Polymer Degradation and Stability 64 (1999) 239±242
Development of an on-line twin capillary rheometer
Shih-Hsuan Chiu*, Sheng-Hong Pong
Graduate School of Textile and Polymer Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 10672,
Taiwan
Received 6 May 1998; accepted 30 August 1998
Abstract
On-line capillary rheometers have been extensively used as a means of measuring the ¯ow properties of polymeric melts during
processing. But, none of them implemented both the Bagley and the Rabinowitsch corrections. In this work, an on-line twin
capillary rheometer was developed in an attempt to measure the true viscosity for polymer characterization. The system was
designed to achieve automatically rheological measurements. It was also equipped on a single screw extruder to verify its practicability. It is pronounced that using the on-line twin capillary rheometer would be more timesaving and manpower saving than use
an o€-line capillary rheometer. # 1999 Elsevier Science Ltd. All rights reserved.
Keywords: On-line capillary rheometer; Bagley correction; Rabinowitsch correction
1. Introduction
Rheological data can be used to determine the structure (like molecular weight and molecular weight distribution) of a polymer under processing. They can also
assist the assessment of processability. Besides, we can
use them as the index of the end-product quality. They
do play a very important role in the polymer processing
industries.
Rheometers can be typically classi®ed, according to
how they are installed, as o€-line, on-line and in-line
types [1]. The rheological properties of polymers are
shear history and heating history dependent. The outcomes from in-line and on-line measurements would be
closer to practical properties than from o€-line measurements. In addition, o€-line measurements would be
much more time-consuming than the others would.
More and more applications based on in-line and online measurements or controls are proposed in the
polymer processing industries [2±6].
A capillary rheometer, in which the polymeric melt is
forced through a circular pipe, is the most popular rheometer both in the polymer processing industry and
laboratory. Rheological properties can be determined
by measuring its pressure drops and ¯ow rates. There
would be reasons of the economic cost and complica* Corresponding author. Tel.: 00886 22737 6532; fax: 00886 22737
6532; e-mail: schiu@hp730.tx.ntust.edu.tw
tion of mechanism, the typical on-line applications of
capillary [7] seem not to provide the Bagley correction
and the Rabinowitsch correction [8], which are important in polymer characterization.
In this work, a twin capillary rheometer was developed in an attempt to provide the Bagley and the
Rabinowitsch corrections on-line. The performance of
this on-line rheometer applied on the on-line rheological
measurement in a signal screw extruder was also discussed in this paper.
2. Theory
A short review of how a capillary rheometer works is
presented. The apparent viscosity, a , according to the
derivation of the Poiseuille law for capillary ¯ow [9] is
the wall shear stress, , over the apparent wall shear
rate, _a ; as
;
_a
a ˆ
1†
where
4Q
;
R3
2†
P R
;
2L
3†
_a ˆ
ˆ
0141-3910/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.
PII: S0141 -3 910(98)00195 -5
240
S.-H. Chiu, S.-H. Pong / Polymer Degradation and Stability 64 (1999) 239±242
where Q is the volume ¯ow rate, R represents the radius
of the capillary, L denotes the length of the capillary,
P is the capillary pressure drop.
For a polymer melt, the shear rate, according to the
Rabinowitsch correction, would be
3n ‡ 1
_a ˆ _a ;
4†
4n
The gear pump, from the extruder, draws the polymeric melt through the reservoir to the capillary. When
operating, one of the capillaries is plugged and the melt
then ¯ow out from the other one. The entrance pressure
drop can be calculated by utilizing the pressure drops of
the two capillaries under the same shear rate and temperature, according to the Bagley correction.
where n is the power in the relationship shear stress
proportional to (shear rate)n at a given shear rate as
4. Experiments
d log nˆ
d log _a
5†
The corrected shear stress in capillary ¯ow, according to
the Bagley correction, would be
ˆ
P ÿ P0 †R
;
2L
6†
where P0 is the pressure drop through an ori®ce die (die
with L/R < 1) of the same diameter at the same ¯ow
rate. Thus, the corrected shear viscosity is given by
a ˆ
:
_a
7†
3. Mechanical design
As shown in Fig. 1, the twin capillary rheometer
contains a gear pump and two capillaries of which the
L/D ratio are 16/1 and 0.5/1 mm/mm, respectively, one
sensor of a combination of pressure transducer and melt
thermocouple, two solenoid valve driven plugs.
Fig. 1. Schematic diagram of the twin capillary rheometer.
The twin capillary rheometer was mounted on a single screw extruder, between the screw and the die as
shown in Fig. 2, to implement the on-line test. The
material used in this test was low-density polyethylene
(LDPE). The sensor in the capillary was the ASAHI
pressure transducer of type TTJ-N67A from Japan. The
pressure range of this sensor is 0±350 kgf/cm2. Temperature range is 0±760 C. The gear pump was connected to a motor,the speed of which was controlled by
the inverter. All the electrical signals from sensors to
instruments were connected to an XT compatible computer with AXIOM AX5411 A/D and D/A converter
board (except temperature signals were to the RS232
interface) for data acquisition. The programming language used was Turbo C.
