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
Experiwntil techniques ......l................-...H..........a~........................... 40 ........................................................................................ Loadiag technique -40
Disk cleaning ................................................................................................ 40 Effect of temperature and disk dimensions , .................................................. 4 1
.................................................................................. Effect of temperature 4 1 . . Initial aspect ratio .......................................................................................... 43
CEAPTER 6 CALIBRATIONS ................................................................................. 44
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
.................................................................................... 6.2.1 Zumbach calibration 5 1 .............................................................. 6.2.2 Calibration of Zumbach positionhg 51
6.3 Vefocity dibmtion, ..,....l..................o............................................œ..œ........... 54
7.1 Newtonirn fluids and thtir s b w propertics .....m............................................ 56 7.2 Non-Newtonian fluids propcrtia .,...m.....m......... ............................................. 57
................................................................ CaAPTER 8 EXTENSIONAL RESULTS 60
Newtoniao calibrations ................. .................................................................. 60 Extensional ruults for Noa-Newtonian Ruids ................................................. 67
.................................................................................................. Fluid SM-1 6 7
.................................................................................................. Fluid SM-2 7 4 Fluid SM-3 ................................................................................................... 78
......................................................................... ....................... Fluid Ml .,, 8 2 Cornparison with other Iaboratories ......e......................................................... 86
......................................................... ................................................ SM-1 .... 87 SM.2. ............................................................................................................ 89 Ml ................................................................................................................ 93
........................................... CakPTER 9 CONCLUSIONS AND FUTURE WORK 96
..................................... 9.1 Conclusions ". ............................................................... 96 .................................................................. 9.2 Recommtndations for future work 98
LIST OF TABLES
Table 5.1 Temperature constants for SM fluids 41
Table 7.1 Properties of the Newtonian test fluids 57
Table 7.2 Composition and physical propenies of the wn-Newtonian test fluids 58
Table 7.3 Steady shear propertïes of the non-Newtonian test fluids at 25 OC 58
LIST OF FIGURES
Conformation of a flexible polymer chah at rest
Conformation of a flexible polymer chah under shear
Steady shear flow
Molecule in shear flow using a dumbbell mode1
Deformation of a fiuid element in shear flow
Uniaxial extensional flow field
Molecule in extension using a dumbbell mode1 becornes aligned dong the
stretching direction
Tbree modes of extensional flow
Schematic diagram of uniaxial eldension of a cylhdrical element
Schematic diagram of the stagnation-point flow device
Spin-line devices
Contraction flow
Converging charnel rheometer
The filament-streîching rheometer developed in Australia
Transient Trouton ratio of fluid Ml against strain
Schematic diagram of the filament stretching rheometer
Diameter measuring principle of Zumbach ODAC measuring head
P ~ c i p l e of the Zumbach positiorhg system
Force balance for the top halfof a filament
The diameter profile for SM-2 when an ideai extension imposed
Length and diameter data for SM-2 filament at an imposed extensionai rate of
2.8 s-', and the best-fit ames
Diameter of SM-2 &er velocity compensation
Calibration curve for the MOD405 force tratlsducer
Force measurement fiom the MOD404 10 g force transducer
Force measurement fiom the MOD405 1 g force transducer
Signal from the force traasducer MOD4û5 at i = 5 S-' during a blank nin
Force transducer noise for MOD405 during test period after noise reduction
Zumbach calt'bration for transparent objects
Zumbach calibration for opaque objects
Calibration of the Zumbach positioning system
Velocity calibration
Shear viscosity of Ml 6om the Brookfield viscameter
Diameter profile for Viscasil 12,500 at E = 5 S-'
Force history for Viscasil 12,500 at E = 5 S-'
Diameter diagram for Viscasil 12,500 at & = 1 0 s-'
Force diagram for Viscasil 1 2,500 at d = 10 se'
Diameter diagram for Viscasil 30,000 at & = 5 s-'
Force diagram for Viscasil 30,000 at É = 5 s"
Diameter d i a m for Viscasil 30,000 at I = 10 s-'
Force diagram for Viscasil 30,000 at i = 10 s-'
Transient Trouton ratio for Newtonian fluids
Cornparison of Newtonian data with two initial aspect ratios, for two nominal
extensionai rates
-viii-
Data for SM4 a$ De = 19.5. a diameter b. force history
Data for SM- 1 at De = 10.7. a diameter; b. force history
Comparison of Transient Trouton ratio for SM4 at ail Deborah numbers
Transient Trouton ratio meamernent at De = 10.7 for SM- 1
Data for SM-2 a De = 3 1.8. a diameter, bb. force history
Cornparison o f the Transient Trouton ratio for SM-2
Reproducibility of the Transient Trouton ratio measurement for SM-2
Data for SM-3 at De = 110. a. diameter; b. force history
Transient Trouton raito for SM-3 at De = 110.1 (t = 28.6 C)
Data for Ml fluid at i = 5.6 s". a. diameter, b. force
Data for Ml fluid at E = 10 s-'. a. diameter, b. force
Transient Trouton ratio for MI
Comparison of the transient Trouton ratio for SM-1, at tow De numbers
Comparison of the transient Trouton ratio at high De numbers, for SM-1
Comparison of the transient Trouton ratio for SM4
Comparison of the transient Trouton ratio for SM-2 with MIT
Comparison of transient Trouton ratio for SM-2 with Monash University
. Comparison of Ml witb Monash University
NOMENCLATURE
Tie-temperature superposition shifl factor
Coefficient in the shift factor
Coefficient in the shift factor
Filament mid-f ength diameter
initial filament diameter
Applied externa1 force on a filament (N)
Gravity coefficient @Lm/s2)
Filament length (mm)
Entrance length (mm)
Weight-average molecular weight @/mol)
Pressure (Pa)
Filament radius (mm)
time (s)
Ab solute temperature (K)
Force induced by surfkce tension (N)
Velocity of the bottom disk ( d s )
Weight (N)
r, e ,z Cylindricai co-ordinates
Greek symbols
Fining parameter in the Arrhenius equation (&as)
Exponent in the Arrhenius equation CK)
Extensionai deformation
Extensional rate tg1)
Shear rate (s-')
Shear viscosity (Pas)
Extensional viscosity (Pas)
ReIaxation time (s)
Rotating angle (O)
Density (kg/m3)
Surface tension c d c i e n t W/m)
Total stress
Characteristic time (s)
Stress associated with deformation
Subscript
O Fluid properties at zero shear rate;
Reference temperature;
Initial conditions
Dimensionless num bers
D e Deborah number
St Stokes number
Tr Trouton ratio
& Initiai aspect ratio
CHAPTER 1
INTRODUCTION
Polymers are found in a range of industrial fields, from plastics manufacturing to
food processing, with a variety of forms and fkctions. Not only are they used in a solid
form, such as plastics, but also in a liquid form like melts and solutions. An example of
the latter is that, a minute addition of a high molecular weight polymer to turbulent flow
can greatly reduce shear stress at a surface and consequently poIymers are used to reduce
wall friction in major oil and gasoline pipelines al1 over the world. In enhanced oil
recovery, dilute polymer solutions are used as pusher fluids to reduce fingering of cmde
oil in the reservoir and direct the oil toward production wells. In ftre fighting, polymers
are used as flow stabilizers because a srnail concentration can inhibit droplet formation at
the surface of the high-speed turbulent fiee jet [Glass 1986; Shalaby et al 1991; Schulz
and Glass 19911. Polymeric solutions also appear in coating, jet printing and many other
industrial applications.
