Simple shear flow (plane Couette flow)
1
H
U
Viscosity of a polymer melt
2 shear thinning: non-Newtonian
(zero-shear viscosity)
viscosity is shear rate dependent
Effect of shear on melts
3
Effect of MW on the viscosity of PS melts
4
c c
M M
M c
M M
cM
, ,
4 . 3
00
Shift factor
(11.7)
)
(
) log (
) (
) log (
2 1
g g T
g C T T
T T
a C T
T
WLF equation:
5 - Temperature dependence of :
260
Polymer coils in solutions
6 A sphere means the hydrodynamic volume of a polymer chain
extremely dilute ↔ dilute dilute ↔ concentrated
concentrated
Effect of concentration on the viscosity of polymer solutions
c*
7
s s
s p
Below c*, viscosity is proportional to
concentration, but above c*, viscosity is approximately
proportional to the fifth power of concentration.
In general, the effect of molecular weight (M) and solution
concentration (c) of viscosity can be modeled as
Effect of shear rate on the viscosity of polymer solutions
8
Constitutive Equations
9 - the power-law (or Ostwald–de Waele–Nutting) model given as
- the dependence of apparent viscosity on shear rate for a power-law fluid is
consistency
Elastic properties of polymer melts: Die Swell
10
Normal stresses for simple shear flow
11
12
13
Melt Instabilities
12 A recent explanation attributes sharkskin formation to chain
disentanglement at the die wall in the exit
region. This may be due to a combination of interfacial slip and cohesive failure.
Velocity profile of a power-law fluid (pressure (Poiseuilli) flow)
13
m n
● r
z
Modified simple shear (drag) flow (axial annular Couette flow)
14 where
Ri/Ro
Capillary Rheometer
15
Dpcap Dp
apparent shear rate
Couette Rheometer
Cone-and-Plate Rheometer
16 torque
for Newtonian
Effect of shear rate on the viscosity of polymer melts
17
Extruder screw geometry for flow analysis
Extruder screw geometry for flow analysis
depends on screw and die geometry
19 power-law index
Figure 11-33 die zone
screw zone
https://www.researchgate.net/profile/Harwin der_Singh4/publication/301598210/figure/fig 7/AS:391588783116297@1470373449866/Fig ure-10-Pressure-developed-during-
extrusion-process-Figure-11-Melt-flow- tester.jpg
screw characteristics
