derakhshandeh at al

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The apparent yield stress of pulp fiber suspensions

Babak Derakhshandeh, Savvas G. Hatzikiriakos,a)

and

Chad P. J. Benningtonb)

Department of Chemical and Biological Engineering, The University of British

Columbia, 2360 East Mall, Vancouver, British Columbia, V6T 1Z3, Canada

(Received 6 November 2009; final revision received 15 May 2010;

published 14 September 2010

Synopsis

The apparent yield stress is one of the most important rheological properties of pulp suspensions in

designing process equipment for the pulp and paper industry. Therefore, determining a reliable

apparent yield stress measurement technique is of importance, not only for pulp suspensions but

for any fluid exhibiting yielding behavior. In this work two established and extensively used

methods for determining apparent yield stress are compared with a velocity profile determination

technique using ultrasonic Doppler velocimetry. The apparent yield stresses are determined for

various commercial pulp suspensions at fiber mass concentrations ranging from 0.5 to 5 wt %. The

results are compared and models are proposed to represent the apparent yield stress of pulp

suspensions as a function of fiber mass concentration. It is concluded that the apparent yield stress

measurements obtained using the local velocity profile determination technique are the most

reliable. 2010 The Society of Rheology. DOI: 10.1122/1.3473923

I. INTRODUCTION

Pulp fiber suspensions consist of fiber networks having considerable strength. Before

they begin to flow, a minimum stress must be applied to disrupt the fiber networks known

as the yield stress. We will refer to this quantity as apparent yield stress since different

methods may result different values. Despite the controversial concept of the yield stress

as a true material property Scott 1933; Barnes and Walters 1985, the apparent yield

stress is considered as one of the most important rheological property of pulp suspensions

in designing process equipment for the pulp and paper industry. Several methods and

definitions have been proposed/developed to predict and measure the apparent yield

stress values both directly and indirectly Pryce-Jones 1952; Head and Durst 1957;

Thalen and Wahren 1964; Van den Temple 1971; Papenhuijzen 1972; Duffy and

Titchener 1975; Nguyen and Boger 1992; Liddel and Boger 1996. They make use

of various pieces of equipment such as a concentric-cylinder shear testerGullichsen and

Harkonen 1981, a rotary shear tester Bennington et al. 1990, and a reservoir-type

parallel plate geometry Damani et al. 1993; Swerin 1998; Wikstrm et al. 1998. In

addition to experimental studies, models of the form y = aCmb have been proposed to

aAuthor to whom correspondence should be addressed; electronic mail: [email protected].

2010 by The Society of Rheology, Inc.1137J. Rheol. 545, 1137-1154 September/October 2010 0148-6055/2010/545/1137/18/$30.00


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represent the apparent yield stress as a function of mass concentration Meyer and

Wahren 1964; Kerekes et al. 1985; Bennington et al. 1990; Bennington et al.

1995.

Pulp rheological characterization is not a simple task due to the unique and complex

behavior of wood fiber suspensions. They consist of roughly cylindrical fibers of averagelength ranging from 1 to 3 mm having aspect ratios of 60100. Fibers entangle to each

other mechanically to form regions of higher fiber mass concentrations of average size of

23 cm referred to as fiber flocs Mason 1950; Stockie 1997. Increasing the fiber

concentration, the number of fiber-fiber contacts increases which results into formation of

network structures throughout the suspension Kerekes and Schell 1992. Coexistence

of individual fibers, fiber flocs, and networks makes pulp fiber suspensions heterogeneous

and multiphase systems with the systems rheology being affected by inhomogeneities in

each phase. This is against the basic homogeneity assumption which is made to predict

simple fluid flow characteristics. The presence of millimeter-sized fibers and centimeter-

sized fiber flocs in a heterogeneous pulp suspension makes it complicated to obtainreproducible rheological data.

Pulp suspensions cannot be regarded as a continuum since they contain a dispersed

phase with dimensions comparable to the characteristic dimensions of the geometry of

the measuring apparatus, i.e., the rheological properties of the suspension depend on the

size distribution of the dispersed phase, even though the overall concentration in the

system is the same Coussot and Piau 1995. The fiber structures are large compared

with the geometry dimensions used in rheological devices and therefore fiber rotation is

limited.