Industrial applications such as these dernand understanding of the flow behaviour
of the fluids. In many of these applications, extensional deformation is dominant.
Consequently it is necessary to investigate the extensional flow behaviour of polymer
fluids. For polymer melts, extensional measurements have been made successfùlly at a
constant extensionai rate or under a constant stress. For mobile polymer solutions,
however, great diffimlty has been experienced in making extensional measurements. A
number of techniques, such as fibre-spinning and converging channel flow, have been
developed to mesu re the flow resistance of polymer solutions in an extensionally-
dominant flow field. However, creating a purely extensioaal flow with a constant
extensional rate is not easy. In fact, the flow fields created in most techniques are not well
defined. Extensional measurements were made by various techniques for a standard
polymer solution, the data were compared (the M 1 project), and large discrepancies were
found [J. Non-Newtonian Fluid Mech., 35, 199 11.
This situation prevailed until a filament stretching technique was developed by
Sridhar et al Cl99 11 in Australia. In this technique, a fluid sample is placed between two
vertical coaxial disks, which move apart in order to pull out a filament. A constant
extensional rate is achieved by programming the stretching of the filament. Extensional
measurements of several non-Newtonian fluids were made and a steady state was
achieved for some fluids. It was the first time that a 'me' measurement of extensional
viscosity of polymer solutions had been achieved.
A rheometer based on the filament stretching technique was constructeci at the
University of Toronto, similar to the original design but with improvernents in force
rneasurement and travel length. In this thesis, extensional measurements for Newtonian
and non-Newtonian fluids obtained tiom this rheometer will be presented and compared
with measurements fiom two other laboratories.
CHAPTER 2
BACKGROUND
The rheology related to this work is introduced in this chapter. This background
material includes the origin of fluid elasticity, types of deformation and an analysis of a
fluid filament under uniaxial extension.
2.1 Origin of elasticity
The polymers of interest in this study have a distinguishing feature: very long
flexible molecular chains. in a good solvent, a polymer chah swells and occupies a large
volume which is roughly spherical (Figure 2.1 a). M e n the solution is flowing, the
configuration of a polymer chain depends on the competition between Brownian motion
effects and hydrodynarnic effects. At low deformation rates, Brownian motion is strong
enough to offset the viscous pull of the solvent, and therefore polymer chains remain
close to their equilibrium configuration and the viscosity of the solution remains constant.
At high deformation rates, on the other hand, hydrodynamic forces overcome the
randomising effect of Brownian motion, and the coils are deforrned and oriented in the
Figure 2.1 Conformation of a flemile poiymer chah. (a) at rest; @) under shear
flow direction, as shown in Figure 2.1 b. niese oriented ellipsoidai-shaped mils impede
the flow less than the original sphericai coils and a decrease in the viscosity is ofien
observed; Le., the fluid is shear thinning. As defoxmation rates continue to increase, the
coils become virtually aligneci with the flow. The viscosity of the solution decreases and
remains at a lower value thereafter. For dilute polymer solutions, where the distance
between the molecules is large that hydrodynamic interactions between them are
negligible, the shear-ihinning effect is very weak.
One of the main probIems in investigating the elasticity of polymers is to
distinguish between elasticity and shear-thinning of these fluids. For moa non-
Newtonian fluids like melts and concentrated solutions, elastic effects are accompanied
with significant shear-thinning. In order to dinerentiate between elastic and viscous
effect, a higldy elastic fluid with a constant viscosity was developed in 1977 poger,
19771. A 'Boger fluid' is a dilute solution of a high molecular weight polymer in a highly
viscous solvent. Aithough the solution does display shear-thinning, the f d in its viscosity
is very smaii compared with the zero-shear value and for practicai purposes, the viscosity
appears to be constant Barnes a al, 19891.
As describeci earliq Brownian motion is always trying to bring the chains back to
the equilibrium random configuration, regardless of the deformation rate. When the
molecules are stretched and then the apptied stress is removed, the molecular chains relax
to their quiiibrium configuration The relaxation is not instantaneous, as it is for
Newtonian fluids, and thus the elasticity of polymer fluids becomes evident. The time
constant associateci with relaxation is a property of the fluid, called the relaxation time 1,
The relaxation time for polymer solutions can Vary from a fiaction of a second to a few
minutes. For fluids with high relaxation times, elastic effects are observed easiiy because
the stresses relax so slowly; for materiais with low k, the elasticity can not usually be
observed but it can be generated provided the defoxmation rate is high enough. In other
words, both the jïuid characteristic time (the relaxation time) and the f70w characteristic
time (such as the inverse of the deformation rate) are important in determining the
amount of elasticity in a fluid or the elastic response of the fluid. The ratio of these two
times is an important dirnensionless group called the Deborah number p i r d et ai, 19871:
where t is a characteristic time of the flow. in extensional flow, this ratio becomes L k ,
where & is the extensional rate. The Deborah number a n also be interpreted as the ratio
of the elastic forces to the viscous forces. At small Deborah numbers, the polymer
molecules are close to their equilibrium configurations and the polymer fluid shows only
minor differences from a Newtonian fluid. When the Deborah number is large, polymer
moiecules are distorted and cannot relax during the defornion, and thus the fiuid
behaves more like an elastic soiid, that is, elastic effects become significant when the
Deborah number is above unity (J3ird et al, 1987).
2.2 Sbear and extensional flows
2.2. f Defulltion of two types of flow
Flows may be classified into weak and strong flows [Giesekus, 1962; Tanner,
19761. A flow is considered strong if neighbouring fluid particles separate at an
exponential rate in the flow field. The flow is coasidered weak otherwise.
Steady simple shear is an example of a weak flow. This flow is illustrateci in
Figure 2.2 a, with the fluid confineci between two parallel plates. The top plate is moving
at a constant velocity V. The velocity components of the fluid element in Cartesian co-
ordinates are:
v, =y,,x,; v , =O; v , = O (2-2)
where y?, is the velocity gradient and its abdu t e value is calted the shear rate. The
distance L between two neighbourîng fluid particles in the x2-direction, initially b apart,
increases Iinemlly with time t as:
In shear flow, molecular chains experience both extensional and rotational motion. In
Figure 2.2 b, where a polymer molemle is depicted as a dumbbeil of two beads joined by
a spring, the molecule rotates and stretches in the flow. The extension and rotation in
shear flow can be iilustrated more clearly by a fluid element. As shown in Figure 2.3, the
shear main can be considered as the sum of extension dong diagonals plus rotation.
