Improving the properties of polymer blends by reactive compounding van der Wal, Douwe Jurjen

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1 University of Groningen Improving the properties of polymer blends by reactive compounding van der Wal, Douwe Jurjen IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 1998 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): van der Wal, D. J. (1998). Improving the properties of polymer blends by reactive compounding Groningen: s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 CHAPTER 6 MODELLING AND EXPERIMENTAL EVALUATION OF -THE TEMPERATURE IN A COROTATING- TWIN SCREW EXTRUDER. Abstract. Following the modelling of the 3D-flow and 3D-temperature in the kneading and transporting section of the extruder we now will calculate and measure the average temperature along the extruder. For processing of polymers in the extruder the temperature in the melt is an important parameter which will be used in chapter 7, and 8. The temperature of Polystyrene (PS) has been measured in the fully filled section and in the partially filled section of a self wiping corotating twin screw extruder. The axial temperature profile obtained for pure PS has been compared with the temperature profile of a blend of PS mixed with High Density Polyethylene (HDPE) processed in the same extruder. The influence of rotation speed and throughput on the power consumption and on heating of the polymer in the extruder have been investigated. A heat transfer model for the kneading section in the closely intermeshing corotating twin screw extruder is proposed based on the temperatures measured. 1 Introduction. With the calculated flow profiles as modelled in chapter 2, 3, and 4 we now are able to develop a model for the temperature and mixing of reactive compounding in the extruder. Therefore a computer code of reactive compounding will be developed in this chapter and chapter 7 and 8. The final goal of this thesis is to improve toughness and impact values of a PS/HDPE blend. Process control is very important for a good homogeneous product quality of the blend. In many cases of blending controlling the temperature may be a problem due to a lack of knowledge of the axial and radial temperature profile. This can be prevented by predicting the axial temperature profile (neglecting the melting process) for which a computer program, written in Turbo Pascal, has been developed. Depending on screw design the barrel temperature for the melting of Polystyrene (PS) or mixing of PS and High Density PolyEthylene (HDPE) ranges from 180 to C. Temperatures above C can cause a loss in the desired physical properties of the extrudate due to degradation. Temperatures below C can cause high extruded-in stress and a loss in the desirable physical properties of the extruded part. Therefore it is important to determine the relation between the actual temperature of the polymer in the extruder and the temperature profile of the extruder wall. 115

3 The heat transfer coefficient in the partially and fully filled part of the transporting and kneading section of the extruder is needed to calculate the heat exchanged with the barrel. Several models for the heat transfer coefficient in the completely filled sections have been developed in which the emphasis was mainly on the metering section in single-screw extruders. In 1953 Jephson (1) considered the wiping action of the flight of a rotating screw responsible for the heat transfer in the extruder. During a rotation of the screw, a fresh layer of polymer becomes attached to the barrel surface just after passing of the flight. The amount of heat penetrated into this layer by conduction is distributed over the channel by mixing at the next passage of the flight. The temperatures at different radial positions in the channel were measured by Janssen et al (2) and Schlaffer et al (3). Van Leeuwen et al (4) have measured the temperature rise at the tip of a thermocouple due to viscous dissipation in PS. In the heat transfer model of Todd (5) the viscosity has a small influence on the heat transfer coefficient. However no influence of the viscosity is expected at creeping flow conditions. The processing of polymers and blends is strongly influenced by processing conditions and the viscosity and has been the subject of much work of which some can be found in Reference Modelling of the average axial temperature in the corotating twin screw extruder. 2.1 The geometry and the throughput of the extruder. In fact the extruder is a pump for viscous liquids and sufficient pressure build up is needed for a stable transportation of polymers in the extruder. In general the screw layout is such that the polymer or polymer mixture is melted and transported into a pressure build up or in a kneading section and then pushed through a die by a transporting section, figure 1. Therefore the following four sections are distinguished here : -Solids transport section : before the first kneading section. In this section frictional forces are experienced by the solid particles, however, no shear on molecular scale is present. In this zone the effective heating of the polymers will not be very efficient since only part of the barrel is in contact with the polymers. Powder particles are assumed to have a much lower flow resistance than molten polymers and a constant is fitted for the frictional dissipation in the powder transporting section. -Melting zone : Melting of the polymer occurs mostly in the part of the transporting section which is fully filled just before the kneading section or for very large throughputs in the first part of the kneading section. 116