Another common behavior of pulp fiber suspensions is their orientation around the

measuring elements and migration of fibers away from solid boundaries which leads toformation of a depletion layer that complicates further rheological measurements

Nguyen and Boger 1992; Barnes 1995; Swerin et al. 1998; Wikstrm et al. 1998;

Archer 2005. Due to these complications, the selection of an appropriate measuring

device to provide large measurement gaps compared with fiber dimensions to eliminate

fiber jamming as well as decrease the possibility of apparent slip at solid boundaries is

needed to obtain reliable data. Various methods have been proposed in the literature to

interpret the rheological data which are affected by wall slip particularly for foams,

emulsions, and polymers Mooney 1931; Jastrzebski 1967; Yoshimura and

Prudhomme 1988. These corrections cannot be applied to raw rheological data ob-

tained from pulp suspensions. For instance, Yoshimura and Prudhomme 1988 consid-ered the wall slip to be a function of wall shear stress and proposed a method to correct

the rheological data by examining the dependency of the rheological data on the gap size

in a parallel-plate geometry. Decreasing the gap size squeezes water out of the suspension

and as a result the fiber mass concentration increases. This leads to imprecise rheological

data. Mhetar and Archer 1998 and Walls et al. 2003 used rough surfaces in their

parallel-plate geometry to prevent slip, i.e., using sand paper or serrated plates.

Another approach to minimize the effect of slip is to make use of complex geometries

such as the vane geometry Nguyen and Boger 1983, 1985; Barnes and Carnali 1990;

Barnes and Nguyen 2001; Cullen et al. 2003. Application of the vane geometry

requires that a number of assumptions be made. First, it is assumed that the fluid in

between the blades rotates along with them so that it generates a cylindrical surface with

a radius close to that of the vane. Second, the shear stress distribution is assumed to be

uniform at the outer virtual cylindrical surface described by the outer edge of the vane

and finally, the fluid, which is trapped between the blades of the vane, is assumed to act

as a rigid body without any secondary flow. These assumptions are valid only at low

1138 DERAKHSHANDEH et al.


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rotational rates and in vanes with four or more blades Nguyen and Boger 1983.Despite these assumptions, the vane geometry has many advantages over the other ge-

ometries especially when used to study pulp suspensions. In this system, the fluid is

usually sheared within itself; thus, the slipping effect is minimized Barnes and Nguyen

2001. In addition to the elimination of wall slip, insertion of the vane causes the least

amount of disturbances to the structure of the sample although it can be significant,

particularly in the case of thixotropic fluids Nguyen and Boger 1983. Most commer-

cial rheometers utilize narrow gaps which impose practical restrictions to sample rheo-

logical behavior. These include fiber jamming, tumbling, orientation, and the formation

of depletion layers. Vane geometry with large cups provides wide gaps which enables the

investigation of fluids containing large particles or fibers that can exhibit considerableapparent wall slip Bennington et al. 1990; Zhang et al. 1998; Baravian et al. 2002;

Martin et al. 2005; Ramrez-Gilly et al. 2007.

A significant amount of discrepancy can be found among the reported apparent yield

stress values Gullichsen and Harkonen 1981; Bennington et al. 1990; Swerin 1998;

Damani et al. 1993; Wikstrm et al. 1998; Ein-Mozaffari et al. 2005. An example

is given in Table I, where the reported values for the apparent yield stress of a 3 wt %

bleached softwood kraft pulp range from 19.3 to 350 Pa, while those of a 6 wt % range

from 60 to 1220 Pa. This discrepancy is due to differences in pulp type, the way the

apparent yield stress is defined and the technique used to measure it.

The apparent yield stress can be measured by means of either stress-controlled or

rate-controlled rheometers by performing creep or steady shear tests, respectively. Using

a rate-controlled rheometer and applying a constant strain rate, the shear stress can be

measured as a function of strain or time. The apparent yield stress can then be calculated

as the maximum shear stress measured, the steady-state shear stress, or the shear stress at

which departure from linearity begins very difficult to establish uniquely. Each of these

TABLE I. Apparent yield stress values of softwood kraft bleached pulp suspension reported in the literature

using different methods.

