Polymer Extrusion
Polymer Extrusion
Pierre G. Lafleur, Bruno Vergnes
Table of Contents
Introduction . ix
Chapter 1. Continuum Mechanics, Rheology and Heat
Transfer Overview 1
1.1. Continuum mechanics . 1
1.1.1. Strain . 1
1.1.2. Strain rate 2
1.1.3. Stress . 4
1.1.4. General equations in continuum mechanics 5
1.2. Rheology . 7
1.2.1. Newtonian behavior 7
1.2.2. General viscous behavior . 9
1.2.3. Effects on pressure and temperature . 10
1.3. Heat transfer [CAR 59, BIR 60, AGA 14] 11
1.3.1. The thermal balance equation . 11
1.3.2. Heat transfer during flow . 13
1.3.3. Cooling temperature 16
1.4. Bibliography . 19
Chapter 2. Calculation Methods . 21
2.1. Introduction 21
2.2. 1D solutions . 22
2.2.1. Isothermal calculation . 22
2.2.2. Non-isothermal calculations . 26
2.3. 2D solutions . 28
2.3.1. Network method (or FAN method) . 28
2.3.2. Finite element method . 32
2.4. Bibliography . 34vi Polymer Extrusion
Chapter 3. Single-Screw Extrusion . 37
3.1. Introduction 37
3.2. Geometry and approximations . 39
3.3. Solid conveying zone 45
3.3.1. Phenomenological description 46
3.3.2. Modeling . 47
3.3.3. Synthesis . 63
3.3.4. Determination of physical parameters 65
3.4. Melting zone . 73
3.4.1. Phenomenological description 73
3.4.2. Modeling . 76
3.5. Metering zone 85
3.5.1. Phenomenological description 85
3.5.2. Modeling . 85
3.6. Overall model 95
3.7. Technological improvements . 99
3.7.1. Grooved barrels . 100
3.7.2. Barrier screws 102
3.7.3. Mixing heads 103
3.8. Conclusion 105
3.9. Bibliography . 105
Chapter 4. Co-rotating Twin-Screw Extrusion 109
4.1. Twin-screw extrusion 109
4.1.1. The different types of extruders . 109
4.1.2. Different flow types 111
4.2. General overview of co-rotating twin-screw extruders 113
4.2.1. Characteristic features of co-rotating twin-screw extruders . 113
4.2.2. Geometry of the screws and barrel 115
4.2.3. Conventional approximations . 119
4.3. Solid conveying zone 120
4.4. Melting zone . 121
4.4.1. Experimental studies 122
4.4.2. Theoretical models . 125
4.5. Flow in the molten state 128
4.5.1. Right- and left-handed screw element 128
4.5.2. Mixing elements 138
4.5.3. Heat transfer . 146
4.5.4. Residence time distribution 147
4.6. An overall model of twin-screw extrusion 151
4.6.1. General description . 151
4.6.2. Calculation algorithm . 154Table of Contents vii
4.6.3. Residence time distribution 155
4.6.4. Example of results using the LUDOVIC© software 157
4.7. Compounding application and production of complex materials 162
4.7.1. Compounding and mixing . 162
4.7.2. Reactive extrusion . 170
4.7.3. Polymer blends . 177
4.7.4. Production of clay-based nanocomposites . 185
4.7.5. Optimization and scale-up . 194
4.8. Conclusion 198
4.9. Bibliography . 198
Chapter 5. Profile Extrusion . 211
5.1. Profile extrusion . 211
5.1.1. Different types of profile dies . 211
5.1.2. Flow calculation inside profile dies . 213
5.1.3. Evaluation of post-extrusion phenomena 214
5.1.4. Design of extrusion dies 221
5.2. Pipe extrusion 229
5.2.1. Introduction . 230
5.2.2. Flow calculation 230
5.3. Calibrators 240
5.3.1. Friction calibrators . 240
5.3.2. External compressed air calibrators . 240
5.3.3. External vacuum calibrators . 241
5.3.4. Internal calibrators . 241
5.4. Conclusion 241
5.5. Bibliography . 241
Chapter 6. Production of Films and Sheets 245
6.1. Introduction 245
6.2. Cast film extrusion . 249
6.2.1. Processing 249
6.2.2. Designing the flat die . 250
6.3. Film blowing . 256
6.3.1. Process overview 256
6.3.2. Film blowing models 267
6.3.3. Multilayer films . 292
6.4. Conclusion 298
6.5. Bibliography . 298viii Polymer Extrusion
Chapter 7. Wire Coating and Cable Insulation 305
7.1. General process . 306
7.1.1. Production line . 306
7.1.2. Wire coating dies 307
7.2. Commonly encountered problems 310
7.3. Analyses and solutions . 310
7.3.1. Theoretical studies . 311
7.3.2. Experimental studies 330
7.4. Conclusion 330
7.5. Bibliography . 331
Index 33
Index
A, B
activation
energies, 276, 296, 298
energy, 11, 31, 172, 232, 274, 276,
294, 296–298
adiabatic flow, 14–15
apparent density, 46, 69, 71
Arrhenius equation, 10, 31, 232, 238,
270, 274, 288
average
residence time, 148–150, 155
temperature, 14–16, 26, 27, 146,
154, 214, 323, 324
barrel velocity, 44, 48, 49, 76, 94
barrier screws, 102–103
