EXTENSIONAL VISCOSITY OF DILUTE POLYMER SOLUTIONS Jin Huang A thesis submitted in wdormity with the requirements for the degree of Master of Applied Science Graduate Department of Mechanical and Industrial Engineering, In the University of Toronto OCopynsht by Jin Huang, 1999
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EXTENSIONAL VISCOSITY OF DILUTE POLYMER SOLUTIONS
Jin Huang
A thesis submitted in wdormity with the requirements for the degree of Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering, In the University of Toronto
OCopynsht by Jin Huang, 1999
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Extensional Viscosity of Dilute Polymer Solutions Jin Huang
Master of Appikd Sckncc, 1999 Deputment of Mechrnicrrl and Industritl Engineering
University of Toronto
ABSTRACT
The purpose of this study was to obtain reliable extensionai viswsity
meanirements for dilute polymer solutions ushg a marnent-stretching rheometer at the
University of Toronto.
Initial extensional measurements of two Newtonian fluids gave data very close to
the expected values, which validated the experimentai technique.
Three dilute solutions of high-molecular-weight polystyrene in oligorneric styrene
and the Ml fluid, were then testeci. For the least viscous fluid, high strains were achieved
and a steady-state Trouton ratio of about 900 was obtained, at dl Deborah numbers. For
the more viscous Liquids, high strains were not achieved because the fluid filaments
detached from their holders. Reasomble agreement was obtained in the data cornparisons
with MIT and Monash University using similar test techniques and the same fluids.
The Fact that the steady-state value of SM-I was independent of the extensional
rate suggests that this value could be used as a m a t d property for SM-1.
ACKNOWLEDGMENT
1 wodd like to express my sincerest tfianks to Professor D. F. James for his
guidance and s u p e ~ s i o n of this work. His enthusiasm and patience have encourageci me
throughout the program. I wodd also like to thank Geoff M. Chandler for uimucting me
in the use of the filament stretching rheometer and for his continuous technical support.
His work has inspued me in many ways.
During the two yean, 1 received help of Mnous kinds from my wlleagues and
Wends. 1 wodd particularly like to thank Dorota Kiersnowsky, W e n g Liu, Navid
Mehdizadeh and Masoud Shams for their consistent assistance. Special tbanks are due to
Alison Collins, Angela Garabet and Vala Mehdinejad for kindly reviewing parts of the
manuscript.
Finally, I wodd like to express my love and appreciation to my parents: thank
you for bringing me to this wonderfùl world and giving me the fieedom to explore it.
............................................................................. The ideal diameter history 3 5 ............................................................................ Velocity compensation 3 7
Disk cleaning ................................................................................................ 40 Effect of temperature and disk dimensions , .................................................. 4 1
.................................................................................. Effect of temperature 4 1 . . Initial aspect ratio .......................................................................................... 43
6.1 Force traasductr crilibration and noise rcduction -r------- ...HC.m...aH....-......... 44 ........................................................................................... 6.1.1 Force calriration 44
............................................................................................ 6.1.2 Noise reduction -47 6.2 Cdibmtion of diameter-mcuuring device and control of its position , ......... 51
7.1 Newtonirn fluids and thtir s b w propertics .....m............................................ 56 7.2 Non-Newtonian fluids propcrtia .,...m.....m......... ............................................. 57
......................................................................... ....................... Fluid Ml .,, 8 2 Cornparison with other Iaboratories ......e......................................................... 86
Table 7.1 Properties of the Newtonian test fluids, from General Electric Company
7.2 Non-Newtonian fluids properties
In this project, three Boger fluids were prepared as standard test fluids. They were
made by Prof Susan J. Muller in the Department of Chemical Engineering at the
University of California, Berkeley, and are referred to as SM fluids hereafler.
The solvent of the three SM fluids is oligomeric styrene (Piccolastic A5 fiom
Hercules). The relaxation time of the solvent is 2.7~ 104 sec and its shear viscosity is 34.0
Pa-s at 25 OC [Anna and McKinley, 19991. The solutes are polystyrene of various high
molecular weights, as listed in Table 7.2. The polymer concentration in each solution is
the same, 0.05 % by weight.
The MIT laboratory of Prof G. H. McKinley provideci complete data of the
physical and shear properties of the SM fluids. In Table 7.3, the zero-shear viscosity qo
and the relaxation time k of these fluids at 25 OC are presented. Both properties are
temperature dependent and the temperature effects can be accounted for using the shifi
factor a~ given by Eqn. S. 12. The shear viscosity data were verined using a Brooffield
viscorneter.