Reference Measurement method

Apparent

yield stress

3 wt % SBKy Pa

Apparent

yield stress

6 wt % SBKy Pa

Bennington et al.

1990

Baffled concentric-cylinder

viscometer, maximum in torque-

time response 176 1220

Swerin et al.

1998

Couette cell geometry, using

oscillatory shear experiments 19.3 117

Damani et al.

1993

Reservoir-type parallel plate

geometry, using oscillatory

shear experiments

60

Wikstrm et al.

1998

Baffled concentric-cylinder

viscometer, maximum in torque-

angle response 131 1100

Ein-Mozaffari et al.

2005

Concentric-cylinder viscometer,

maximum in torque-time response 350

1139THE YIELD STRESS OF PULP SUSPENSIONS


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definitions gives a different value for the apparent yield stress Thalen and Wahren

1964; Nguyen and Boger 1985; Liddel and Boger 1996. Another approach is to

apply a slow shear rate ramp to obtain the variation of torque as a function of rotational

speed. The apparent yield stress is calculated using the maximum torque measured during

the experiment Bennington et al. 1990. Using a stress-controlled rheometer and in-creasing the shear stress in a linear manner, the variation of the instantaneous viscosity

instantaneous shear stress divided by the instantaneous shear rate versus shear stress can

be obtained. The apparent yield stress is the value at which the instantaneous viscosity

exhibits a maximum Cheng 1986; Zhu et al. 2001; Brummer 2005; Coussot 2005;

Nguyen et al. 2006.

The main objective of this work is to identify a reliable technique for measuring the

apparent yield stress of pulp fiber suspensions that yields consistent results. To establish

this technique, the apparent yield stress of several commercial pulp fiber suspensions

over a wide range of mass concentrations is measured by using conventional apparent

yield stress measurement methods utilizing both a stress-controlled and a rate-controlledrheometer. The apparent yield stress values obtained using these techniques are compared

with those obtained from a velocity profile determination technique using ultrasonic

Doppler velocimetry UDV described in Sec. II. The reliable data from this compari-

son are used to obtain models for the apparent yield stress values of pulp fiber suspen-

sions. Finally, the velocity profiles from the ultrasonic Doppler velocimetry are used to

determine the flow curves of some of the pulp suspensions and compared with the

corresponding flow curves from macroscopic measurements.

II. VELOCITY PROFILE DETERMINATION USING ULTRASONIC DOPPLERVELOCIMETRY

While conventional rheometers are widely used to measure the apparent yield stress,

other techniques such as velocity profile determination using UDV have been found

useful in rheological characterization Takeda 1986; McClements et al. 1990; Bache-

let et al. 2004; Becu et al. 2006; Koseli et al. 2006. UDV is a simple, non-intrusive

acoustic measurement technique, which utilizes the Doppler effect. In this technique, a

short ultrasonic burst is sent to the fluid periodically and the echoes issuing from the

suspended particles are collected. Using the time delay and the frequency content of these

reflected pulses, the location and the velocity of the particle can be obtained. UDV has

been coupled with conventional rheometry to provide a robust device to study the flow

behavior of complex fluids, including the local flow curves and apparent yield stressManneville et al. 2004. The torque T imposed on the moving vane by the rheometer

yields the stress distribution r across the gap, while the velocity profile permits de-

termination of the local shear rate r according to Eqs. 1 and 2 Bird et al. 2001:

r =

2hr2, 1

r = r

rur

r , 2

where h is the vane height, R1 is the vane radius, and R2 is the cup radius with R1r

R2 Fig. 1. By using large gaps to study the rheological properties of viscoplastic

fluids that exhibit an apparent yield stress, such as paper pulps, polymers, and ceramic

pastes, the vane creates a sheared yielded zone within which the material is in flow;

however, when the shear stress falls below the apparent yield stress value, the fluid is



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stationary un-yielded zone, i.e., the velocity is practically equal to zero between Ry and

R2 Fig. 1. By knowing the radius of shearing Ry obtained using UDV measurements and

the steady-state shear stress at the vane surface T obtained using the torque reading from

the rheometer, the apparent yield stress y can be calculated from Eq. 3 Fisher et al.