4 -The kneading section, which may partially overlap with the melting zone. The large shear in the kneading section causes a large increase in temperature due to viscous dissipation. -The melt transport section. From this section material is pushed through the die. figure 1 Transporting and kneading elements in the intermeshing corotating twinscrew extruder, number of kneading elements : 8, upper figure : front view, below : side view. In the transporting elements and pressure build up elements the pressure, needed for the material to be pushed through the kneading section, must be built up. After the kneading elements, transporting elements or pressure build up elements are used to supply the pressure needed to transport the material through the die. Experiments have been done with 7, 8, 9, 10, 11, and 18 kneading elements. The temperatures are measured in the partially filled transporting section before the kneading section and in the fully filled kneading section of a screw extruder as shown in figure 1. The positions where the temperature has been measured in the kneading section are at the first (T 1 ) and the seventh paddle (T 2 ) along the extruder. The temperature increases in the fully filled sections. This is mostly determined by the relation between viscous dissipation and cooling of the barrel. In our modelling a large number of general equations are used of which a few will be given here. The following expressions are valid for the self-wiping twin screw extruder and can be found in the work of Elemans (11). The number of independent channels in a corotating twin-screw extruder are (2n-1). The channel width in a corotating twin-screw extruder is given by equation 1. W = ((2n-1)/n) πdsinϕ(1-ne) (1) 117

5 e = W f /W tot = W f /(πdsinϕ) (2) where W is the width, D is the diameter, e is the relative width, ϕ is the pitch of the screw, and the index f means of the flight. The throughput, the specific energy, and the degree of fill are of interest for the temperature modelling. The geometry of the solid particles in the partially filled section, the degree of fill in the partially filled section and the energy consumption of the melt are used in the modelling and will be described in this section. The theoretical throughput yields: Q th = ½VcosϕHW (3) where V is the velocity of flight and H is the height of the channel. According to Elemans (11) the local throughput, Q, that must be transported to the die is larger than the metered (real) throughput (Q m ), due to leakage flow (Q L ) through clearances over the flights : Q = Q m + Q L (4) with : Q L = ½Vδ π Dsinϕcosϕ(1-ne) (5) -The degree of fill equals: f = Q m π D HNcos ϕ sin ϕ (1- n e) δ + H (6) where j is the pitch angle, n is the number of channels per screw, and d is the distance between flight and barrel. It has been assumed that the amount of fill of the channel in the self wiping corotating twin screw extruder determines the contact surface with the barrel and therefore the heat transferring area. The fully filled length, preceding the kneading section and die is calculated. The kneading section is totally filled as has been verified by visual observations. The area of the barrel which cools the melt in the channel of a twin screw extruder has been modelled with : A = ( πd 2 θd) * L (7) The effective surface area for the flights equals: A f = nea [m 3 ] (8) The surface area which cools the melt in the transporting channel is assumed to depend on the degree of fill : A c = f(1-ne)a [m 3 ] (9) 118

6 2.2 The temperature model. The temperature of the melt in the fully filled section is mostly determined by the viscous dissipation, which is a function of the shear rate in the fluid. The polymer in the transporting elements experiences a relatively small shear stress. In the kneading section larger shear stresses are applied. Part of the heat generated by viscous dissipation is transferred to the barrel. An expression for the heat transfer coefficients will be derived both in the partially filled and in the completely filled sections. This is needed for modelling the temperature of the melt in the transporting section and the kneading section 2.3 The viscous dissipation. A number of assumptions are used in these calculations For the transporting section it is assumed that: -The solid particles are heated by direct contact with the barrel or the screw both having the same uniform temperature. -The heat from the barrel penetrates directly into the solid. If the surface of the solid particles has a temperature higher than the glass transition temperature the solid becomes sticky and the frictional forces increase. This increase is assumed to be linear with the percentage of material within a particle having a temperature higher than the glass transition temperature. For the kneading section the following is noted : -The kneading section is assumed to be completely filled because it is a pressure consuming section (the stagger angle used is ). -The influence of the pressure on density and viscosity of the polymers has been neglected. -The dominating term in the overall heat balance is the viscous dissipation which is calculated with the average values of the shear rate (6-11) and elongation rate from 3-D flow calculations in chapter 2 and chapter 3. It is assumed that the average value of the shear rate calculated can be used to calculate the viscous dissipation. A constant has been found which represents the fact that the temperature increase is slightly delayed because energy is consumed when granules melt. -An experimentally measured viscosity model for PS and HDPE has been used in the modelling 119