Figure 2.2 a Steady shear flow
Figure 2.2 b Moleaile in shear flow using a dumbbell mode1 [Tirtaatmadja, 19931.
Figure 2.3
extension rotation
Deformation of a fluid eiement in shear flow
Extensional flow is a strong flow and the streamlines for one type of extensional
flow, namely uniaxial extensional flow with a constant rate of extension, are shown in
Figure 2.4 a. The velocity cornponents for this flow, in Cartesian cc~ordinates, are
1 v, = &x,; v , = -- 1
Lx,; v , = --éx, 2 2 (2-4)
where ti is the extensional rate. Fluid is stretched in the XI-direction and contracts in the
other two. Two fluid particles, which are initiaüy a distance Lo apart in the xpdirection,
are a distance of L apart d e r time t according to
L = L , exp (kt) . (2-5)
In this flow field, molecules become aligned and stretched dong the xi-direction, as
shown in Figure 2.4 b. In a purely extensional deformation, there is no rotation or
shearing of the fluid element; the element experiences only extension.
Figure 2.4 a Uniaxial extensional flow field
Figure 2.4 b Molecule in extensional flow using a dumbbell model bewrnes aligned
dong the stretching direction [Tirtaatmadja, 19931.
2.2.2 Types of extensional flow
There are three major types of extensionai flow: uniaxial, biaxial, and planar.
Figure 2.5 shows the three types of extension for a cubicai element of material. The
dotted lines represent the shape of the element &er deformation. In uniaxial extension,
the material is stretched in one direction and compressed equally in the other two; in
biaxiai extension, the material is stretched equally in two directions and compressed in
the third; and in planar extension the material is stretched in one direction ody,
compressed in the second direction, and held to the same dimension in the third.
2.3 Uniaxial extensional flow of a fluid filament
Of the three modes, uniaxial extension is of particular interest because of its
industrial applications, such as in coating and printing- Moreover, it is easier to make
extensional measurements under this mode in a laboratory. Therefore most extensionaI
rheometers are designed to create a predominantly uniaxial extensional flow and to
rneasure the fluid response.
This mode of extension can be visualised as stretching a rod of material along its
length. The general flow field is given by Eqn. 2.4 in Cartesian CO-ordinates. In this
section, a material element of a particular shape is considered for convenience, a
cylindncal one with initial diameter Do and initial length Lo. As shown in Figure 2.6, the
elernent is stretched homogeneously at a constant extensional rate dong the axial
direction z and the radius of the element decreases uniformly dong the length.
The strain in the z-direction is
Uniaxial extensional flow
Biaxial cxtensiona l flo w
Phar cxttnsianal flow
Figure 2.5 Three modes of extensional flow. (a) uniaxial (b) biaxial (c) planar
and the deformation rate is
where v, is the axial velocity . Hence
For an incompressible flui4 fiom the continuity equation,
from which the radial (inward) velocity is found to be
Figure 2.i 6 Schematic diagram of uniaxial extension of a cyiindricai element
with the other velocity component ve king zero. For this flow field, strearnlines are
given by
r ' z = contant . (2-1 1)
By integraing Eqn. (2.8), it is found that the length of the specirnen L(t) increases
exponentially fiom its initiai length La, as given by Eqn. 2.5. From Eqn (2.10), the
filament diarneter De) at any time t decreases fiom its initial value Do as
In this work, E is referred to Hencky strain, which is defined as hm), where
is the original length and L is the length of the sample. In a constant extension, the
Hencky strain can be alço wntten as Et , where É is the effective extensional rate.
Now consider the uniaxial extension to start at t = 0, with the fluid initially in a
stress fiee state. The fiuid resists this motion and the resistance to extensional
deformation is expressed as exfemiomI viscosity, analogous to the term shear viscosity,
which expresses resistance to shearhg motion. Extensional viscosity is wrïtten as q ~ , in
acwrdance with nomenclature suggested by the Socim of RheoIogy.
In the same way that shear viscosity is defined as stress divided by shear rate,
extensional viscosity is defined as stress in the fiow direction, a,, divided by extensional
rate E . The total stress o, can be measured experimentally but it includes the dmown
pressure p. This pressure p is eliminated by subtracting the n o r d stress in the r-
direction um fiorn G. The difference is quivalent to 'tn - T~~ the difference between the
stresses associatecl with deformation in the two directions. Thus, the definition for q~ is
For Newtonian fluids with a shear viscosity of qo,
and
so that
q E = 3 % -
Hence q ~ : is mt an independent fluid property for Newtonian fluids.
For mobile viscoelastic fluids, QE depends on both duration t and main rate & . In
most cases, E is not constant during the residence time t, and thus q~ is a tùnction of
strain history. For extensional flow, the preferred strain history is the one in which the
fluid is initially stress-fiee and then subjected to a constant- 6 deformation (a step change
in strain rate). The extensional viscosity is then a fiinction of extensional rate and time:
T ~ E =%(kt)- (2.17)
Hence, extensional viscosity is a fr-ent matend property.
It is common in rheoiogy to report extensional viscosity data in terms of the
Trouton ratio Tr, dehed as
where r\ is the shear viscosity. For al1 inelastic fluids, including Newtonian fluids, the
Trouton ratio gives a constant value of 3. This fact will be used in the calibration of the
extensional rheometer.
CHAPTER 3
TECHNIQUES FOR MEASURING EXTENSIONAL VISOCSITY
In non-Newtonian flows, the extensional viscosity may be at least as important as
the shear viscosity. In applications such as fibre spinning, jet break-up and turbulent drag
reduction, it is the more dominant property. The industrial importance of this property
has motivated the development o f rheorneters to measure it and thereby characterise a
fluid's resistance to extensional motion-
While analogous to shear viscosity, it is very difficult to create experimental
conditions to measure extensionai viscosit y properly . In the same way that shear viscosity
is measured in a simple shear flow with a uniform shear rate throughout, the extensional
viscosity should be measured when the deformation is purely extensional and the
extensional rate is constant throughout. The t k s t challenge in extensional rheometry is to
generate a well-defined extensional field, fiee of signifiant shear. As discussed
previously in Section 2.3, uniaxial flow is ideai for experimental investigation. However,
most measuring techniques do not create the requud shear-free flow field. It is also far
fiom easy to achieve the preferred strain history, Le., to generate an extensional flow
instantaneously fiom a state of rest so that the liquid is stress-& before experiencing
extensional motions, and to provide a constant extensional rate, even for a short penod of
tirne.