2007:

y = TR1

Ry2

. 3

III. MATERIALS AND EXPERIMENTAL TESTING

Pulp fiber suspensions were prepared from bleached softwood kraft SBK and

bleached hardwood kraft HW Domtar Inc., Windsor, QC, thermal-mechanical-pulp

TMP Howe Sound Pulp and Paper Limited Partnership, Port Melon, BC, and stone-

ground wood SGW Paprican, Pointe-Claire, QC by breaking up the dried pulp sheets

and rehydrating the fibers with tap water using a disintegrator TMI, Montreal, QC for

30 min at 120 rpm. Suspensions of 0.5, 1.0, 2.0, 2.5, 3.0, 4.0, and 5.0 wt % were

prepared. The pulp fiber properties are summarized in Table II. The mean fiber length is

an important parameter as will be shown below. In this study, it varies from 0.67 to 2.96

mm Table II.

A four-bladed vane, 38.5 mm in height and 25 mm in diameter, was placed in a

transparent cylindrical cup having an internal diameter of 100 mm and a height of 64 mm

FIG. 1. Schematic of the vane in a large cup geometry and the characteristic dimensions.



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resulting in a gap size of 37.5 mm. A series of tests were conducted to determine the

optimum pre-shearing conditions for each sample. Tests were conducted at each suspen-

sion mass concentration with different levels of shear stress applied for different lengthsof time. Samples were then redistributed evenly in the gap and left to rest for 15 min

followed by checking the dependency of the viscosity on the shear rate. The optimum

pre-shearing conditions were identified as those for which different samples exhibited the

same viscosity versus shear rate relationship. These conditions were then used in all

subsequent tests.

The apparent yield stress values of the pulp suspensions were measured using three

methods. In the first, a stress-controlled Bohlin C-VOR rheometer Malvern, Worcester-

shire, UK was used to increase the shear stress in steps linearly and the variation of the

instantaneous viscosity instantaneous shear stress divided by the instantaneous shear

rate versus shear stress was obtained. The apparent yield stress was measured as thestress value for which the instantaneous viscosity exhibited a maximum Cheng 1986;

Zhu et al. 2001; Brummer 2005; Coussot 2005; Nguyen et al. 2006.

The second method used a rate-controlled Haake RV12 Rotovisco viscometerThermo

Fisher Scientific Inc., Waltham, MA at a rotational speed of 8 rpm. For this experiment

the torque-time response was measured with the peak torque used to calculate the appar-

ent yield stress. This technique has commonly been used to measure the apparent yield

stress of various substances Cadling and Odenstad 1950; Donald et al. 1977; Bowles

1977; Nguyen and Boger 1981, 1983; Ein-Mozaffari et al. 2005.

The third method used the Haake RV12 viscometer at two rotational speeds of 8 and

16 rpm and a pulsed ultrasonic Doppler velocimeterModel DOP2000, Signal Process-ing, Switzerland to measure the velocity profiles across the gap. The ultrasonic trans-

ducer has an active diameter of 20 mm and a pulse repetition frequency of 100 Hz to 15.6

kHz, which can be changed depending on the magnitude of the expected velocity. A cup,

identical to those used in the other methods, was made with an indentation of 14 at the

surface to attach the UDV probe. The space between the transducer and the Plexiglas wall

was filled with an ultrasonic gel to establish an efficient acoustic coupling between the

probe and the vessel.

Finally, to have a better understanding of the flow behavior of pulp suspensions, the

stress-controlled Bohlin C-VOR rheometer was used to measure the flow curves of the 2

wt % pulp suspensions. Constant shear stress values above the yield stress were applied

on the suspension and the steady-state shear rate values were obtained. The flow curves

were fitted to a HerschelBulkley HB model which was subsequently used to calculate

numerically the velocity profiles. The calculated profiles were then compared with those

determined by the UDV method to check the consistency between the two sets of experi-

mental data.