The procedure of experiments for routine testing the
melt viscosity was set as the following 12 steps.
1. Set the extruder screw speed at 300 rpm and operating temperature at T1.
2. Actuating the solenoid valve to plug the ori®ce.
3. Set the gear pump speed at N1 and acquires the
pressure drop of the long capillary, P1, from the
pressure transducer to determine the ¯ow volume,
Q 1.
4. Use Q1 and P1 to determine _a;1 and 1 by means
of Eq. (2)Eq. (3), respectively.
5. Change the gear pump speed, N1, to N2 for deriving a di€erent ¯ow rate, Q2.
6. Use Q2 and the pressure drop, P2, in this condition, to determine _a;2 and 2 by means of Eq.
(2)Eq. (3), respectively.
Fig. 2. Schematic diagram of experimental apparatus.
S.-H. Chiu, S.-H. Pong / Polymer Degradation and Stability 64 (1999) 239±242
241
Fig. 3. Viscosity curves of LDPE at 190 C.
Fig. 4. Viscosity curves of LDPE at 180 C.
7. Use _a;1 ; 1 ; _a;2 and 2 to determine the n, by
means of Eq. (5). Then, calculate the corrected
shear rate, _a , by means of Eq. (4).
8. Actuating the solenoid valve to plug the long
capillary and open the ori®ce.
9. Acquire the pressure signal, P0, from sensor.
10.Use P0 in Eq. (6) to determine the true shear stress,
. Find the corrected viscosity by the true shear
stress over the corrected shear rate.
11.Change a di€erent gear pump speed and return to
step 2.
12.Change a di€erent operating temperature and
return to step 1.
The parameters, Cn, was determined by using the
least square regression [11] with six pre-test pump
speeds, pressure drop and corresponding ¯ow rate data,
is shown in Table 1.
5. Flow rate measurement
In this work, the volumetric ¯ow rate was determined
according to the rotation of gear pump and the pressure
drop as was proposed by Kramer [10]. The volume ¯ow
rate was calibrated by using a volumetric graduate. The
¯ow rate data, according to the experimental result,
were ®t to a second order polynomial for temperature
with pump speed held constant and to a linear ®t of
pump speed with temperature held constant. The two
functions were combined to form a single equation in
the form of
Q ˆ C1 ‡ C2 P ‡ C3 N ‡ C4 NP ‡ C5 N2 ‡ C6 PN2 ;
6. Results and discussions
Three typical rheological curves (solid lines) by means
of the on-line twin capillary rheometer at 170 C, 180 C
and 190 C are shown in Figs. 3±5, respectively. In order
to verify the consequences, the same conditions and
material as used in on-line were tested in an o€-line
standard capillary rheometer. The results (dashed lines)
by using the Rosand Precision Capillary Rheometer are
also shown in Figs. 3±5, respectively. The results from
the on-line twin capillary rheometer have almost the
same trends compared to that from the o€-line standard
rheometer. This seems to be a good outcome. But there
are o€sets from the standard test results. The maximal
viscosity error with the same shear rate is 41 Pas. The
reasons for these o€sets could be from the e€ect of the
power law index, n. As shown in Table 2, the power law
8†
where Q is the volumetric ¯ow rate, N is the pump
speed, P is the capillary pressure drop, Cn is the coecient in which n is a positive integer.
Table 1
Values of coecients in Eq. (7)
Coecient C1
C2
C3
C4
C5
C6
Data
0.097328 ÿ0.007413 0.014097 0.000045 0.000014 0.0
Fig. 5. Viscosity curves of LDPE at 170 C.
242
S.-H. Chiu, S.-H. Pong / Polymer Degradation and Stability 64 (1999) 239±242
Table 2
Partial rheological data of LDPE at 170 C
On-line twin capillary rheometer
O€-line Rosand capillary rheometer
Shear rate (corrected)
n
2600.203
2297.595
568.390
285.477
0.21
0.24
0.28
0.33
2789.900
2297.800
643.700
246.500
0.29
0.30
0.35
0.39
indexes of LDPE derived from the on-line twin capillary
rheometer are a little smaller than that from the Rosand
capillary rheometer. This is because the interval of two
shear rates that are used to calculate the power law
index is larger, in this work, than the one of the o€-line.
A suitable interval for determining n is still in study.
7. Conclusion
In this work, an on-line twin capillary rheometer was
developed. The experimental results of the on-line twin
capillary rheometer have a similar trend against that of
the o€-line measurement. It is concluded that the twin
capillary rheometer can implement viscosity measurements with both the Bagley and the Rabinowitsch corrections on-line, which is more timesaving and
manpower-saving than using an o€-line capillary rheometer. Since the problem in viscosity errors still exist,
the further project would focus on more precise measurements.
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