of twin screw extruders

The operation of a twin screw extruder processing a powder or granular solid is reviewed. The operating variables of screw speed and barrel temperature profile interact with a number of design parameters— screw design, die geometry, feed zone geometry and with the material properties, in determining machine performance. The factors that determine output and pressure development are specified in a sequence of block diagrams. The dynamic response of an operating machine to disturbances in the steady state conditions is explained in the light of the established relationships and interpreted in conventional control theory terms. Attention is drawn to the importance of mixing in the chambers formed by the screw channels and of the residence time distribution in determining the quality of the final product.     

The melting performance of single screw extruders

A number of recent screw designs is analyzed for melting performance, using a simple analytical approach based on Tadmor's original work. The melting length for a screw with constant depth channel is used as reference. An ideal compression screw will have a melting length of one-half the melting length of the reference screw. The Maillefer melt separation principle is discussed. The Maillefer screw melts in 2/3 of the length of the reference screw. Screws by Barr, by Dray and Lawrence and by Kim are shown to approach the ideal compression screw. A new design screw, using ideal compression and multiple channels and having a very large screw pitch, is shown to be a considerably more efficient melting device than any of the other, screws discussed.     

Melting of thermoplastics in single screw extruders

Some experiments on the melting of thermoplastic polymeric materials in single screw extruders are described. Although these were of the now familiar screw extraction type, special care was taken to distinguish between material melted by screw rotation and that melted during the subsequent cooling operation. A barrel which could be split longitudinally was also used, thus avoiding some of the disadvantages of axial extraction. A theoretical model is proposed which, unlike previous models, allows the solid bed of material in the screw channel to accelerate naturally, and also allows for the presence of a film of molten material between the bed and the screw. This model gives satisfactory predictions of melting performance. Comparison with experimental results shows that break-up of the solid bed occurs when the model predicts rapid acceleration of the bed. Bed break-up and the resulting surging may be reduced or prevented by the use of screw cooling which has the effect of inhibiting the formation of a melt film at the screw surface.     

The melting performance of single screw extruders. II

In the previous paper (1) the melting performance of a number of recent screw designs was analyzed, using a rather simple theory. A new screw design was proposed. Here the results of more elaborate calculations, are given in which the influence of the flight clearance and of a shear-thinning temperature dependent viscosity are investigated. The former conclusions are not altered in essence by these effects. Experimental results with a prototype screw are presented, showing that melting capacity is increased. Up to 100 percent increase in throughput is possible in the high RPM range (in comparison with a much longer traditional compression screw), provided that the feed capacity is sufficient. This usually requires the use of a grooved, well-cooled, feed section; the capacity of such a feed section depends, for a given screw geometry, on channel depth and granule dimensions. The melt leaves the melting section at a relatively low temperature. The melting section only melts the material and does not raise, its temperature unnecessarily. A further step towards separating distinct tasks of the extruder by functional screw design has been made.     

Analysis of mixing in modified single screw extruders

A numerical model of mixing in single-screw extrusion is developed which uses a two-dimensional unsteady analogue to three-dimensional continuous mixing. This two-dimensional unsteady analogue uses the transverse and axial velocities to calculate an apparent tránsverse streamline velocity which is used to simulate mixing. The mixing calculations are rigorously correct for continuous mixing of well-metered streams of equal-viscosity Newtonian fluids in continuous mixers of constant envelope. This scheme is applied to the analysis of singlescrew extruders with stepwise varying cross-section, particularly beginning and ending flights. The numerical simulation produces patterns qualitatively similar to those observed in mixing experiments and predicts behavior for unmodified extruders in close quantitative agreement with experiments.     

Theory of mixing sections in single screw extruders

A discussion of the effect of deformation on mixing leads to reorientation of fluid interfaces as a proposed mechanism for special “mixing sections” in single screw extruders. Based on the kinematics of mixing it is shown how a mixing section can greatly decrease the amount of work necessary to accomplish extensive mixing through orienting the fluid more favorably for mixing by subsequent shear. Mathematical development quantitatively describes favored configurations of mixing sections. An upper bound for the mixing performance of a simple model of an extruder with special sections is shown to be similar to turbulent mixing. Based on this theory the key actions of the special sections are identified.     

Mixing and residence time distribution in melt screw extruders

The residence time distribution (RTD) functions were derived for screw extruders, based on the “parallel plate” and curved channel flow models. The results indicate a relatively narrow distribution, and they explain several characteristics of screw extruders. The strain distribution in the fluid across the channel was also derived. With the aid of these two functions an average strain of the fluid leaving the extruder was defined. The resulting weighted-average total strain (WATS) provides a quantitative criterion to the “goodness of mixing” in extruders.