biot number, 322
blow-up ratio, 257, 292
breaks, 165
Brinkman number, 27
C
C-chamber, 111, 120, 122, 128, 130,
133
Cameron number, 27
capillary number, 178, 179–181, 183
Carreau’s law, 9, 22
Carreau-Yasuda law, 9, 172, 188
cast film extrusion, 249–255
centerline distance, 115–117
channel
depth, 40–42, 53–55, 64, 80, 81,
115, 118
width, 41, 42, 87, 119, 120, 130,
152
characteristic
curves, 87, 88, 132, 134, 135
value, 22, 25
coalescence, 178, 180–184
coat-hanger geometry, 249
coextrusion, 309
coextrusion die, 257, 259, 309
compaction zone, 46–47
compounding, 162–170
continuity equation, 5–6
controlled degradation, 170, 172,
176, 177
conversion rate, 172, 175, 195
cooling ring, 263, 264, 272, 273, 276,
277, 291, 295
co-rotating extruders, 112
counter-rotating, 12, 109–112, 236
cross-head die, 306, 307
crystallization, 264, 273, 274, 279,
298
cumulative strain, 165336 Polymer Extrusion
D, E
Deborah number, 278
delay zone, 38, 47, 59, 60, 66, 75
dimensioning of extrusion dies, 223–
229
dispersive mixing, 165–170
distribution channel, 250–254, 258,
259, 329
distributive mixing, 163–165
energy
equation, 26, 57, 77, 78
transfer cables, 305
equilibrium equation, 6
erosion, 166, 167, 169, 177, 192
extrudate swell, 214–217
F, G,
feed
rate, 80, 114, 120, 121, 124, 173,
190, 196
zone, 40, 45–47, 49, 57, 66, 75,
114, 120, 121, 308, 310, 311,
329–330
filling ratio, 114, 121, 123, 150, 151,
159, 160
film blowing dies, 258–261
flat die, 250–255, 310, 329
flexible packaging, 245, 246, 248
flight thickness, 116, 117
flow
balancing, 226–227
rate of the solid, 49–53
force of interaction, 324–325
friction coefficient, 65–69
functional zones, 38, 40, 95, 113, 120
H, I, K
heat
flux, 12, 16, 17, 57, 77, 78
transfer coefficient, 12, 16–18, 126,
146, 147, 154, 158, 271, 273,
279
transfer, 11–19, 146–147
hydrostatic pressure, 5, 45, 63
independent channels, 118
instability problems, 264–266
interface temperature, 19, 47
interpenetration zone, 111, 112, 116,
118–120, 131, 141
kneading elements, 113, 114
L, M, N
lateral pressure coefficients, 72–73
longitudinal flow, 86–88
lubrication approximation, 139, 141,
231, 237, 262, 318, 320, 325, 328
mean temperature, 231–233, 238,
239, 288
melting
model, 76, 125, 152, 196
rate, 78, 79
zone, 73–84, 121–127
metering zone, 85–94
mixing
heads, 103–105
indices, 163
nanocomposites, 162, 185–193
network
method, 28–32
model, 29, 213, 223, 224, 229
Newtonian
behavior, 7–8
fluid, 76–82
number of flights, 115, 117, 118, 119
Nüsselt number, 16, 146, 158, 159,
232
O, P, R
optimization, 194–197
overall model, 95–99
penetration depth, 18
pitch angle, 41
planar shear flow, 3
Poiseuille flow, 3
polymer blends, 177–185Index 337
power
dissipated, 11–13, 16, 126, 154
law, 9
law fluid, 12, 22, 25, 30, 31, 60, 82,
85, 90, 91, 156, 214, 227, 252,
253, 261, 262, 317
pressure
field, 136, 137, 142, 143, 144, 145,
163, 164, 214, 253
flow, 316–318
profile, 58–60, 63, 82, 98, 139,
140, 160, 161, 314, 324
temperature fields, 238
profile dies, 211–214, 224
pulling force, 269, 288
reactive extrusion, 170–177
residence time distribution, 147–151
restrictive elements, 114, 158, 159,
197
right-and left-handed screw element,
128–137
S
scale-up criteria, 99
screw
body diameter, 41
cross-section, 115
diameter, 42, 115, 117, 120, 146,
147
elements, 113–115, 121, 123, 125,
129, 136, 138, 144, 150, 152
screw-barrel system, 38, 41, 105
shape factors, 90, 132, 152
shear
flow, 315–316
flow rate, 129, 130, 132, 316
shrinkage, 217
single-screw extruder, 37, 65, 73, 95,
99, 103, 109, 110, 112, 113
slab method, 27, 232, 319, 324
solid
bed profile, 80, 82, 83
conveying zone, 45–73
specific
energy, 99, 124, 152–154
mechanical energy (sme), 152
strain rate, 2–3
stress, 4–6
stretching, 217
T, V, W
take-up ratio, 257
telephone wire, 305, 308, 329, 331
temperature profile, 233
thermal
balance equation, 11–13
diffusivity, 14, 17, 232
effusivity, 19
time-temperature superposition, 10
transfer coefficient, 12, 16–18, 126,
146, 147, 154, 158, 217, 273, 279
transverse flow, 88–89
tubes, 19, 211, 284
twin-screw extrusion, 109–112
velocity profiles, 42, 62, 92, 133,
134, 227, 271, 277, 278
viscosity, 7
volumetric flow rate of the solid
polymer, 49
Weissenberg number, 216, 217
wire coating dies, 307–309
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