While the filament-stretching technique of Sridhar et al meets these conditions, it
is useful to review other techniques which have been deveIoped for measuring
extensional viscosity. In this chapter, they will be describeci, and their advantages and
drawbacks discussed. Then the objectives of this thesis are addressed.
3.1 Stagnation-point flow techniques
Fuller et al 119871, Laun and Hingmann Cl9951 and others pioneered a technique
based on stagnation-point flow. The principle is illustrated in Figure 3.1 : fluid is drawn
I
Pivot 1
Hinged Tube
Figure 3.1 Schematic diagram of the stagnation-point flow device [James and
Walters, 19931
into opposing tubes to create a stagnation-point Bow about the mid-plane. One inlet is
stationary and the other is part of a balance ami to mesure the force exerted by the
entering liquid. By measuring the force requued to keep the tube entrances a fixed
distance apart, an apparent extensional viscosity can be determineci.
With this technique, viscosities can range fiom 1 mPa.s to 10 Pas, and a wide
range of strain rates can be achieved. Easy operation is another advantage of this
technique.
The technique, however, has severai disadvantages. One is that the overall strain
cannot be changed systematically. Secondly, the strain history is not the same for al1
particles in the flow field even though the extensional rate in the stagnation zone is
constant. The closer a particle is to the stagnation point, the longer is its residence time in
the flow. In an analysis carried out by Schunk and Scriven Cl9901 using a finite element
method, the velocity and strain rate fields around the opposed entry tubes were
determined for a Newtonian fluid. It was found that the fluid enters the tubes in a state
which consists much more of shear than extension. The flow close to the stagnation point
is purely extensional, but the region is much smaller than expected. Overall, the fluid is
not subjected to pure extensional motion except near the stagnation point.
Another disadvantage of this technique is that inertia is a factor in testing low
viscosity fluids vermansky and Boger, 19951, so that inertial effects have to be
separated out.
3.2 Fibre-spinning Devices
The first method developed for measuring q~ was one based on fibre spinning. As
shown in Figure 3.2, fluid is drawn down fiom an orifice or a tube, using either a rotating
drum, as in Ferguson's original design [1976], or a suction device of the sort descnbed by
Gupta and Sridhar [1984).
For an elastic Iiquid, a steady downward flow can usually be generated. Tension
in the filament is measured either kom the torque on the drurn or fiom the force on the
exit tube. The diameter and length of the filament can be determined with reasonable
accuracy using a video carnera. The stress is therefore readily determined fiom the
measured tension, flow rate and filament dimensions.
This technique provides an approximate value of the extensionai viscosity, and an
accurate value is not possible because of several problems. First of dl, varying the strain
Figure 3.2 Spin-line devices [James and Walters, 19931
rate in the thread is not easy and hence the extensional strain rate range with this
technique is quite limited. Secondly, the extensional strain rate is generally not constant
along the filament and, thirdly, significant shear can be present.
The possibility of a sig~ficant and largely unexpected shearing component brings
non-ideality in the flow field. The main disadvantage of the fibre-spiming methods is the
shearing in the upsueam tube or orifice. Since q~ is a function of strain history for mobile
fluids, the preshear bas a significant influence on the stress field.
3.3 Contraction-flow devices
This technique was pioaeered by Cogswell [1972] for melts and advanced by
Binding and CO-workers [1988,1990] for mobile fluids. As shown schematically in Figure
3.3. a device based on sudden-contraction flow has the advantage of easy operation-
Figure 3.3 Contraction flow [Cogswell, 19721
Vortex enhancement generally occurs on the upstream side of the contraction, and flow in
the core is primarily extensional. The relevant dynamic measurement is provided by a
pressure transducer which detects the pressure drop across the sudden contraction or
across an orifice plate.
The extensional rate is not constant in a contraction flow. When the flow pattern
is known, the rneasured flow rate yields a simple measure of overall strain rate. However,
converging flow is complex and therefore assumptions are required for data
interpretation.
3.4 Converging cbannel rheometer
An instrument based on converging-channel flow has been developed by James et
al [1990]. Its primary component is a converging channel of a shape such that the
extensional rate is constant in the central region. A schematic diagram is shown in Figure
3.4. An important aspect of this design is that the flow is at high Reynolds numbers so
that shear effects are restricted to the wall region. To determine q~ for elastic liquids,
knowledge of the behaviour of the inelastic component of the fluid is required and this is
provided by using the known viscous behaviour of the test fluid and assuming the flow
field. The boundary Iayer is taken into account in the analysis and a major assumption
(which is yet to be verified) is that the boundary layer characteristics are not unduly
modified by viscoelasticity. If this assumption stands, flow in the converging-channel
rheometer will provide an approximation to the Heaviside strain rate assumption (that the
strain rate E is irnposed at the entrance of the channel) and the technique will be useful in
determining transient extensional viscosity function [James and Walters, 19931.
Figure 3.4 Converging channel rheometer [James et al, 19903
This technique is suitable for low-viscosity fluids due to the high Reynolds
numbers required. Ln addition, high strain rates can be achieved. Drawbacks are the large
inenia effects at high Reynolds nurnbers and shear effects in the boundary layer. Also,
this device cannot be calibrated using Newtonian fluids.
3.5 Filament-stretching rheometer
A filament-stretching technique for extensiond viscosity measurement was
initiated by Matta and Tytus [1990J and fiilly developed by Sridhar and CO-workers
[I99 1, 19931. A liquid sample is initially held between two closely-spaced coaxial disks,
forming a stress-fie cylindrical filament. As show in Figure 3.5, the sample is then
stretched into a thin filament by moving both disks @) apart at an increasing velocity.
Figure 3.5 The filament stretching rheometer devekoped in Australia [Srid har and
Tirtaatrnadja 19931
For a viscoelastic fluid, a long filament is usualfy obtained before it breaks. The disk
motions are controlled by a DC motor such that the extensional rate at the mid-length of
the stretched filament is constant. The tension in the filament is measured by a force
transducer connecteci to one disk, and a laser measuring device is used to measure the
midpoint diameter dunng the stretching process.
Using this technique, Tirtaatmadja and Sridhar [1993] obtained constant
extensional rates and deterrnined values of the transient Trouton ratio for a few fluids.
Figure 3 -6 is a plot of the transient Trouton ratio for a special international fluid, obtained
with their original filament-stretching rheometer [Ti~atmadja, 1993, p. 1951. Steady state
values at high strains were achieved for this fluid.
Sridhar's method is the only accurate one to date of measuring the extensional
viscosity of a fluid. This technique provides the possibility of generating an extensional
motion fiom a state of rest, Le., there is no prehistoiy of deformation. Constant
extensional rates can be obtained by controlling the stretching velocity of the disks.
Furthemore, this technique prevents the presence of significant shear component. For the
tirst tirne, proper measurements of extensional viscosity were made for polymer
solutions.