TABLE II. Properties of pulp fibers used in the present study.

Fiber

system

Fiber properties

Mean length

Lw

mm

Percent fines

L =0.070.2 mm

Mean

curl index

Mean

kink index

SBK 2.96 1.9 0.27 2.11

HW 1.28 8.17 0.105 1.98

TMP 1.36 11.9 0.05 0.50

SGW 0.67 23.1 0.09 1.43



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IV. RESULTS AND DISCUSSION

A. Apparent yield stress measurement using linear shear stress ramps

Figure 2 depicts a typical apparent yield stress measurement for a 1 wt % bleached

softwood kraft pulp suspension at 23 C. Measurements were performed at least five

times to check the reproducibility and to minimize experimental errors. Figure 3 shows

the typical behavior of the transient strain t when shear stresses, which are lower and

greater than the apparent yield stress, are applied to the pulp suspension. For stresses

lower than the apparent yield stress, an initial jump in strain elastic response was

observed followed by a gradual increase in the strain until reaching a constant value

solid-like behavior. For stresses above the apparent yield stress value, the strain in-

creases monotonically, reaching a constant slope fluid-like behavior.

FIG. 2. Repeats of apparent yield stress measurements for a bleached softwood kraft pulp suspension SBK ofmass concentration of 1% at 23 C applying a linear shear stress ramp.

FIG. 3. Creep response of a bleached softwood kraft pulp suspension SBK of mass concentration of 1% at23 C for shear stress values lower and higher than the apparent yield stress. Note that pulp suspension exhibitsa solid behavior below the apparent yield stress while a fluid behavior can be observed above the apparent yieldstress.



8/18

The apparent yield stress values obtained by applying linear shear stress ramps are

listed in Table III and plotted in Fig. 4 as a function of mass concentration. The depen-

dency of the apparent yield stress values on fiber mass concentration has been correlated

using a power-law model y = aCmb. The resulting fitted constants are listed as an inset

in Fig. 4 and are within the range of previously reported results Kerekes et al. 1985.

The measured apparent yield stress values depend on the physical properties of the

fibers. Fibers tend to form networks due to a number of attractive forces, including

colloidal, mechanical surface linkage, elastic fiber bending, and surface tension, although

mechanical entanglement is the greatest Kerekes et al. 1985. Fiber properties, such as

fiber length, flexibility, and elastic modulus, contribute to these forces and affect theapparent yield stress of the suspension. More flexible and longer fibers permit greater

contact between adjacent fibers, increase mechanical linkages, and therefore the apparent

yield stress. Due to differences in fiber length and flexibility, the apparent yield stress

decreases from SBKTMP HWSGW at a given mass concentration. Increasing sus-

pension concentration increases the number of fiber entanglements, the strength of the

fiber network formed, and hence the apparent yield stress, as shown in Fig. 4 for all the

pulp suspensions tested.

TABLE III. Apparent yield stress values obtained by using the linear

shear stress ramp method.

Cm

Apparent yield stress

Pa

SBK HW TMP SGW

0.005 20.60 0.330.1 0.180.05 0.110.03

0.01 134 41.5 11 0.730.1

0.02 576 142 163 91

0.025 11416 264 271 171

0.03 15413 488 5011 284

0.04 24245 8010 12512 692

0.05 38449 1667 24532 1509

FIG. 4. The apparent yield stress values of all tested pulp suspensions as a function of mass concentrationobtained by using the shear stress ramp method at 23 C.



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B. Apparent yield stress measurement using the start-up of shear flow

experiment

Apparent yield stress measurements were also performed using start-up of steady

shear experiments in the Haake RV12 rheometer. Each experiment was performed five

times and the apparent yield stress values were measured as the maximum shear stress

achieved in the shear stress vs time response. Typical measurements are plotted in Fig. 5

for a 3 wt % bleached softwood kraft pulp suspension. The apparent yield stress valuesobtained using this technique are listed in Table IV. Generally, these values were larger

than those obtained by using the pervious linear shear stress ramp method, although the

same trend as a function of fiber type and mass concentration was observed Fig. 6. The

resulting fitted constants to power-law model y = aCmb are also listed in the inset of

Fig. 6.