The Ml fluid was also a test fïuid for the preliminary investigation because its
extensional viscosity has been investigated b y many researchers (the M 1 project). This
Fiuid
Ml Polyisobutylene Aldrich Chern. 0.244 %
(MW. 4-6x10~)
SM- 1
SM-2
Table 7.2 Composition and physical properties of the non-Newtonian test fluids, the
SM fluids and Ml wulier, 1997; Tirtaatmadja, 19931.
Solute
Polystyrene (M. W. 2 . 0 ~ 1 06)
Polystyrene (M. W. 6.9~ 1 06)
Table 7.3 Steady shear properties of the non-Newtonian test fluids at 25 OC [Anna
and McKinley, 1999; Binding et al, 1990; Tirtaatmadja, 19931
Concentration Surface tension
coefficient (Nh)
Fluid
SM- 1
SM-2
SM-3
Ml
Density
(ks/m))
0.05 wt %
0.05 wt %
MW (glmol)
2x 106
7 x 106
20x10~
4-6x 106
0.03
0.03
1 O00
1 000
rlo 0'a-s)
39
46
56
2.04
(sec)
3 -7
31.1
155
0.86
fluid was prepared in the Chernical Engineering Department at the Monash University in
1988. It is a 0.244 % solution of polyisobutylene in a sotvent consisting of 93%
pol ybut ylene and 7% kerosene (Shell) mguyen and Sridhar, 1 990). Other rheological
properties can be found in a special issue of foumai of Non-hrewtonian Fiztid Mechzics
[Vol. 3 5, 199 11. Its shear viscosity was measured in our laboratory using a Brookfield
viscometer, and the results are plotted in Figure 7.1.
100
Shear rate, 11s
10
u! Q
Ç; 8 .- > L (P Q) r u3
Figure 7.1 Shear viscosity q of Ml from the Brookfield viscometer.
O Temp = 25 O C
A Temp = 20 OC
a
ff
CHAPTER 8
EXTENSIONAL RESULTS
In this chapter, values of extensional viscosity obtained from the filament
stretching rheometer for both Newtonian and non-Newtonian fluids will be presented in
terms of the Trouton ratio. Constant extensional rates were rnaintained for the duration of
the expenments for al1 four non-Newtonian fluids- The reproducibility of the extension&
data, as weil as the errors involved, wiil be discussed. Finally, the extensional
rneasurernents for S M 4 and SM-2 will be comparai with data fiom two other
laboratories.
8.1 Newtonian calibrations
Stress in Newtonian fluids, unlike non-Newtonian fluids, does not depend on
deformation history. Their Trouton tatio is three, independent of strain or strain rate.
Thus it is not necessary to obtain a constant extensional rate for these fluids. For the two
Newtonian fluids tested, Viscasil 12,500 and 30,000, experimental data were obtained at
nominal extensional rates of 5 s" and 10 S? The diameter and force traces for these two
iiquids are s h o w in Figures 8.1-8.4. In each case, the diameter starts at 3 mm, the size of
Figure 8.1 Data for the Newtonian fluid, Viscasil 12,500, at a nominal extensional
rate of d =S s-': (a) diameter profile (b) force history
Figure 8.2 Data for Viscasil 12,500 at a nominal extensional rate of t 4 0 5':
(a) diameter profile (b) force history
Figure 8.3 Data for Viscasil 30,000 at a nominal extensional rate of f. =S S-':
(a) diameter profile (b) force history
lime. s
Figure 8.4 Data for Viscasil 30,000 at a nominal extensional rate of 1 =10 s-':
(a) diameter profile (b) force history
the disks. Even without correction, the diameter plots are close to the ideal shape: a single
slope on a serni-log scale. In the force plots obtained, the force rises quickiy at the start of
stretching and then decays exponentially, as seen fiom the straight lines on the semi-log
force versus tirne plots. The Newtonian measurements were possible after the transducer
noise was reduced.
The figures show more scatter at the end of the force plots, which is related to the
force transducer. As described in Section 6.1, the noise Ievel for the MOD405 transducer
is of the order of 10" N. Near the end of the stretching process, the filament is very thin
and the measurable force decreases to 0(10'~) N, quivalent to the noise level. Therefore,
the noise added a random signal of the same amplitude to the measured force.