Figure 3.6 Transient Trouton ratio of fluid Ml against strain [Tirtaatmadja, 19931
3.6 Thesis objectives
As discussed previously, the filament stretching technique is a breakthrough for
the nieasurement of extensional viscosity of mobile polymer fiuïds. After Tirtaatmadja
and Sridhar, severai groups amund the world, including Spiegelberg a al [1996], Kroger
[1992] and Berg et al [1994]. Solomon and Muller [ 19961, van Niaiwkoop and Muller
von Czernicki [19%] and Verhoef et al [1999], constnicted filament-stretching devices of
various designs. In most of the devices, high strains could aot be achieved because of
limitations of length and motor speed-
Another filment stretching rheometer was built in the Wwology Labratory at
the University of Toronto in 1998. In this design, a travel length of ZOO0 mm is possible
to overmne the length constraint and to achieve high strains. The measurement of force
was irnproved by fixing one disk and attaching the force transducer to it, so that the
vibration-induced noise was reduced.
To evduate extensiona1 measurements fiom this rheometer, dslta fkom it should be
compared with data fkom other instruments. However, as discussed previously, the
extensional viscosity of dilute polymer fluids is a fùnction of strain history. Therefore TE
data fiom different instruments can be properly compared only when the strain histow is
the same or when differences in strain histories are s d l and can be accounted for. To
ensure proper cornparisons, a collaborative project was undertaken with other
laboratories. The objective of this project was to compare extensional viocosity
meawements of some specially-made polymer soiutions using the filament stretching
rheometers at MIT, Momh University, and the new oae et the University of Toronto.
In this thesis, the fmt objective was to achieve accurate extensional
measurements for Newtonian fluids using the new rheometer, to validate the instrument.
The second objective was to obtain reproducible extensionai viscosity measurements of
three standard polymer solutions and to compare these data with results from MIT and
Monash University.
CHAPTER 4
EXPERIMENTAL SETUP
The filament-stretching technique has been reaiised in different designs, and in
this chapter the details of the filament stretching rheometer at the University of Toronto
will be presented.
The instrument was designed and built by G. M. Chandler in 1998. It consists of
four basic parts: the force transducer system, the diarneter measuring system, the actuator
and the control system. As shown in the schematic diagram (Figure 4. l), a test sample is
placed in the initial 2 mm gap between two 3 mm-diameter coaxial Teflon disks (B) and
stretched downward. The top disk is attached to a force transducer (C) to measure the
force exerted by the stretched filament. The bottom disk is attached to an actuator (D)
that is driven downward by a motor at a controlled speed. A laser device (E) is used to
measure the instantaneous diameter at the mid-point of the filament. To measure the
diarneter at the midpoint, the motion of the device is controlled so that its displacement is
half of the displacement of the actuator. A computer is used to generate controlling
signals and to process signals from the transducer and diameter measuring systems.
Laser beam .--------------
Force Transducer C
Disk B D = 3.0
Control cornputer
F A
w Diameter
Measuring , , , , , ,
Actuator
Figure 4.1 Schematic diagram of the filament-str&ching rheometer. The diameter-
measuring device moves half the distance L of the actuator.
4.1 Force transducer system
Since tensile force is a crucial element in determining the extensional viscosity,
accuracy in the force measurement is essential. In this experiment, the tension in the
stretched thin filament is smaii, the magnitude being of order 104 N. Also, a test run
takes only a few seconds or less. Therefore the transducer rnust be accurate at small
forces and be able to respond quickly.
Because tensile forces in the filaments Vary widely, in order to obtain accurate
force rneasurements, two transducer systems were selected, MOD405 and MOD404,
supplied by Aurora Scientifk Inc., Canada. Each transducer is a variable displacement
capacitor whose plates are formed by vacuum metalization on the surface of cantilevered
fûsed silica barns. A matched reference device of identical construction is placed beside
the capacitor to compensate for thermal effects, mechanical vibration and extemai noise.
For the MOD404 transducer, the fiII scale force is *10 g force, its resolution is
200 pg force and its resonant fiequency is 2.0 kHz. For MOD405, the fi11 scale is *l g
force, with a resolution of 15 force and a resonant fiequency of 0.6 kHz. The latter
transducer was used for the lower-viscosity fluids.
Initially, a force transducer was mounted on the support stand for the actuator.
Since this set-up produced high levels of noise, the transducer was then mounted on a
nearby wall. Translation stages were part of the wall mounting. The upper disk was
comected to the transducer by a g las rod and the weight of both the disk and the rod
were compensated for in the design of the transducer.
4.2 Diameter measuring device
Accuracy on a srnail s d e and fast response were also required for the diameter
measuring system The systern, fiom ZUMBACH Electronics, consists of a measuring
head Zumbach ODAC 16J and a processor unit Zumbach USYS 10. They are normally
used to obtain ou-Iine diameter measurement of extnided fibres (both transparent and
opaque) for quality fontml at manufacturing plants. As shown in Figure 4.2, the
measuring head scans the filament with a laser beam. The size of the shadow cast by the
filament is detected eIaPoncaiIy by a receiving window and sent to the processor unit,
where it is converteci into a digital signal and sent to the control computer.
This device can measure diameters in the range of 0.05 mm to 8 mm with a
Figure 4.2 Diameter measuring principle of Zumbach ODAC meamring head.
a. laser generator; b. laser sheet; c. fluid filament; d. laser detedor
resolution of 0.00 I mm, at a scan rate of 240 scandsec.
Since it is essential to measure the response for the same portion o f fluid
throughout the process, and because only the mid-point fiuid in the filament experiences
pure extension at al1 tirnes, that point was chosen for extensional measurernent. White
total stress at the mid-point can be obtained by measuring the force at the top disk, as
analysed in Section 5 - 1, the diameter must be measured at the mid-point itself. Hence, the
Zumbach measunng head must be at the midpoint initially and during the extension. This
can be achieved using another actuator, a separate one, to give the required displacement
!hL(t), where L(t) is the displacement of the bottom disk. This idea has been applied to
some filament stretching rheometers. In this rheorneter, only one actuator is used and the
Zumbach position is controlled by a simple mechanism.
The initial midpoint position of the Zumbach was set as follows. The translation
stage on which the transducer was mounted could be adjusted vertically with an accuracy
of 0.01 mm. M e r the disks were set to the initiai distance, = 2 mm, the translation
stage was adjusted to lower the top disk by 1 mm, the bottom one remaining at its
position. Then the Zumbach position was shifted so that the laser beam pointed along the
bottom edge of the top disk. At this stage, the measuring laser sheet was 1 mm away fiom
the bottom disk. The top disk was raised 1 mm, back to its original position, and so the
laser beam was set at the midpoint of the two disks.