Under the application of constant rotational rates constant shear rates, viscoelastic

thixotropic fluids exhibit an initial stress growth that is followed by a slight stress decay.

However, pulp suspensions do not attain an ultimate constant shear stress; instead they

exhibit an oscillatory behavior, as shown in Fig. 5. This characteristic is due to the

behavior of fiber flocs during flow. Pulp fiber suspensions are composed of individual

FIG. 5. Stress response after imposition of steady shear at the nominal shear rate of 0.83 s1 rpm=8 for a 3wt % bleached softwood kraft pulp suspension SBK at 23 C. Multiple tests indicate the level ofreproducibility.

TABLE IV. Apparent yield stress values obtained by using the start-up of

steady shear flow experiment.

Cm

Apparent yield stress Pa-Controlled rate-RPM= 8

SBK HW TMP SGW

0.005 51.6 1.50.1 0.850.4 0.140.03

0.01 392 94 42 31

0.02 1056 308 3310 3590.025 20516 5523 5316 4823

0.03 24840 8731 6525 5517

0.04 38858 15140 18045 11838

0.05 51860 29252 28942 19634



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fibers, which aggregate to form flocs. In flow, some flocs tend to move in and out of the

region between the rotor vanes, while others move along with the vane but slow down as

the contact with the vane tip is lost. When a floc moves into the region between blades or

moves along with a blade, the required shear stress to maintain constant rotational rate

increases. On the other hand, stress decreases when a floc moves out of the region

between the vane blades or looses the contact with the blade tip. Due to this behavior the

shear stress does not reach a true steady-state value.

C. Apparent yield stress measurement by UDV

An ultrasonic Doppler velocimeter was used to determine the velocity profile in the

gap of various pulp suspensions in conjunction with torque measurements made with the

Haake RV12 rotovisco viscometer. Two constant vane rotational rates of 8 and 16 rpm

were used. The UDV probe was adjusted to 14 so that velocity measurements could be

made at the tip of the rotating vane. Velocity profiles for different pulp suspensions at the

rotational rate of 8 rpm are presented in Figs. 7a7d.

The velocity decreases across the gap, starting from a maximum value at the vane tip

and falling to zero at a certain distance which is referred to as yielding radius RyFig. 1

.The shear stress decreases in the gap according to Eq. 1. The suspension contained in

the region between the vane tips and the yielding radius is in flow, while the fluid beyond

this region remains stationary. Increasing the mass concentration of pulp suspension

increases the apparent yield stress and decreases the yielding radius, while the velocity

profiles tend to move closer to linearity Figs. 7a7d.

The yielding radius and the steady-state shear stress at the vane were used to calculate

the apparent yield stress of all pulp suspensions tested by using Eq. 3. The results are

summarized in Table V and depicted in Fig. 8 along with power-law fits to the data.

For an ideal yield stress fluid, the shear rate and thus the mean velocity must decrease

gradually from a maximum value at the tip of the vane toward zero at the yielding radius,

Ry Fig. 1. As seen from Figs. 7a7d, the mean velocity indeed decreases gradually

from a maximum value at the tip of the vane and reaches zero at the yielding radius, Ry,

resulting a discontinuity in the velocity profiles at the transition point from the yielded to

the un-yielded region. This rheological behavior has also been observed in concentrated

colloidal suspensions, referred to as shear-banding or shear-localization effect, which

FIG. 6. The apparent yield stress values of all tested pulp suspensions as a function of mass concentrationobtained by applying the start-up of steady shear flow at 23 C.



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results from the yielding and the thixotropic characteristics of the fluid. Rheological

models such as Bingham, Casson, and HerschelBulkley cannot predict the velocity

profiles accurately particularly with respect to discontinuity and the apparent yield stress

of the fluid depends on the procedure for determining it Coussot et al. 2002.