Figure 8.5 presents the transient Trouton ratio for both Newtonian fluids at the
two nominal extensional rates. It is encouraging that the Trouton ratio values are not only
constant, but also fall very close to the predicted ratio of 3. The error band is I 0.5. The
accurate extensional measurements for Newtonian fluids provide a solid basis to continue
with non-Newtonian measurements. The scatter is greatest at the end of the Trouton ratio
plot, corresponding to the larger scatter in the force plot.
Tests were conducted With the Newtonian fluids to determine the effect of initial
aspect ratio. As discussed in Chapter 4, usually I\o a 1 is necessary to prevent sagging and
breakup of the initial filament. However, in this rheometer & < 1 could not be achieved
due to the loading procedure. Initial distances of Lo = 1-5 mm and 2.0 mm, equivdent to
aspect ratios of 1 and 413, were used in testing Viscasil 30,000 at two nominal
extensional rates. As shown in Figure 8.6, the Trouton ratio values are identical at both
Figure 8.5 Transient Trouton ratio for Newtonian fluids
rates. Moreover, the Trouton ratios with Lo = 1.5 mm show more scatter than those with
La = 2 mm close to the end of testkg. This is reasonable because the sample size is
smaller with =1.5 mm, resulting in a smaller tensile force. Based on these results, the
initial aspect ratio of 4/3 was used in subsequent experiments.
8.2 Extensional results for Non-Newtonian fluids
There were four non-Newtonian test fluids investigated in this work Their
extensional data - diameter, force and Trouton ratio - are presented in this section. Since
temperature control was not avadable at this stage, experiments were undertaken at the
laboratory temperatures, and the parameters such as shear viscosity, Deborah number and
the relaxation time, were correcteci to the reference temperature, 25 OC, using the shift
factors given in Section 5 -4.1.
The velocity compensation for this fluid was perforrned using the method
describeci in Chapter 4 and singie-dope diameter profiles were obtained. Figwe 8.7 a
shows the diameter profile for SM- L after correction, at De = 19.5. The extensional rate
& =3 .O S-' was determineci from the best fit of a straight line through the data The ideal
diameter is the solid line and the symbols represent the rneasured diameter values f?om
the Zumbach. The graph confirrns that the actuai diameter is close to ideai. Analysis of
the data showed that the diameter
Deborah numbers. The minimum
lower limit of the Zumbach-
was within B % of the ideai diameter for SM-1 at ail
diameter rneasured was 0.10 mm, which is above the
O Lw1.5 mm, at 10 11s Lo=2 mm, at 10 1/s
A Lo=1.5 mm, at 5 1/s
x Lw2 mm. at 5 Ifs
0.1 1 0.5 0-7 0.9 1.1
Time, s
Figure 8.6 Comparison of Newtonian data with two initial aspect ratios, for two
nominal extensional rates.
Figure 8.7 Data for SM-1 at De = 19.5 ( 6 =3 8): (a) diameter (b) force
Since the fluid's shear viscosity is Iow, 39 Pas ai 25 OC, the MOD405 force
transducer was used for the force measuremeats. Extensional data for SM-1 were
obtained at De numbers of 10.7, 19.5 and 46.7. The tensile force trace corresponding to
the diameter in Figure 8.7.a is shown in Figure 8.7.b. The minimum force measured d e r
the start-up was 5 x 1 0 ~ N, above the noise level of the MOD405 transducer used. As
stretching commenced the force increased rapidly to a maximum and then decreased
when further stretched. This initial rapid increase is sirnilar to what is found for
Newtonian fluids. The peak is the viscous response of the fluid to a sudden change fiom
rest. The force reached a minimum before approaching a second maximum at high
strains. During the initial extensional motion, the polymer molecules in the solution are
aiigned dong the flow direction and stretched from their equilibriurn conformatioas.
After alignment, the tensile force decreases with the filament diameter because the stress
in the filament remains unchangecl. At large mains, large hydrodyoamic forces cause the
molecular chahs to uncoil and the resistance increases rapidly. This is reflected in an
increase in the tende force while the diameter continues to decrease. The second peak in
the force plot has a larger magnitude than the fint one. At the higher extensional rates for
SM-1, the force decreases exponentially after reaching the maximum, as illustrated in
Figure 8.7.b. This exponential decrease implies that a steady state has been achieved in
the extensional stresses, Le., the moldes are w longer extending and have fixed
conformations.
