A theoretical melting model for plasticating extruders

A theoretical model for melting in plasticating extruders is described. Compared to previous models, this model introduces more accurate and less restrictive assumptions, adds a mass balance on the entire channel, and replaces certain approximate solutions by exact solutions. Flow of the solid bed is represented by a solid bed acceleration parameter, SBAP, which permits solid bed acceleration in a screw compression section. New experimental melting data for a variety of screw designs, polymers, and extruder sizes are presented and compared to the theoretical predictions. With the optimum SBAP, reasonably accurate model prediction of the melting profiles is observed for a wide variety of cases.     

A mathematical model of the melting of polymeric materials in extruders

Conclusions The contemporary state of the theory of melting of polymeric materials in plasticizing extruders has been discussed.A new, more refined theory of melting in the screw channel has been presented, based on solution of the fundamental equations of motion, energy transfer, heat conductance, and state.Translated from Khimicheskie Volokna, No. 3, pp. 51–53, May–June, 1984.     

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.     

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.     

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.     

Plastification or melting: A critical process for free radical grafting in screw extruders

This paper shows for the first time that when a monomer is to be grafted onto a polymer backbone by a free radical mechanism in a twin screw extruder, the grafting process occurs mainly, if not exclusively, in the plastification (melting) zone. For this purpose, the free radical grafting of glycidyl methacrylate (GMA) onto polypropylene (PP) and polyethylene (PE) was chosen as model systems. A co-rotating self-wiping twin screw extruder of type Werner Pfleiderer ZSK-30 (L = 42D) was used to process the grafting. Owing to its modular character in terms of barrel arrangement, screw element combination and barrel temperature, the position and length of the plastification zone can be adjusted virtually at will. This allowed us to follow up the grafting not only at the die exit, but also in the plastification zone under different grafting conditions. Our results clearly show that it is in the plastification (melting) zone that the entire grafting process occurs. This length is usually very short in a co-rotating twin screw extruder like ours. Under the grafting conditions, it varied from 1D to 5D. Thus, any relevant analysis or model of a free radical grafting process carried out in a screw extruder must be based on detailed information generated not only at the die exit, but also and most importantly in the plastification zone. Otherwise, it may lead to incomplete and/or wrong conclusions.     

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.     

Mathematical modeling of melting of polymers in barrier-screw extruders

Some of today's modern screws contain melt-separating secondary (barrier) flights in the transition zone. With increasing utilization of barrier screws, the availability of proper and accurate design methods for the melting zone remains of paramount importance. A modified version of a mathematical model developed by the authors previously is applied to two most common types of barrier screws, viz. —The Mailefer screw (varying pitch and constant depth); —The Barr screw (constant pitch and varying depth). The present analysis provides valuable insight into the operating principles of these screws. A comparative study is presented demonstrating the possible advantages and disadvantages of the Maillefer and Barr screws in relation to conventional compression screws.     

Theoretical model for non-intermeshing twin screw extruders

A simple theoretical model for flow in nonintermeshing twin screw extruders has been derived. The assumptions which in single screw extruders result in the “two parallel plates” model, in twin screw extruders result in the “three parallel plates” model. The flow rate equation can be expressed, for Newtonian fluids, in terms of drag and pressure flow terms, as in single screw extrusion theory, but each term is multiplied by a geometrical factor. This factor incorporates the effect of one screw on the drag and pressure flow terms of the other. The theoretical model was experimentally verified on a 1 inch diameter Bausano twin screw extruder.     

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.     

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.     

The effect of design and operating conditions on melting in plasticating extruders

A previously proposed but further modified theoretical model for melting in plasticating extruders, in the form of a computer program, which predicts the amount of unmelted polymer at any point in the extruder, was used to simulate the effect of geometrical and operating variables on the melting performance of the extruder. The results indicate in increasing screw length required to complete melting with increasing throughput and a decreasing length of melting with increasing frequency of screw rotation. They further indicate the existence of an optimum barrel temperature for a maximum rate of melting, an optimum number of threads for a maximum melting rate, and a significant decrease in the rate of melting with increasing flight clearance. The effect of other geometrical variables and of operating conditions on the rate of melting and power consumption are also discussed.     

