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Encyclopedia of Physical Science and Technology EN012c-593 July 26, 2001 15:56

618 Polymer Processing

FIGURE 9 A slit-die rheometer consisting of two parallel plates
through which polymer melt is pumped. The wall shear stress
is determined from the pressure measurements along the up- FIGURE 10 Two methods for generating uniaxial extensional
per wall and the shear rate from the volumetric flow rate. [From flow: (a) Ballman method and (b) Meissner method. [From
Baird, D. G., and Collias, D. I.(1998). “Polymer Processing: Prin- Baird, D. G., and Collias, D. I. (1998). “Polymer Processing: Prin-
ciples and Design,” Wiley, New York.] ciples and Design,” Wiley, New York.]

Slit-die rheometers (Fig. 9) are useful devices for mea- D. Rheometry: Shear-Free Flow Measurements
suring the viscosity of polymer melts because it is possible
Two techniques for measuring the extensional viscosity of
to measure the pressure gradient directly. The geometry
polymer melts are shown in Fig. 10. In the first technique
is that of two flat plates with a rectangular cross section.
(Ballman method) polymer melt is either glued or clamped
If the aspect ratio, W /H, is greater than or equal to 10,
atbothends,andthenoneendismovedinsuchamanneras
then there is no sidewall effect. The wall shear stress, τ w , is
to either generate a uniform extension rate or a constant
then
tensile stress. In the Meissner method, both ends of the

−dp H P 3 − P 1 H melt are pulled at either a constant velocity to achieve a
τ w = = , (17)
dz 2 d 31 2 uniform extension rate or to provide a constant stress.
For the Ballman method in order to generate a uniform
where P 3 and P 1 are the pressures recorded by transducers
extension rate throughout the sample, one end of the sam-
T 3 and T 1 , respectively, and d 31 is the distance between
ple must be deformed such that the length of the sample
the center of the transducers. The wall shear rate, ˙γ w , is ˙ εt
is increased exponentially with time; i.e., L = L 0 e . The
obtained from the following relation:
Meissner method has several advantages and disadvan-
tages relative to the Ballman method. First, it is possible

˙ γ a d ln ˙γ a
˙ γ w = 2 + , (18) to reach very high strains (of the order of 7.0). Second, the
3 d ln τ w
sample is usually deformed horizontally so that the match-
2
where ˙γ a = 6Q /WH (this is just the wall shear rate for ing of the oil density with that of the polymer melt is not as
a Newtonian fluid) for flow through flat plates. critical. Finally, finding a suitable glue is not necessary. On
The slit-die rheometer also offers the possibility of ob- the other hand, the construction of the apparatus is more
taining values of N 1 at high shear rates. The method is complicated and expensive. Larger samples are required,
based on the measurement of a quantity called the hole and they must be nearly free of inhomogeneities.
pressure, P H , which is the difference of pressures P 1 and There are two methods for obtaining approximate val-
ues of ¯η. The first method is based on the fiber spin-
P 2 where P 2 is the pressure measured by transducer T 2
mounted at the bottom of a rectangular slot placed per- ning technique shown in Fig. 11 (the device is called the
pendicular to the flow direction, i.e.: Rheotens). The second method for estimating ¯η is based
on entrance pressure data. It must be emphasized that these
P H = P 1 − P 2 . (19) two methods will give only approximate values for ¯η,but
the correlation between values obtained using exact meth-
The value of N 1 is obtained from the following equation:
ods and the approximate values is sometimes quite good.
dP H
N 1 = 2τ w . (20)
d τ w E. Squeeze Flow Rheometer
Hence, from data of P H versus τ w one can obtain N 1 as a A device that can be used to handle complex materials,
function of τ w . such as highly filled polymers, and that can generate both