At a smaller extensional rate, & = 1.32 sml, a plateau instead of a peak was found
in the force diagram for al1 runs while the diarneter decreased exponentially, as shown in
Figure 8.8.
Results of transient Trouton ratio versus Hencky strain for SM4 at three Deborah
numbers-10.7, 19.5 and 46.7-are shown h Figure 8.9. Generally, the Trouton ratio rises
rapidly to a value close to 3 within 0.1 strain unit and remains roughly constant until the
strain goes above 2. Experimentaiiy, the Trouton ratio values start at 2.3 to 2.9 for De =
19.5 and 46-7, whereas the value is 3-4 for De = 10.7. ûverall, these values Ml in the
reasonable range of 2.3 to 3.4. The values fùrther indicate of the accuracy of the results.
As the fluid is stretched m e r , the extensional stress in the filament Increases
dramaticaily. In this region, the significant stress growth is a result of macromolecules
being extendeci from their equilibrium confguration~~ As shown in the figure, the
transient Trouton approaches steady-state values at large strains. For SM-1, the steady-
state vdue was found to be around 900 for De = 19.5 and 46.7; for De = 10.7, the steady
state value was fond to be 1500, somewhat higher than the other two. These values are,
however, lower than the steady-state values obtaïned for other fluids. Tirtaatmadja and
Sridhar [1993] reported steady-suite values of 2-5x10~ for Ml fluid and two other high
molecular weight P B solutions, and van Nieuwkoop et al [1996] obtained values as high
as 6x 103 for some similar dilute PIB solutions. A Hencky strain of 6.4, i-e., L& = e6-q
was achieved for this fluid,
Several runs were made at each Deborah number. The reproducibility is
illustrated in Figure 8.10, which is for De = 10.7.
1 O
o measured diameter - O=Doexp(-1 -32U2)
Figure 8.8 Data for SM- 1 at De = 10.7 (0 4-32 s-'): (a) diameter (b) force history
Figure 8.9 Cornparison of Transient Trouton ratio for SM-1 at al1 De numbers
8.2.2 Fluid SM-2
Extensionai data at four Deborah numbers were obtained for SM-2. This fluid is
more viscous than SM-1, with a shear viscosity of 46 Pas at 25 OC.
Figure 8.1 1 a shows a representative corrected diameter profile for this solution,
at De = 3 1.8. The extensional rate 6 = 1.65 S-' was determineci by a best-fit straight line to
the diameter data. Verification of this extensional rate was carried out by plotting hD/D
vs. time. The maximum error was &4%.
The corresponding force history is presented Figure 8.1 1 b. Similar to SM-1, the
force shoots up quickly, deches exponentidly, and then increases again. However, no
second peak was observed for SM-2 at any Deborah number. It was observed that the
filament detached fkom one of the disks at a high strain but before a second peak would
have been reached. Detachment of the filament terminated the stretching, in contrast to
termination caused by either the motor speed limit or the length of travei, as happened
with SM- 1.
Figure 8.12 presents Trouton ratio renilts for SM-2 at De numbers of 20.9, 3 1.8,
and 58.5, which were chosen to be dose to values obtained in the other two Iaboratories
for cornparison purposes. The start-up value is 2.8 for De = 31-8 and 58.5, and Tr
increases slightly fkom this value with Hencky strain. A sharp rise occurs at a strain of
about 1.8. For De = 20.9, the Trouton ratio starts at a lower value of 2.2 but increases
faster than the other two for the first stage, Le., there is no fkst plateau. Because of the
detachment, the maximum strain is 4.1, in contrast to the maximum strain of 6.4 achieved
with SM- 1. However, the maximum Trouton ratio for SM-2 is 2200, somewhat larger
Figure 8.10 Transient Trouton ratio measurement at De = 1 0.7 ( 5 = 1 -32 5') for SM- 1.
Figure 8.1 1 Data for SM-2 at De = 3 1.8 (É =2.8 S-'): (a) diameter @) force history
than the value of 2000 for SM-1.
The reproducibility is given by a representative example, at De = 58.5, as shown
in Figure 8.13. For the four runs, the values of the start-up plateau agree well, and there is
some scatter in the following rapid growth section. The data agree more closely again at
high strains.
