Page 301 - Academic Press Encyclopedia of Physical Science and Technology 3rd Polymer

P1: GQT/MBQ P2: GPJ Final Pages
Encyclopedia of Physical Science and Technology EN014C-660 July 28, 2001 17:14

Rheology of Polymeric Liquids 239

◦
FIGURE 2 Photograph describing the swelling of a molten high-density polyethylene melt at 180 C exiting from a
cylindrical tube.

climb-up effect shows that polymeric liquids exhibit a v z = f (y), v x = v y = 0. (1)
“normal stress” effect.
We then have a constant velocity gradient dv z /dy,
Figure 2 shows the swelling of a molten high-density
polyethylene extrudate exiting from a cylindrical tube, ˙ γ = dv z /dy = constant, (2)
which is believed to occur as a result of the recovery of the
elastic deformation (or the relaxation of normal stresses) where ˙γ is called steady-state shear rate. The flow field
imposed on the polymeric liquid in the capillary. satisfying Eq. (1) is called “uniform shear”flow field or
“simple shear”flow field.
When a liquid flowing through a long cylindrical tube,
III. DEFINITIONS OF MATERIAL
FUNCTIONS FOR POLYMERIC LIQUIDS the velocity profile of the liquid may look like that shown
in Fig. 4. The exact shape of the parabolic velocity pro-
file may vary depending on the type of liquid dealt with;
Consider the flow fields in which a polymeric liquid can
in other words, whether the liquid has small molecules
undergo shear deformation, which is encountered when
or large molecules. The shape of the velocity profile can
the liquid flows through a confined geometry, such as
be predicted only when we have information on the flow
through a pipe or channel. Under such circumstances,
properties of the liquid. It is clear from Fig. 4 that the axial
some practical questions come to mind. (1) How much
velocity v z is a function only of distance in the radial (r)
pressure drop (or mechanical or electrical power) are re-
direction in cylindrical coordinates, that is,
quired to maintain liquid flow through a pipe at a desired
flow rate? (2) What would be the most cost-effective de- v z = f (r), (3)
sign for a pipe to transport a specific polymeric liquid at a
and therefore the velocity gradient dv z /dr varies with r,
desired flow rate? These questions can be answered intel-
ligently only when we know the relationships between the
rheological properties of the liquid and the rate of defor-
mationandbetweentherheologicalpropertiesoftheliquid
and its molecular parameters, such as the chemical struc-
ture, molecular weight, and molecular weight distribution.
Consider a flow of liquid flowing through two infinitely
long parallel planes, where the upper plane moves in the
z direction at a constant velocity V (i.e., v z = V )at y = h
while the lower plane remains stationary (i.e., v z = 0). Re-
ferring to Fig. 3, the gap opening h is very small compared
to the width w of the plane (i.e., h w). Under such a
situation, the velocity field of the flow at steady state be- FIGURE 3 Schematic describing the velocity profile of a liquid
tween the two planes is given by flowing through two parallel planes.