A melting model for reciprocating screw injection-molding machines

A theoretical model for melting in reciprocating screw injection molding machines is proposed. The model permits the calculation of the solid bed profile as a function of time during the injection cycle. It consists of a dynamic extrusion melting model for the rotation period, a transient heat conduction model with a phase transition for the screw rest period, and a proposed model for the drifting of the beginning of melting during the injection cycle.     

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.     

Melting model for modular self wiping co-rotating twin screw extruders

A model for the melting process in a self wiping co-rotating twin screw extruder is described. Self-wiping co-rotating twin screw extruders are modular and starve fed. This leads to melting mechanisms that are different from single screw extruders. The melting process in the modular screw configurations generally occurs in specialized sections such as kneading disk blocks. The model, based on our previous experimental observations, considers the formation of two stratified layers of melt in contact with the hot barrel and solid pellets in contact with the relatively colder screw. In the kneading disk blocks, a part of the solid bed is blocked because of the relative stagger between successive disks. The model predicts both the location of melting and melting lengths in a screw configuration. Calculations for individual screw elements and kneading disc elements are presented first. Melting in a modular configuration of these elements is then considered. The effect of operating variables such as mass flow rate and screw speed on melting is then studied. The model is put in a dimensionless form and the effect of various dimensionless groups is discussed. We make a comparison to the experiment and agreement is good.     

A mathematical model of the melting of polymeric materials in extruders. Investigation of the form of the interface and of melt velocity profiles

Conclusions The form of the interface in the melting of a polymer in an extruder has been studied. It has been found that it differs considerably from right-angled, and melting of the polymer takes place over its entire curvolinear surface.The three components of polymer melt velocity have been constructed: The change in these both over the cross-sectional area of the extruder screw and also along its length has been noted.In the liquid phase of the polymer, an intense circulation of the melt takes place in the transverse plane of the screw channel.Translated from Khimicheskie Volokna, No. 5, pp. 40–42, September–October, 1984.     

Investigation of the melting behavior and morphology development of polymer blends in the melting zone of twin‐screw extruders

The melting behavior and the morphology development that runs parallel to it play central roles in the processing of polymer blends. We studied the impact of speed, melt throughput, continuous‐phase viscosity, screw configuration, and disperse‐phase content on the melting behavior and morphology development in the melting zone of a twin‐screw extruder. The polymer blend used incorporated polyamide‐6 (PA6) as its disperse phase and a high‐viscosity or low‐viscosity polypropylene as the matrix phase. The melting behavior of the polymer blend was investigated with press plates. A qualitative assessment was made of the processes, on basis of the optical impression gained from the transilluminated press plates. One key result was that the PA6 granules melted very rapidly in the polypropylene melt. We took samples over the length of the melting section to permit a quantitative assessment of the morphology. The results show a finely dispersed morphology already at the start of the melting section. This did not undergo any essential change as the blend passed through the extruder, and only a limited correlation was evident with the process parameters. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1986–2002, 2001     

A theoretical melting model for a reciprocating-screw injection molding machine

A theoretical model for the transient melting behavior in a reciprocating-screw injection molding machine is proposed. The model is based on a steady state extrusion model, Neumann's melting problem, and a heuristic postulate for the transient behavior. The model predictions are compared to experimental melting data for low density polyethylene, acrylonitrile-butadiene-styrene polymers and polyvinyl chloride for a variety of operating conditions and two screw designs. A useful degree of correlation is demonstrated for all experimental cases.     

A mathematical model of the melting of polymeric materials in extruders. Effect of various heat sources on the form and size of the solid plug

Conclusions The form and size of the solid polymer plug in melting polymeric materials in plasticizing extruders depend on the source of heat: external, dissipation of mechanical energy, or preliminary warming of the flake.The length of the polymer melting zone is determined by the rate of rotation of the extruder screw.Translated from Khimicheskie Volokna, No. 4, pp. 49–50, July–August, 1984.     

A mixing model for multicomponent reactions in twin screw extruders applied to the polymerization of urethanes

To understand the performance of multicomponent reactions in twin screw extruders the mixing mechanism in the extruder had to be understood. Therefore, two new relevant mixing parameters are defined; the mixing efficiency, which is the average number of passages of material through a high shear region; and the mixing deficiency, which is the fraction of material that does not pass through a high shear region. With these parameters an analysis can be made of the mixing circumstances in the extruder. The new model was applied to the polymerization of urethanes in a counter-rotating twin screw extruder. The results agreed very well with the theoretical expectations.