Pulp suspensions are heterogeneous systems containing millimeter-sized fibers and

centimeter-sized fiber flocs. The discontinuity in the velocity profiles at the transition

from the yielded to the un-yielded zone can also be due to the existence of large moving

FIG. 7. Velocity profiles across the gap for a SBK, b HW, c TMP, and d SGW pulp suspensions, at

23 C and several mass concentrations. Note that the apparent yield stress increases nonlinearly with increaseof the mass concentration and thus the yield radius decreases.

TABLE V. Apparent yield stress values obtained using UDV coupled with

a rate-controlled viscometer.

Cm

Apparent yield stress Pa-Velocity

profile determination technique

SBK HW TMP SGW

0.005 10.6 0.20.1 0.240.05 0.080.03

0.01 112.5 31.5 1.70.6 0.470.1

0.02 4611 112.4 143 810.025 10521 205.3 255 153

0.03 13718 4012 4511 234

0.04 22145 7154 11821 5613

0.05 35849 18162 23854 12735



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flocs in the layer next to the un-yielded zone. In this case, UDV results finite velocities

for the moving fiber flocs and drops to zero in the next layer. Therefore, it is not clear

whether pulp suspensions display shear localization or banding as they go through the

yielding transition.

To analyze the yielding transition further, the steady-state flow curves were measured

for 2 wt % pulp suspensions and a HB model Eq. 4 was fitted to the data. Figure 9

depicts the flow curves along with the HB model fits to the data. It is noted that the HBfitted apparent yield stress parameters are in close agreement with those obtained using

the linear shear stress ramp and velocity profile measurements. The parameters of the HB

model are listed in the inset of Fig. 9:

= y + Kn. 4

Furthermore, using Eqs. 1, 2, and 4, the following integral expression can be

derived for the velocity profile across the yielded zone:

FIG. 8. The apparent yield stress values of all tested pulp suspensions as a function of mass concentrationobtained using local velocity profile measurements at 23 C, at a constant rotational rate of 8 rpm, at pulsedrepetition frequency of 8000 Hz and incident angle of 14.

FIG. 9. The flow curves of 2 wt % pulp suspensions, at 23 C. The solid lines are the best fits to theexperimental data of a HerscheBulkley model.



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ur = rr

Ry

2hr2 y

K

1/n

dr

r, 5

where y, K, and n are the HB parameters and R1 and Ry are the vane and the yielding

radii, while R1rRy. The HB fitted constants were then used with Eq. 5 to predict

the velocity profiles for the two investigated rotational rates.

Figure 10 shows the velocity profiles predicted by Eq. 5 and those obtained experi-

mentally using UDV for SBK and SGW pulp suspensions at two different rotational rates.

The HB predictions and the experimentally measured velocity profiles are in good agree-

ment. Given this, it can be argued that pulp suspensions seem to behave as yield stress

fluids. On the other hand, shear localization or banding cannot be excluded.

D. Comparison of the different apparent yield stress measurement methods

A comparison of the apparent yield stress values determined using each method is

given in Figs. 11a11d for the pulp suspensions studied with the constants fitted to thepower law model summarized in Table VI. There is satisfactory agreement between the

apparent yield stress values obtained using the linear shear stress ramp and the velocity

measurement techniques, while the apparent yield stress values obtained using start-up of

shear flow method have considerably larger values.

Fiber networks consist of large flocs which attach to each other by weaker fiber

networks. Under the application of shear stress, the weaker bonds between the different

fiber flocs break down and the behavior of the suspension deviates from that of an elastic

solid departure from linearity in the shear stress-time data. This deviation possibly

occurs at a shear stress equivalent to the shear stress at which the instantaneous viscosity

results a maximum value. This regime which occurs at low shear stress values is referred

to as the macro-scale deformation regime Wikstrm 2002. The critical shear stresses

for the onset of deviation from the linearity in the shear stress-time data would have

resulted values closer to those determined by the shear stress ramp test; however, it is

difficult to accurately establish such critical stresses experimentally and this is the reason

these values are not reported in the present work.