7 -The screw surface is considered to be adiabatic As a model for the shear stress in the flight gaps we use : V τ f = ηf (10) δ where h is the viscosity, as calculated from the experiments with a Cross Carreau model (12-14), and d is the flight gap. The Torque, To, is needed to calculate the average temperature rise due to the viscous dissipation : 1 To = DFt 2 with: F = ηγ πdl( 1+ 2( 3f + 4) l / f ) f ( 12) t t (11) Where F t is the total force and f is the (local) degree of fill (equation 9), and l t is the total length. The power consumption depends on the screw element, the degree of fill of the elements and the viscosity of the material. The total power consumption consists of the power consumption over the flights and the power consumption in the channel. The forces (F) acting on the wall are the product of shear stress and surface area where the stress is active. The power consumption (Watt) equals torque times screw speed : P o ηπ Lfγ& (1 + 2(3 f = 2 + 4) l / t f ) D 2 N (13) 2.4 The temperature profile. The overall energy balance has been solved, providing an average value for the axial temperature of the materials in the self wiping corotating twin screw extruder : Q C m p dt dx dpo = ho( T Tw ) (14) dx Where Q m is the throughput, C p is the specific heat, O is the circumference, and h is the heat transfer coefficient. The energy needed for phase changes and pressure changes of the polymer is generally small and has been neglected for the screw geometry without a pressure build up section in front of the kneading section. The influence of heat exchange with the screw has been neglected. The following solution has been derived to calculate the change in melt temperature one step further along the channel (from equation 14) : 120

8 ho x Po QmCp QmCp T = [ Tw + ( 1 e ) ( Tw T0 ) e ] (15) ho x ho x The temperature of the melt in equilibrium with the barrel is : P T = [ o + Tw ] ho x (16) Since the power P o depends on the screw speed, N, also the equilibrium temperature depends on the screw speed. The axial position of this equilibrium is within the kneading section in most of our experiments because of a relatively small throughput, Q m. With equation 15 the temperature profile over the length of the screw can be calculated for each screw speed and throughput. For the modelling of the energy balance in the extrusion process two different models for the heat transfer coefficient have been compared. The model of Todd implies a dependence of the heat transfer coefficient on N, Q and D. 2 λ D Nρ C p η ηb h = [ ] [ ] [ ] D η λ η w (17) The model of Jephson (1) is based on the penetration theory : λ( T ) h = erf z z 2 inthiscase: h = 0.57 λ( T ) ρ( T ) C C p p z λ( T ) ( T ) ρ( T ) N ( T ) N z= h : (18) The viscosity and the screw diameter influence the heat transfer in the model of Todd which is not the case in the Jephson model. The heat conductivity of PS (l) can be written as : T λ( T) = ( ( ) + ( )) T < T T g T λ( T) = ( 0. 2( ) + ( )) T > Tg ( 20) T g g (19) 121

9 Both models are combined with the computer model and the results are compared with measured axial temperatures. From these measurements the heat transfer coefficient in the kneading section has been determined. 3 Experimental. The torque, measured during processing with a Brabender plasticorder, is a direct measure of the viscosity. Therefore the torque has been measured during processing of PS, HDPE, and a mixture of HDPE with maleic acid (MAH), figure 2. From figure 2 it is possible to calculate the ratio between the viscosity of PS and HDPE. figure 2 The torque measured with a Brabender plasticorder, T b = 200 C. The viscosity of the HDPE/MAH mixture (MAH is not grafted) is very small because of the porous structure of the HDPE granule. The material flows easily due to the presence of MAH. The torque as measured when pure accurel (porous HDPE) is melted hardly depends on the rotation speed. 3.1 Extrusion and viscosity. Extrusion of PS and PS/HDPE was performed on a Baker Perkins, 50 mm, self-wiping corotating twin-screw extruder. The screw geometry has one kneading section (figure 1). In the first series of experiments this kneading section consisted of 7 kneading elements, with a stagger angle Our goal is to determine which heat transfer model is valid in the fully filled kneading section and in the partially filled transporting section. Three different barrel temperatures are used, 160, 180 and 200 C. The extruder parameters varied are one of the screw speeds and one of the throughputs in table