Controlling the Zumbach to follow the midpoint of the filament during extension
was achieved by a lever system. The prînciple is s h o w in Figure 4.3: one end of the
lever (O) is fixed while the other end (C) follows the movement of the bottom disk (the
top disk is stationary). The mid-length of the lever (B) is the support for the Zumbach
measuring head. Thus, if the displacement in the r-direction is negligible, the
displacement of the Zumbach measuriag head is half of that of the bottom disk. In
Figure 4.3 Principle of the Zumbach positioning system
practise, in order to avoid a significant r-direction displacement, the lever rotation was
Iimited to s d l angles. Therefore, the Zumbach measuring head did not foliow the entire
travel of the bottom disk. However, the Zumbach measuring head need not follow the
whole length because photograpbs by Sridhar et al [1991] show that the filament
diameter is uniforrn over alrnost its entire length after a main of 1.8 has been reached. If
the Zumbach measuring head follows the midpoint position until the critical strain is
reached, the diameter can be measured anywhere dong the length afterward.
The positioning lever used in the rheorneter is 200 mm long and the total
Zumbach displacement is 48 mm. D u ~ g the process, the maximum an@e of the lever
arrn is 14 O, producing an error of l e s than 3% in the Zumbach position.
4 3 Actuator
The actuator moves the bottom disk according to a velocity signal sent fiorn the
wmputer. A carriage holding the bottom disk moves down a vertical track by a
transmission belt driven by a DC motor. The motor is controlled by a computer
programmeci to produce the desired speed history. The position of the actuator carriage,
and therefore the position of the bottom disk, is sent as a feedback signal to the control
system for verification.
The total length of travel is 2000 mm, the longest arnong al1 filament-stretching
rheometers. The maximum speed of the motor is 3000 mdsec with a resolution of 3
mrn/sec.
4.4 Control system
The rheorneter is controlled by a computer using a Visual Basic program d e n
by G. M. Chandler of Aurora Scientific Inc. and revised by the author. Control
parameters are calculateci by the program according to required experimental conditions
and then converted to executive signals by a data acquisition processor. Thus signals to
the actuator create the desired constant extensional motion in the filament. The
measurements of force and mid-length diameter, as fùnctions of time, are sent back to the
computer for processing.
CHAPTER 5
EXPERIMENTAL METHODS
As mentioned in previous chapters, the three filament stretching rheometers in the
joint research project have different mechanical designs. in this chapter, a detailed
discussion of the experimental method and data reduction procedure of the instrument at
the University of Toronto is presented. The operation and data processing of the other
two are described in the literature rirtaatmadja and Sndhar, 19933 [Spiegelberg et al,
19961. Data cornparison between the three labs will be shown and discussed in a later
chapter.
5.1 Force balance
To find the stress difference r, - T, fiom the measured force, which is required
for t l ~ , it is necessary to derive an equation based on force balances in the axial and radial
directions. The balance in the axial direction is made on a deforming fluid filament in the
region O < z I W2, as shown in Figure 5.1. In addition to the viscous stresses fn and T, in
the fluid, surface tension, weight, and inertia contribute to the tension in the filament.
Figure 5.1 Force balance for the top half of a stmching filament, O S z < U2.
Because sample sizes are small and the polymer solutions used in this work are highly
viscous, inestia is not a factor until very high mains are achieved or high strain rates are
imposed.
The filament starts as a cylindrical shape, with an initiai diameter do and initial
Iength b. WhiIe the filament is stretched a distance L, a force balance in the axial
direction z, between the top disk and the mid-point, yields
where o, is the total stress in the z-direction at the mid-point, d is the mid-point
diameter, T is the force due to sunace tension, W is the weight of the liquid and F is the
applied force. The surface-tension induced force T is at the interface of the filament and
the surrouding air, expressed as zda, where a is the surface tension coeffecient for the
fluid. Since half of the filament is wnsidered in the balance, the weight in Eqn. 5.1 is half
of the liquid loaded, ~4~g7c&~/4), where p is the density of the fluid,
where p is the isotropie pressure in the deforming filament at z = U2.
A force balace in the radial direction on the free surface at z = W2 gives
- 2 0 6, - 2, -Po-.
d (5.3)
Combining (5.2) and (5.3) gives the tensile stress difference
Since the tensile force and the mid-point filament diameter are measued, the
stress ciifference can be calculated f?om Eqn 5.4. Eqns. 2.17 and 2.23 are then used to
obtain the extensional viscosity and the Trouton ratio.
5.2 Generating a constant extensional rate
5.2.1 The ideal diameter history
As shown in Chapter 2, for uniaxial stretching, the ideal diameter and length as
hnctions of time are
D(t) = D ,exp(- W2) , ( 5 - 5 )
L(t) = L , exp( lt) . (5-6)
Ideally, the stcain rate experienced by every fluid element is identicai to the strain rate
i m posed b y the extensional apparatus. However, non-homogeneous kinematics is induced
by the disks, Le., because of them, the test sample is exposed to shear as well as extension
prior to the predominantly extensional motion. For polymer melts, a long test sarnple is
used to localise the influence the end regions and thus to decrease the errors. For mobile
polymer solutions, their low viscosity requires a short initial sample length in order to
stablize the filament, that is, to prevent it from sagging under gravity and fkom breaking
up because of surface tension. Therefore, non-homogeneity in the filament under
elongation is not negligible. Figure 5.2 is a typical mid-length diameter profile on a semi-
log plot for non-Newtonian fluids when the controiied length L is hexp($ t). In this case,
instead of a straight tine, two distinct regions for D(t) are obtained, where the filament
diarneter decreases exponentialty with time. In the first region, the filament undergoes
significant necking, and the mid-point diameter decreases faster than that for
homogeneous deformation. Therefore, the actud main rate is higher than the imposed
1 1.5
Time, s
Figure 5.2 The diameter profile for SM-2 when an ideal extension imposed.
suain rate. In the second region, the strai-n-hardeneci central portion of the filament pulls
out some of the end Iiquid (not strain-hardened) at each disk, making the volume of the
filament larger. Thus the amial extensional rate is lower than what is imposed. For
Newtonian fluids, the second strain-hardening region is not observed and the effective
strain rate is always greater than the imposed value.
Because of these non-ideal kinematics, the midpoint diameter profie is not an
indication of the deformation experienced by the whole filament. However, a numericai
analysis carried out by Kolte et al [1997] indicates that, if a fluid element at the midpoint
of the filament contracts in the same rnanner as a cylindricai column undergoing ideal
uniaxial extension, then the measured rheological response will be virtually identical to
that experienced in homogeneous shear-fiee flow. So, the desired fluid property can still
be obtained if mid-point quantities are measured. The challenge now is to create a
velocity control such that the mid-point diameter follows D(t) = D,exp(- W2) .
5.2.2 Velocity compensation
A procedure for getting the desked velocity fùnction was developed, which is as
foilows:
1. Run tests at a nominal extensional rate, with the bottom disk velocity given by
V(t) = EL,exp( Ét) . (5-7)
2. Plot the measured diameter and length as D n ( t ) versus L(t)/Lo plot, an
example of which is shown in Figure 5.3.