FIG. 10. Velocity profiles across the gap for 2 wt % SBK and SGW pulp suspensions at 23 C and tworotational rates of 8 and 16 rpm. The solid lines are the predictions of the HerschelBulkley model.



14/18

With further increase in the shear stress, the sheared area increases and more fiber

flocs rupture Steen 1990. This regime is referred to as the micro-scale deformation

regime Wikstrm 2002. Beyond a specific shear stress equivalent to the maximum

shear stress in the start-up of shear experiment the whole fiber network in the suspension

is ruptured, which results higher values of the apparent yield stresses compared with

those obtained by the other methods.

As velocity profile measurement technique uniquely identifies the real velocity distri-bution and yielding radius in the gap, this technique gives a more accurate determination

of the apparent yield stress. However, this technique is time consuming and thus not

convenient compared with macroscopic rheological techniques as the application of equa-

FIG. 11. Comparison of the apparent yield stress values obtained using three different methods for a SBK, b

HW, c TMP, and d SGW pulp suspensions, at 23 C and several mass concentrations. Note that the apparent

yield stress values obtained by using the linear shear stress ramp and the velocity profile determination tech-niques are in good agreement.

TABLE VI. Summary of fitted constants to the power-law model y = aCmb for all tests.

Pulptype

Mass fractionrange used

Linear shear stressramp method

Constant shearrate method

Velocity profiledetermination method

a105 bGoodness

of fit a105 bGoodness

of fit a105 bGoodness

of fit

SBK 0.005Cm0.05 4.950.20 2.330.10 0.99 2.220.15 1.950.11 0.98 8.100.50 2.500.13 0.98

HW 0.005Cm0.05 3.940.23 2.600.21 0.98 1.220.10 1.120.10 0.98 7.250.70 2.800.21 0.98

TMP 0.005Cm0.05 35.22.22 3.180.25 0.99 1.800.15 2.170.20 0.97 20.00.18 3.000.25 0.97

SGW 0.005Cm0.05 19.00.96 3.160.16 0.96 32.01.9 3.100.15 0.96 26.00.13 3.260.13 0.98



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tions must be made to infer the rheological properties from the velocity profiles. When

applying a constant shear rate, the shear stress increases rapidly which ruptures the fiber

network abruptly thus reducing the accuracy of the apparent yield determination. How-

ever, by increasing the shear stress or the shear rate slowly, the fiber network ruptures

gradually making it easier to determine the shear stress at which flow begins. Since theapparent yield stress values obtained using the linear shear stress ramp method are in

good agreement with those obtained by the velocity measurement technique, applying

linear shear stress ramps by using a stress-controlled rheometer is an easy and reliable

alternative for apparent yield stress measurements.

V. CONCLUSIONS

Pulp fiber suspensions are composed of fiber networks and flocs which possess mea-

sureable apparent yield stress. The two most widely used apparent yield stress measure-ment methods are linear shear stress ramps and start-up of steady shear flow experiments.

These were used in this study to measure the apparent yield stress of different pulp fiber

suspensions at low fiber mass concentrations up to 5 wt %. Results obtained using these

techniques were significantly different from each other. To determine the most reliable

technique, an UDV was coupled with a rate-controlled rheometer to provide a robust

device and reliable method which can be used to measure the apparent yield stress. By

explicitly determining the velocity profiles, the results from this technique were found to

be in agreement with those obtained from the linear shear stress ramp method. Therefore,

this technique can be used to obtain experimental data safely and efficiently.

NOMENCLATURE

h vane height, mm

R1 vane radius, mm

R2 cup radius, mm

Ry yield radius, mm

r local radius within the cup, mm

T torque, N m

Cm mass fraction

ur velocity distribution, mm/st time, s

GREEK LETTERS

shear stress, Pa

T steady-state shear stress at the vane, Pa

y yield stress, Pa

strain, %

shear rate, s1

instantaneous viscosity, Pa s

ACKNOWLEDGMENTS

The authors would like to acknowledge NSERC for the collaborative grantGrant No.

CRDPJ 379851.



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