8.2.3 Fluid SM-3
SM-3 is the most viscous of the three SM fluids, with a shear viscosity of 56 Pa-s
at 25 OC. Measurements were made at a single De number, 1 10.
Diameter and force plots for this fluid are shown in Figure 8.14. The extensional
rate obtained fkom the best-fit tine is 1.6 s-'. The maximum error between the measured
diameter and the ideal diameter in this case was *7%.
Since the maximum force with this fluid exceeds the measuring range of the
MOD405 force transducer, the MOD404 transducer was used. As happened with SM-2,
the filament detached fiom one of the disks before the force reached a second maximum.
The extensional stress growth of SM-3 is similar to the other two. As Figure 8.15 shows,
the Trouton ratio value rises fiom 2.6 in the linear viscoelastic region and remains
approximately at this value until the strain is around 1.3. It then increases rapidly to
values in excess of IO'. in accordance with the force measurements, no steady suite is
seen in the Trouton ratio plot for this fluid.
The four nuis at De = 110 (t =1.6 sa') in Figure 8.15 indicate the reproducibility
of data for SM-3.
O diameter
- ü=Doexp(-l.6VZ)
Figure 8.14 Data for SM-3 at De = 1 10 (1 = 1 -6 s*'): (a) diameter (b) force history
O Run 1
o Run 2 A Run 3 o Run 4
Figure 8.15 Transient Trouton ratio for SM-3 at De = 1 10 (t = 28.6 OC, É 4.6 S-')
8.2.4 Fluid M l
Fluid Ml was the standard fluid in the Ml project for the extensional viscosity
study about a decade ago. Its pnmary rheological properties were found by many
researchers, and Tirtaatmadja and Sridhar [ 19931 made TE measwements. in this work,
extensional measurements were made for Ml at two extensional rates. Its shear viscosity
is 2.04 Pas at 25 OC, which is an order of magnitude smailer than the viscosities of the
SM fluids presented earlier.
Corrected diameter plots of Ml for two extensionai rates are shown in Figures
8.16 and 8.17. The extensional rates of 5.6 S-' and 10.0 S-' are obtained fiorn the best-fit
lines of the diameter plots. High extensional rates are necessary with this fluid because of
its low viscosity. Plots of ADD versus time show that the actual diarneter data are within
B % of the ideal diameter, for both extensional rates.
Tensile force measurements were made using the MOI3405 (1 g) force transducer
because Ml is less viscous. The force profile is generally similar to those of the SM
fluids and no steady state is show in the force diagram at either extensional rate. The
minimum measured force was 8x IO-' N, which is the sarne order as the noise level for the
transducer. Hence the force data and Trouton ratio results are not as reliable as those for
the SM fluids.
At the higher extensional rate, 10 S-', the Trouton ratio data of Ml are similar to
those of the SM fluids. The data points start with a plateau close to 1.8, then rise to values
above 2000 at a strain of 4.7, as shown În Figure 8.18. At the lower extensional rate, f =
5.6 S-', however, the Trouton ratio increases rapidly to about 1.5, quickly decays to
negative values at 1.5 strain units, and then rises drastically to above 2000 at a strain of
Figure 8.16 Data for Ml at t =5.6 S-': (a) diameter profile (b) force history
Figure 8.17 Data for Ml at i 40 .0 S-' : (a) diameter @) force history.
O 1 2 3 4 5 6 Hencky strain
Figure 8.18 Transient Trouton ratio for Ml, at two extensional rates. i L =5.6 S-l,
+ i = 10 S"
This dedine in the Trouton ratio may be caused by several factors. First, as
mentioned before, the tende force exerted by the filament is too small to be accurately
measured by the transducer- Secondly, since the measured force is small, the correction
terms for gravity and d a c e tension in Eqn. 5.3 become more iduential, even critical,
in detennining the Trouton ratio. To assess the effêct of gravity, an analysis was carried
out by Anna and McKinley [1999]. in this analysis, another important dùnensionless
number appears, the Stokes number, defined by
St = P@ o/(tlo&) - (8- 1)
Gravity effects become important when the Stokes number is greater than unity. A
cntical De number can be computed which corresponds to St = 1. Ml has a smail
relaxation time, 0.86 s [Tirtaatmadja, 19931, compared with the SM fluids. With & = 1.5
mm, = 0.86 s, the Deborah number corresponding to St = I is 5.4. For f = 10 s'l, the
operating Deborah number is 8.6. but for E = 5.6 s", the number is 4.8, which is below
the criticai De of 5 -4, Le., the Stokes number is greater than 1 . This is probably the reason
for the unusual Trouton ratio profile at I = 5.6 8'. Methods of compensating for this
gravity effect are still under study.