3. Curve fit the data DdD(t) versus L(t)/Lo, to describe
= f[~,/D(t)]. L(t)k 0 -
More than one curve is usually rquired because a single n w e cannot f i t the data well.
The solid line in Figure 5.3 represents the curves fitted for SM-2 at an imposed
extensionai rate of 2.8 S.' .
4. Substitute the ideal diameter
D(t) = Do exp(- Éd2) (5-9)
into the ftnction for L(t), so that
L(t) = L , f [exp (a )] - (5.10)
DiEerentiate Eqn. (5.10) with time t to yield the correct velocity fùnction V'(t):
Figure 5.3 Length and diameter data for SM-2 filament at an imposed extensionai
rate of 2.8 s-', and the bestfit curves.
df v '(t) = L , - . dt
This fiinction applies to a specific fluid at a specific elongation rate.
5. At the sarne temperature, remn the test with V'(t) to obtain a new diameter plot.
Figure 5.4 shows the resulting diameter for SM-2 &er the velocity compensation. It is a
straight line on a semi-log plot and the actuai extensional rate is found fiom the slope of
the straight line.
6. Verie the resuithg diarneter by plotthg @-d - Dideri) / Didd as a hnction
of time for the test period.
1 O Measured diameter
Figure 5.4 Diameter of SM-2 after velocity compensation.
7. Ifthe diameter deviation is greater than 5%, repeat Steps 5 - 7 until the error is
smaller than 5%.
In this procedure, temperature measurements are essential because the test fluids
are highly sensitive to temperature. It is necessary to perform extensional measurements
at the same temperature in order to obtain a satisfactory diameter profile.
Under the nominal extension, as descnbed by Eqn. 5.5, the two slopes in the
diameter plot Vary acwrding to the fluid and the extensional rate. Since a fluid's response
is generally di fferent at each extensional rate, the velocity compensation needs to be
performed at each rate.
5.3 Experimental techniques
5.3.1 Loading technique
The loading consists of setting the two disks apart at the desired initial distance of
2 mm and loading a test sample between them by a syringe. The amount injected is
carefùlly controlled to obtain a cylindrical test sample. M e r the injection, the sample is
allowed to relax before a test is run. Since the initial distance Lo is 2 mm, the injecting
needle is required to be smaller than 2 mm in diameter. It was observed that a needle with
a diameter smaller than 1 mm caused crystailisation of the polymer in the injected
sample. Hence B-D16G surgical needles with an outside diameter of 1.65 mm were used.
5.3.2 Disk cleaning
In addition to carenil filling, other procedures are necessary before deformation
commences. A wet edge on the bottom disk can cause the fluid to drip over the edge, and
so the disks should be cleaned before a sample is loaded. For hydrocarbon liquids like the
test fluids, cleaning with water or alcohol is not sufficient, and hence acetone was used as
the cleaning agent and solvent. To d u c e the Wear of the Teflon disks, Q-tips were used
to apply the acetone.
5.4 Effect of temperature and disk dimensions
5.4.1 Effect of temperature
Lie most viscoelastic fluids the test fluids are very sensitive to temperature- For
the specially-made test fluids, the shear viscosity at temperature T is given by
where qo is the shear viscosity at the reference temperature To and a~ is the shift factor.
The factor a~ is given by
where T is the absoiute temperature [KI, To is a reference temperature w] and a and b are
constants. Values of the two constants are listed in Table 5.1. The temperature sensitivity
- --
Table 5.1 Temperature constants for SM fluids [Anna and McKinley, 19991.
Fluid
SM- 1
SM02
SM-3
a
16.9
22.4
36.9
b
75 -4
99.6
160
wi be illustrateci by the fàct that a shifl of 0.5 OC in the experimental temperature can
cause a change as high as 12 % in the shiA factor a,.
As for Ml , the shear viscosity of this fluid was measured by many researcbers
[eg. Binding et al 19901 and its zero shear viscosity obeys the Arrhenius relationship:
7 = ae ( 5 - 14)
where a=3.7x 1 o - ~ P a s and P=6000 K pinding et ai, 1 9901.
Temperature dso affects the relaxation time and therefore the Deborah number.
The shifi fiictors used for shear viscosity, as given by Eqn. 5.13 and 5.14, were also used
to correct the De number and the relaxation tirne.
It is therefore important to know and maintain the temperature in the experiments.
Since the rheometer cannot control the temperature, the foilowing steps were taken to
reduce temperature fluctuations and errors in the temperature measurement:
1. A uniform and stable temperature was achieved in the laboratory by using
heating and cooling devices.
2. A test sample was exposed to the ambient temperature of the laboratory for
some time.
3.The temperature of the test sample was measured by a thermocouple
irnmediately before being loaded between the disks. This temperature was taken as the
experi mental temperature.
The temperature error was estimated to be Hl. 1 OC, corresponding to a Si% error
in the shifi -or.
5.4.2 Initial aspect ratio
The initial aspect ratio of the filament is defined as
-Ao = LJR, - (5.15)
where Lo and & are the initial length and radius of the filament. This ratio was first
introduced in the measurements for polymer melts in order to deal with the non-
homogeneous kinematics generated by endplate fixtures. For meits, I\o is usuaily larger
than 20, which minimizes the error in the measured tende force [Anna et al, 19991. For
polymer solutions, however, to insure an initial cylindncal sample, I\o has to be less than
about one. In this work, because of the loading procedure and the small disk size, AO was
4/3.
Tests with Newtonian fluids were camed out with two initial aspect ratios to
analyse the effect of the initial ratio. The results are reported in Chapter 8.
CHAPTER 6
CALIBRATIONS
Calibrations are crucial steps in an experimental investigation. Accuracy and fast
response are requued in the present experiment and this chapter describes the calibration
procedure for the force tansducers, the diameter-measuring device and the actuator
system-
6.1 Force transducer calibration and noise reduction
6.1.1 Force calibration
As described earlier in Section 4.1, two force transducers were used to rneasure
tensile force over a wide range. For the MOD404 transducer with a fùll scale of 10 g
force, standard weights were used for the calibration- The standard weights were hung on
the upper disk by fine nylon thread. For the MOD405 transducer with a full scale of 1 g
force, custorn-made calibration weights were used. A piece of thin soit metal wùe was
shaped into a hook and hung on the disk to hold the weights. The centre of mass was
along the tine of the glass rod attsched to the transducer. The weight of the hook was
added to the calibration weights, which were d m made of thin wire. The caiibration
weights were measured by a microbalance, to an accuracy of 0.001 g.
The force transducers were calibrated several times, at different temperatures, and
linear calibration curves were obtained. Figure 6.1 gives a typical calibration m e for
the MOD405 1 g force transducer. The symbols are the output voltages fiom the
transducer and a calibration coefficient of 1 . 3 2 ~ 1 ~ ' NNolt was obtained fiom the
straight line fitted to the data. The coefficient for the MOD404 transducer was found to
be 1 . 3 0 ~ 1 O" NNolt.