10 N [rpm] Q [kg/h] table 1 The rotation speed, N [rpm] and throughput Q [kg/h] used in the experiments. figure 3 The measured and modelled viscosity of PS. The viscosity of the commercial grade PS (Styron 7000, SHELL) used in the experiments has been measured and fitted to this model, as shown in figure 3. This viscosity has been modelled with a generalised Cross-Carreau model. Data sets for the viscosity of pure HDPE have been taken from the literature and verified for the PE used (13,14). 4 Results. 4.1 The power. Under normal operation conditions the temperature of the melt in the extruder is strongly influenced by viscous dissipation. The power of the motor is a direct measure of the 123

11 viscous dissipation. This power consumed by the extruder is measured when a PS from Shell is extruded, shown in figure 4a. The power consumed by the extruder as modelled for Styron 7000 corresponds very well with measured values. The influence of the length of the kneading section has been studied and therefore also experiments with a new screw geometry with 11 kneading paddles have been done. From the calculations of the power consumption along the extruder it was found that most of the power is consumed in the kneading section. figure 4a Comparison between calculated and measured Power of the extruder. PS, T b = 200 o C, Q = 0.3 kg/h, PS : Styron 7000 (SHELL) For the successive experiments a PS from Atochem was chosen because it appeared to be more suitable for our blending experiments, figure 4b. In this case the screw geometry has 7 kneading paddles. For processes such as mixing the specific energy is an important factor for extrusion of viscous fluids. This energy decreases with an increase of throughput as shown in figure

12 figure 4b The power versus rotation speed, various throughputs PS, T b = 180 o C, PS : Lacquerene (ATOCHEM) figure 5 The specific energy consumed by a melt of polystyrene, N = 267 rpm, T b : 200 C. Figure 5 shows the specific energy consumed by the melt : E spec = P o /Q m [kw/kg] (21) 125

13 4.2.1 The temperature profile in the partially filled section. The melting mechanism in the single screw extruder has been the subject of much work in the past but is expected to differ from the melting mechanism in a twin screw extruder. In the barrel two openings are present in the partially filled zone before and after the kneading section. This allows us to measure the temperature of the polymer in the partially filled zone by use of an IR thermometer, Scotchtrac Heat tracer (3M). The temperatures along the axial length in the fully filled part are measured at three axial positions with an IR thermometer suitable to measure in the melt (DYNESCO). PS or a polymer mixture of PS-HDPE is fed into the transporting section at 20 C. The barrel has a temperature of 150 C, 160 C, 170 C, 180 C or 200 C. The heat from the barrel penetrates into the granules transported in the partially filled section. figure 6 The geometry of the granules in the partially filled section (side view). Heat penetration from the barrel into the granule in the partially filled section has been modelled with Fourier theory, figure 6. The temperature profile has been calculated in a geometry completely consisting of transporting elements. 126

14 figure 7 The temperature profile in the partially filled transporting section. PS, T b = 200 C, Q = 8 kg/h, N = 107 rpm If the temperature of the outer layer of the granules exceeds the glass transition temperature (96 0 C) the outer layer of the granules becomes sticky leading to an increase of friction. The temperature development of the granules in the partially filled section is shown in figure 7. This temperature profile shows a strong initial increase which levels off along the transporting section. figure 8 The temperature dependency on the rotation speed and throughput in the partially filled section ; PS, T b = 200 C, l = 0.4 m. 127

15 The temperature of the melt decreases when more material is heated, figure 8. The degree of fill increases with increasing throughput. Heating and cooling by the barrel increases with an increase of the degree of fill because an increase of the part of the barrel surface having direct contact with the granules. Therefore the power consumed increases as calculated with equation 11. figure 9 Calculated and measured temperature and degree of fill (f) versus throughput, partially filled section ; PS, T b = 200 C, N = 107 rpm The temperature of the material measured with the IR thermometer in the partially filled (transporting) zone before the kneading section for various throughputs, Q, shows a reasonable agreement between theory and experiments as shown in figure The fully filled section. The temperature profile has been calculated for a screw geometry with transporting elements and one fully filled kneading section with a stagger angle of 150 (figure 10a). The radially averaged temperature in the melt of the extruder has a maximum near the entrance of the kneading section. This maximum occurs due to the interaction between the viscous dissipation and the heat transfer to the barrel. When entering the kneading section part of the material is not melted yet and therefore the viscosity is very large. The phase transition is not taken into account at the position in the extruder where the temperature of PS reaches the glass transition temperature. Therefore the temperature of the material entering the kneading section is expected to be slightly overestimated. 128