8.3 Cornparison with other laboratories
The SM fluids were developed as standard fluids for comparing extensional data,
fiom different rheometers. Since the rheometers are based on the sarne filament
stretching technique, cornparisan of extensional data fiom them will assess the robustness
of this technique. In this section, our SM-1 and SM02 data are compared with data
provided by MiT and Monash University, Australia.
8.3.1 SM-1
Being the least viscous and having the smallest relaxation time among the SM
fluids, SM-1 is expected to generate the srnailest tensile forces and the smallest Deborah
numbers, Le., it is the most difficult SM fluid for extensional viscosity measuements-
Data fiom the three laboratories, however, agree well.
First, Figure 8.19 shows data at reasonably-close low Deborah numbers. The
Deborah numbers are 10.5, 14.0 and 19.5 for MiT, Monash University and the University
of Toronto respectively. The figure shows that, for al1 three sets of data, Tr increases
rapidly at the beginning of stretching, to a Newtonian plateau dose to the predicted value
2.6. The Tr values al1 remain at the pIateau until a strain of 2.3 and then dramatically
increase to values around 900. The ascents are identical for al1 three sets of data. Slight
discrepancies occur at the tum 6om fast increase to steady state at strains around 4.
Steady-state values were achieved for al1 three laboratories at strains of 5 to 6.
An initial overshoot of 4.3 is seen in the data fiom MIT, at the start of stretching.
The overshoot indicates non-ideality of the flow at the beginning of the test. If the
filament remains cylindrical throughout the test, the meaaired Trouton ratio would rise to
2.6 (for SM-1) immediately. The disks in MIT'S rheometer are 7mm in diameter, more
than twice the size of those at Monash University and the University of Toronto, which is
likely the cause of the non-ideality.
x De= 19.5 (Toronto) A b 1 4 . 0 Wonash) O b 1 0 . 5 (TMlT)
f
Figure 8.19 Cornparison of SM-1 Trouton ratio data fkom three laboratones, at low
Deborah numbers.
Figure 8.20 shows a cornparison at higher Deborah numbers for S M 4 The three
sets of data are almost identical and steady state was achieved. However, the Tr data of
MIT reach a steady state of around 700, while the other two have steady-state values
around 900.
The extensional data at ail Deborah numbers nom the three laboratories, as
plotted in Figure 8.21, show good agreement since about three quarters of the data points
€dl on each other. The steady state is attained at lower strains for higher Deborah
nurnbers, Le., at higher extensional rates. The steady state values at dinerent Deborah
numbers are reasonably close except for De = 10.7 from Toronto. As discussed earlier,
constant stresses are produced when the polymer chains are no longer extended and have
fixed conformation. If molecular chains are fully extended without intermolecular
entanglement, the stress at fuil extension should be independent of the path to that state
[James and Sndhar, 19951. The independence of the steady state values on extensional
rate suggests that the molecular chains in SM-1 fluid are fùlly extended.
For SM-2, data at three Deborah numbers from the present rheometer are
compared separately with similar data fiom MIT and from Monash University. In Figure
8.22, the Tr values of Toronto are larger than those of MIT at most strains. No steady
state was achieved in the six cases.
It is noticed that a trough, similar to that observed with Ml at a low extensional
rate, occurred in the SM-2 data fiom MIT at the lowest De, 15.5.
Since data at comparable Deborah values from Monash University are not
f i O of:
o De= 10.7 ('ïorunto)
O C b l 9 . S (Toronto) A b-46.7 (Toronto)
b l 4 . O (Monash) A b 4 7 . 5 (Monash)
ûe= 10.5 (MIT)
0 b 4 6 . 5
Figure 8.2 1 Cornparison of transient Trouton ratio for SM- 1
0 De = 58.5
O De = 31.8 AD^ = 20.9
O b 5 8 . 3 (MIT) A b 2 5 - 4 (MIT)
De=lS.2 (MIT)
Figure 8.22 Cornparison of transient Trouton ratio of SM-2 with MIT
available, the only possible cornparisons are at different Deborah numbers. As shown in
Figure 8.23, gwd overall agreement is obtained, despite the Merent ranges. The ascents
d e r the Newtonian plateau are identicai, as for SM-1. The highest strain attained at
Toronto was oniy 4 due to detachment of the filament and therefore no steady state was
observed. However, strains up to 6 were achieved at Monash (no detachment reporteci)
and steady-state values in excess of 10,000 were attained.