Force measurements afier calibration fiom the two transducers are given in
Figures 6.2-6.3. The force data, represented by the symbols, agree with the known
Figure 6.1 Calibration curve for the MOD405 force transducer. and O are the
output voltage data.
i d e a l force
transducer nading
O 0.02 0.04 0.06 0.08 O. 1
Weight. N
Figure 6.2 Force measurements f?om the MOD404 10 g transducer.
i d e a l brce
transducer reading
O 0.002 0.004 0.006 0.008 0.01
Weight, N
Figure 6.3 Force meanirements £kom the MOD405 1 g force transducer.
weights.
6.1.2 Noise reduction
Problems with noise first arose in Newtonian measurements because of the small
tensile forces. To put the noise level in perspective, 'blank' nuis were made, i-e., without
loading fluid samples between the disks. The force signal was recordeci, as shown in
Figure 6.3. Since there was no sample, the force reading should have been zero
throughout the process. Because the noise level is of order 104 N, and because the fùll
range of the MOWOS transducer is 10'~ N (1 g force), the noise is well above the
acceptable level for accurate measurements of an extensionai property.
There are several possible sources of the noise. The accuracy itself is not the
reason since the resolution of the transducer is 15 pg force (1.47~ IO-' N), as specified in
the MOD405 manual. Another possible source is electncal interference during signal
transmission. The eIectrical signals for force, diameter, actuator position and speed
control etc. are transmitted through common cables, and so interference between them
could be a source of the noise. Noise could also result fiom mechanical vibration. This
possibility increases when one sees the noise signal kom the transducer: the magnitude of
the noise increases with speed. As shown in Figure 6.4, the scatter goes up to 5 x 1 o4 N. In
the rheometer, the DC motor is powered to provide speeds up to 3000 mm/sec, and so
vibration certainly o c a n . The force transducer was onginally fixed on the support track
of the actuator, which was co~ected to the motor. Vibration in the moving part of the
actuator was inevitably transmitted to the rest of the system, including the upper disk.
Figure 6.4 Signal from the force transducer (MOD405) at O = 5 5' during a 'biank'
mn.
Two ways to reduce the vibrations were considered. One was to d u c e the
vibration of the system as a whole, and the other was to separate the tmnsducer fiom the
rest of the system. In terms of system vibration, decreasing the vibration energy or
increasing the system mass were considered. Since exponentid acceleration and high
speeds were necessary, the total energy input by the motor could not be reduced. But
increasing the total mass of the rheometer was possible. However, the frst idea tried was
to separate the transducer fiom the vibration source, by mounting the transducer to a
nearby wall.
Trial experiments were nin after mounting the transducer ternporarily to a wall.
Output fkom the transducer showed significant noise reduction at al1 tested extensional
rates. Isolating the transducer was (total mass 105 g) much easier than making the whole
rheometer more rigid.
Hence the transducer was mounted on a two-dimensional translation stage
combined with an additional stage to provide movement in the third dimension. The two-
dimensional stage was fixed to the wall such that it was separate from al1 parts of the
rheometer.
Figure 6.5 is a force reading tiom the 1 g transducer MOD405 without a test
sampie after the separate mounting of the transducer. The plot shows that the noise is
reduced to a level of order of IO-' N, which is about +5% of the force measuring range.
This level was considered satisfactory.
Figure 6.5 Force transducer noise for MOD405 during test period after noise
reduction
6.2 Calibration of the diameter-measuring device and control of its position
6.2.1 Zum bach calibration
As descnbed previously, the filament diarneter was measured by the Zumbach
system, consisting of the measuring head (ODAC 16J) and the process unit (USYS 10).
They satisfy the rquuements of precision and fast response: the smallest meanirable
diameter is 0-OSmm, with a resolution of 0.001 mm and the device provides 240 sans or
80 readings per second.
The device can meanire both opaque and transparent cylinders and calibrations
were conducted for both cases. A calibration wire was placed in the centre of the
measuring field and then measured in a 'blank' run. The readings fiorn the Zumbach
were compared with the ideal diameter of the caiibration wires determined by a
micrometer (Figures 6.6 and 6.7). The measured d u e s represented by the symbols fa11
on the solid line representing the ideal diameter- The Zumbach measurements were found
to be accurate to within SYO for al1 diameters.
6.2.2 Calibration o f Zumbach positioning
As discussed previously, the rnid-point of the filament is the crucial location for
measurement. Locating this position is as important as measuring the diameter itself
The positioning systern for measuring the diameter, as discussed in Section 4.2,
was calibrated by comparing twice the value of the Zumbach position with the filament
length L(t). Good agreement was obtained, as shown in Figure 6.8.
Figure 6.6 Zumbach calibration for transparent objects
O 0.5 1 1 .S 2 2.5 3 3.5
Achirl diamater, mm
Figure 6.7 Zumbach calibration for opaque objects
6 3 Velocitycalibration
The rheometer is designed so that the desired extensional motion is achieved by
contro1ling the velocity, and therefore important to know how ciosely the actuator
velocity follows the commanded velocity. The control prograrn recorded the velocity of
the actuator during every run. The actual velocity as a fùnction of time was then
compared with the commanded velocity, and an example is plotted in Figure 6.9. As
shown, good agreement was obtained.
Figure 6.9 Velocity calibration
CHAPTER 7
TEST MATERIALS AND THEIR SHEAR CHARACTERIZATIONS
In this work, the test fluids were two standard Newtonian fluids and several
international non-Newtonian test fluids. The formulation and relevant physical properties
of these fluids, as well as their shear properties, are introduced in this chapter.
7.1 Newtonian fluids and their shear properties
A Newtonian fluid is an appropriate calibration fluid because its extensional
viscosity is known to be three times its shear viscosity, Le., its Trouton ratio is three,
independent of strain or strain rate. Measurements for two Newtonian fluids were carried
out to provide conf~dence in the extensional measurements for the later non-Newtonian
ffuids.
The two Newtonian fluids were Viscasil 12,500 and 30,000 silicone oils, two
fluids made for test purposes by the General Electric Company, U.S.A. The shear
viscosity of these fiuids, and the other physical properties used in this work, density and
57
surface tension coefficient, are listed in Table 7.1. The shear viscosity data were verified
using a Brooffield viscometer in our laboratory at roorn temperatures.
1 Fluid 1 Shear viscosity 1 Surface Tension Coefficient 1 Density
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.
REFERENCES
Anna S. L., C. Rogers and G. H McKinley, On Controllhg the Kinemarics of a Filment Stretching Rheometer Using a Real-Cime Actnle Control Mechanim, submitted to I. Non- Newtonian Fluid Mech., 1999
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