16 figure 10a The modelled temperature development along the length of the extruder. PS : Styron 7000 (SHELL), T b = 180 C, Q = 3.5 kg/h In figure 10b an additional pressure build up section is present in front of the kneading section and melting is taken into account. In the pressure build up section the temperature is almost constant because the energy dissipated is consumed by the phase transition. figure 10b The temperature development along the length of the extruder. PS : ATOCHEM, T b = 150 C, Q = 8 kg/h, pressure build up section = 10 cm For all measurements the temperature in the melt in the fully filled kneading section has a higher value than the temperature of the barrel due to the relatively large viscous dissipation. The viscosity of the melt entering the kneading section is relatively high and decreases when it enters the kneading section. The comparison between calculated and 129

17 measured values is good, figure 11. The temperature decreases with increasing throughput, figure 11. figure 11 Calculated and measured temperature versus Q [kg/h]. PS, T b = 180 C, N = 107 rpm The temperature at the entrance of the kneading section. In figure 12a the temperature of the melt decreases with increasing throughput in the (fully filled) kneading section. figure 12a The measured temperature of the melt versus throughput ; PS from Atochem ; T b = 180 C, position : first kneading paddle. 130

18 It is obvious that a large resemblance in the shape of the lines is found for the different rotation speeds of the screw. figure 12b Calculated and measured temperatures of the melt versus rotation speed [rpm], T b = 200 C, Q = 0.3 [kg/h], position : seventh kneading paddle. Since only an overall energy balance is solved it is difficult to accurately calculate the average temperature and the average viscosity in the melt. Nevertheless the comparison between calculated and measured average temperatures in the kneading section is reasonable, as can be seen in figure 12b. The measurements shown are the temperatures in the melt at the end of the kneading section. The temperature at the exit of the kneading section decreases with increasing throughput, figure 13a. figure 13a The measured temperature of the melt at the seventh paddle, T b = 200 C. 131

19 The heat transfer coefficient calculated, the kneading section. At a large rotation speed the measured temperatures in figure 13b all are the same. This means that T 1 =T 2 in equation 22, and for relative small throughputs the temperature of the melt is constant along the kneading section. From this figure it is clear that, at low throughputs and large rotational speeds, the temperature is almost independent of the throughput. Therefore Q ρ C p (T 1 - T 2 ) in equation 22 is small in the kneading section. figure 13b T 1 and T 2 of the melt in the kneading section, T b : 200 C. If the temperature is constant along the kneading section the following overall energy balance is valid : = Qρ C ( T T ) hs( T T ) + H 0 p 1 2 av. barrel e H e : if T = T heat due to viscous dissipation 1 2 H e h = S( T T ) av : barrel (22) To calculate the heat transfer coefficient from the energy balance the viscosity of the PS melt in the kneading section as a function of shear rate and temperature (and therefore also the viscous dissipation) has been found by iteration. The average shear rate in the volume of one kneading paddle has been calculated in chapter 2 and 3 and has been used in this modelling for the shear thinning behaviour to calculate the viscosities. 132

20 figure 14 The heat transfer coefficient, theory : penetration theory. Figure 14 gives a comparison between the experimental values for the heat transfer coefficient in the kneading section and the models proposed by Todd (5) and Jepson(1). It is clear that the penetration theory (Jepson) shows a reasonable comparison with the measured values for the heat transfer coefficient in the fully filled kneading section. From the 3D temperature modelling, in chapter 4 it was also found that penetration theory provides a reasonable value for the power law (a function of N) to which the heat transfer coefficient in the transporting section has been fitted. The model of Todd, equation 18, as shown in figure 14 was found to be slightly different from the heat transfer coefficients as we measured them in the kneading section The temperature of a blend (PS/HDPE). The temperature of a blend of PS and HDPE has also been measured and modelled. The measured values at the end of the kneading section for different rotation speeds are shown in figure 15. The temperature of the melt is relatively low compared to the measurements for pure PS. The measured values of the temperature in the melt of a blend of PS/HDPE above the fourth kneading elements for increasing rotation speeds are shown in figure 16. The differences between the temperature of the melt of pure PS and of a PS/HDPE blend are mostly attributed to the differences in the viscosity between PS and PS/HDPE. 133

21 figure 15 The temperature of a blend of PS/HDPE versus N [rpm]. fully filled section. figure 16 The temperature of PS/HDPE versus rotation speed [rpm]. fully filled section, T b = 160 C. The modelling of temperature and mixing will be used in chapter 8 in a modelling of reactive compounding in the extruder. 134