8.3.3 M l
The Ml data are compareci with the data fiom Monash U~versi ty at 5. = 6 a' and
i = 9 S-' [Tirtaatmadj* 19931 using the rheometer shown in Figure 2.5.
As shown in Figure 8.24, both sets of data fiom Monash University reasonably
agree with the one at É = 10 S-' nom Toronto, and the data at i =5.6 9' fiom Toronto are
lower than the rest. The difference at b =5.6 S-' can be explained by the more influentid
gravity effects which should be compensated for in the data at 8 4.6 S-', as dixvssed in
Section 8.2.4. The gravity problem was avoided at similar rates in Monash's data because
the stretching in their instrument was horizontal.
The Newtonian plateau value fiom Manash University is around 4, higher than
the value around 2 for Toronto, but its subsequent growth is slower than that of Toronto's
data. Kgh strains up to about 5.5 were achieved in both laboratories, and no steady state
was obtained.
SM-3 data fiom the other two laboratories are not available for cornparison.
Figure 8.23 Cornparison of transient Trouton ratio of SM02 with Monash University
É = 6 s" (Monash) B = 9 r' (MO&)
Figure 8.24 Cornparison of Ml with Monash University
CHAPTER 9
CONCLUSIONS AND FUTURE WORK
9.1 Conclusions
In this work, extensional measuements of two Newtonian fluids Viscasil 12,500
and 30,000 were conducted using the new filament stretching rheometer. The Trouton
ratio values at two nominal extensional rates 5 se' and 10 S-' were in the range of 2.4 to
3.5, very close to the predicted value of 3. This indicates that the new rheometer can
produce reliable extensional data and therefore that the subsequent non-Newtonian
measurements presented herein are likely accurate.
Constant extensional rates were achieved in the range of 1 to 10 S-' in the filament
stretching rheometer by controlling the bottom disk velocity. Extensional measurements
in terms of Trouton ratio were made for international test fluids-the three standard non-
Newtonian SM fluids and the Ml fluid. For each of the SM fluids, the Iow-strain
Newtonian plateau was close to the predicted value of 2.6 for the Trouton ratio. Growth
of the Trouton ratio Eom 3 to the order of 1,000 indicates significant strain-hardening of
the poIymer fluids.
Data for SM-1 from the three laboratones show that the Trouton ratio values are
independent of extensional rates and nearly identical steady-state values at high strains
was achieved at al1 tested Deborah numbers. The fact that the steady-state values of SM- I
are independent of Deborah numbers indicates that the polymer molecules in the solution
either were fuUy extended or reached the sarne level of entanglement, regardless of
extensional rates, at al1 three laboratories. This suggests that this steady-state value can be
used as a true material property of this fluid.
Good overall agreement was obtained for SM02 data comparisoe, the good J
agreement of the SM data arnong three laboratories suggests that al1 three instrument
designs are satisfactory and validates the unique lever positioning design for diarneter
measurements in the Toronto rheometer.
However, the measurernents of this rheometer are limited by the measuring range
of the current force transducers. For exarnple, reliable force measurement cannot be
obtained for Ml because the viscosity of this fluid was too srnail. Therefore, fluids with
viscosity close to that of M l can be tested only at high extensionai rates, while fluids
with lower viscosity cannot be tested.
For the more viscous fluids, SM-2 and SM-3, very large strains could not be
achieved because of detachment of the filament fiom a disk. Because of the detachment,
the rheometer cannot be used to test fluids with very high viscosities.
9.2 Recommendation for future work
A better way of loading highly viscous and elastic non-Newtonian fluids would
likely improve reproducibility of the data That is, the volume of the fluid sample needs
to be well controlled to obtain the ideal initial cylindrical filament. The current manual
Ioading is not easy to perform and requires practise to obtain satisQing (i-e. reproducible)
results. While optimising the manual procedure may be helpful, it is recommended that
automatic loading by a controlled syringe pump be incorporated in the apparatus.
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