22 5 Conclusions. With the operating conditions used here there is little difference between the heat transfer models as proposed by Todd and Jepson. The Jepson model shows a slightly better agreement with the experiments. In our 50 mm extruder viscous dissipation has a much stronger influence than the heating and cooling effects of the wall. This is expected to be even more prominent when the extruder is scaled up. A strong increase in temperature occurs when the material enters the kneading section. Therefore kneading zones are effective for increasing the melting capacity of twin screw extruders. The rotational speed of the extruder was varied between 57 and 450 rpm. When the rotation speed of the screw increases the viscous dissipation in the melt increases. Therefore the temperature of the melt increases. -The modelled average temperature and the power consumed has been validated with measured values. -The heat transfer coefficient in the kneading section could be calculated from an energy balance and the measurements fitted reasonably to penetration theory. -The results in chapter 4 will be combined with the results in this chapter which allows us to obtain both an average temperature and a maximum temperature in the channel of the corotating twin screw extruder. -The temperature modelling can be improved by refining the work in chapter 4 by including the Cross-Carreau viscosity in the 3D modelling and combining this with the modelling in this chapter. More attention should be given to : - The viscosity of the powder in the powder transporting section and the heat transfer of the powder to the barrel. Nomenclature. A Area [m 2 ] C p Heat capacity [J.kg -1. C -1 ] D Diameter [m] E spec Specific energy [kw.kg -1 ] f Degree of fill [-] F Force [N] H Channel depth [m] He Heat generated by viscous dissipation in the channel [W] 135

23 h Heat transfer coefficient [W.m -2. C -1 ] L (axial) Length along the channel [m] 2n-1 Number of independent channels [-] N Screw speed [rpm] N spec Specific energy [kw.kg -1 ] P o Power [W] Q Throughput [m 3.s -1 ] S Surface of the barrel [m 2 ] T (average)temperature [ C] T1 Temperature at the first paddle of the kneading section [ C] To Torque [N.m] V Circumferential speed [m.s -1 ] W Width of the channel [m] x Axial coordinate [m] z Radial coordinate [m] Greek symbols γ& Shear rate [s -1 ] δ Space between flight and barrel [m] Difference [-] λ Heat conductivity [W m -1 C -1 ] h Viscosity [Pa.s] ρ Density [kg.m -3 ] ϕ Pitch [rad] θ Angle (not covered) between the screws [-] τ Shear stress [Pa] σ Surface tension [N.m -1 ] Subscripts b c f g m k tot Barrel Channel Flight clearance Glasstransition temperature Melt transition temperature Kneading element Total 136

24 References. 1 C.H. Jephson, Ind. Eng. Chem., (1953). 2 L.P.B.M. Janssen, G. H. Noomen, and J.M. Smith, Platics and Polymers, 43, , (1975). 3 W. Schlaffer, J. Schijf and, H. Janeschitz-Kriegel, Plastics and Polymers, 39, , (1971). 4 J. van Leeuwen, Polym. Eng. Sci., 7, 98 (1967). 5 D. B. Todd, Proc. ANTEC 88 conf., Vol 1 P (1988). 6 D.J. van der Wal, E. Klomp, D. Goffart L.P.B.M. Janssen, H. Hoogstraten, Pol. Eng. Sci., 36, 912 (1994). 7 D. Goffart, D.J. van der Wal, L.P.B.M. Janssen, H. Hoogstraten, Pol. Eng. Sci., 36, 901 (1996). 8 Chapter 4, this thesis. 9 Chapter 7, this thesis. 10 D. J. van der Wal, L.P.B.M. Janssen, Proc. ANTEC 94 conf. 1-5 may 1994 San Fransisco, Vol 1 P SPE (1994). 1 P.H.M. Elemans, Ph.D. thesis, Eindhoven, (1989). 12 H.H. Hieber, C.H. Chiang, Rheol Acta 28:321 (1998). 13 H.F. Mark, Encycl. of Polym. Science and Technology, Interscience Publ., New York, Vol J.E. Mark, Physical properties of polymers handbook, (1996). 15 L.P.B.M. Janssen, Twin-screw extrusion, Elsevier, Amsterdam (1987). 16 M.L. Booy, Pol. Eng. Sci., 18, 937 (1978). 17 K.J. Ganzeveld, PhD thesis, University Groningen (1992). 18 C.A. Hieber, H.H. Chiang, Polym. Eng Sci, Vol. 32, Vol. 14, 931 (1992). 137