Rheological properties of cellulosic fibre suspensions flocculated by cationic polyacrylamides

Colloids and Surfaces A: Physicochemicaland Engineering Aspects 133 (1998) 279-294

ELSEVIER

COLLOIDS AND SURFACES

A

Rheological properties of cellulosic fibre suspensions flocculated by cationic polyacrylamides Agne Swerin Swedish Pulp and Paper Research Institute (STFI), Box 5604, S-114 86 Stockholm, Sweden

Received 28 March 1997; accepted 14 July 1997

Abstract

Cellulosic fibres in suspension form three-dimensional networks which display shear strength as a result of the mechanical entanglement of flexible fibres. The effect of high molecular weight cationic polyacrylamides of different charge densities on the viscoelasticity of softwood kraft pulp suspensions was investigated by rheological measurements in oscillatory shear as a function of straining frequency, straining amplitude, added amount of cationic polyacrylamide and fibre concentration. The flocculants increased the fibre flocculation and this was shown as an increase in the shear modulus and in the critical strain. The critical strain marks the onset of structural breakdown of the fibre network. The threshold concentration of fibres c* for a measurable shear strength was lower for suspensions flocculated by cationic polyacrylamide. The shear modulus showed a scaling relationship as a function of the fibre concentration in excess of the threshold concentration, c-c*. The effect of a flocculant is suggested to be due primarily to an increase in the number of fibres that are active in the network. The flocculant probably also increases the bonding strength in the fibre~bre contact points. An attempt is made to discuss the results according to an elastic site/bond percolation concept. © 1998 Elsevier Science B.V. Keywords." Rheology; Suspensions; Flocculation; Cellulosic fibre; Cationic polyacrylamide

1. Introduction

Suspensions in water of anisotropic particles such as cellulosic fibres form coherent three-dimensional networks that display viscoelastic properties. This has practical implications in m a n y stages of the papermaking process, e.g. during the pumping of fibre suspensions and the forming of paper. The first extensive study of viscoelastic properties of cellulosic fibre suspensions, both theoretically and experimentally, was made by Wahren [1 ]. It was concluded that a three-dimensional network develops since fibres bend in turbulent shear and are constrained in a network structure as they try to regain their original shape. Some practical 0927-7757/98/$19.00 © 1998 ElsevierScience B.V. All rights reserved. PII S0927-7757(97) 00212-4

implications of this model for the formation of fibre networks have later been reviewed [2]. There is a threshold concentration below which no three-dimensional network is formed in a fibre suspension. In newer terminology this m a y be called the threshold for percolation [3]. A threshold concentration exists because a certain number of contact points between fibres must exist for a network to form. The percolation behaviour in systems containing anisotropic particles, e.g. fibres, has been investigated theoretically and experimentally with application to e.g. magnetic suspensions [4] and to fibre-composites [5,6]. In the case of suspensions in water of cellulosic fibres, flocs of fibres exist both below and above the threshold

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concentration. These flocs may be considered as fragments of the network. The state of flocculation affects the rheology of a suspension. In the case of cellulosic fibre suspensions, this was recognized in a rheological investigation in which the valency of the counterions to the charged groups of the fibres was changed [7]. The shear modulus of the suspension increased when the valency of the counterions was increased from monovalent Na + to tetravalent Th 4+, presumably due to a change in the state of flocculation. During paper manufacture, chemical flocculants, e.g. cationic polyacrylamides, are added to flocculate mineral fillers and cellulosic fine material onto fibre surfaces and thereby retain them in the paper web formed. The flocculants also create flocs of filler particles and affect the fibre flocculation. The latter process is undesired because it affects the paper properties negatively. The influence of chemical flocculants on the fibre network strength has been investigated [8-10] in studies where the network strength was evaluated from measurements of the breaking length of fibre plugs. It was concluded that the network strength increases when chemical flocculants are added and shows a maximum strength when a zero charge of the fibre material is reached. Polymers of high molecular weight which give flocculation by a bridging action have not, however, been used in investigations of fibre network strength until recently. The effect of high molecular weight polyacrylamides was studied in oscillatory shear using a rheometer equipped with a measuring cell with a broad gap [11]. The present study focuses on the effects of flocculation in fibre suspensions using cationic polyacrylamides of different charge densities. The viscoelasticity of fibre suspensions has been investigated as a function of straining frequency, straining amplitude, fibre concentration and added amount of cationic polyacrylamide. Fibre suspensions show a measurable shear strength at a lower fibre concentration when a chemical flocculant is added. The threshold concentration is a function of the number of contact points per fibre in the network. Without flocculant at least three contact points per fibre are needed to form a coherent network. Since the threshold concentration is lower in the

presence of a chemical flocculant, this means that less than three contact points are then needed to form a coherent network.

2. Experimental 2.1. Materials The cellulosic fibres used were from dried, fully bleached softwood (mixture of spruce/pine) and hardwood (birch) kraft pulps. The softwood pulp was beaten to 25 SR (SCAN-C 19:65) in a Valley beater (SCAN-C 25:76) and the hardwood pulp was beaten to 24 SR in an Escher-Wyss laboratory conical refiner. After beating, the fibre fines, < 100 gin, were removed by repeated filtration on a Celleco laboratory filter. Some properties of the fractionated fibres are given in Table 1. The fibre dimensions and the coarseness (fibre weight per unit length) were determined from measurements in the wet state using a Kajaani FS-200 instrument (Kajaani Electronics, Finland). From the measurements, the number of fibres per gram was estimated to be 4 x 106 fibres g- 1 softwood pulp and 15 x 106 fibres g - t hardwood pulp. The fibre width was measured with an image analyser which determines the fibre dimensions in Table 1 Properties of the cellulosic fibres used in the experiments Fibre property

WRV (g H20/g fibres)" Fibre length averages weight-weighted,/r w (mm) length-weighted,/2 l (mm) number-weighted,/5 n (mm) Lw/L n b Width (~rn) Coarseness (mg m - 1) Sediment concentration (g 1-1) Charge density (laeq g - 1)

Softwood pulp fibres

Hardwood pulp fibres

1.36

1.14

2.8 2.2 1.3 2.1 24 0.21 3.2 26

0.9 0.8 0.6 1.6 20 0.13 8.8 45

a Water retention value, i.e. degree of fibre swelling determined according to Ref. [12]. b Given to characterise the distribution of fibre lengths.

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294

a flowing, dilute fibre suspension. Assuming that the fibres are cylindrical, the average fibre radius is 12 ~tm for the softwood pulp fibres and 10 ~tm for the hardwood pulp fibres. The length-to-diameter ratio Lid for the fibres is used as a measure of the degree of anisotropy. The L/d values were 117 for the softwood pulp fibres and 46 for the hardwood pulp fibres. The sediment concentration is the concentration in the sediment if a fibre suspension is allowed to settle from a very low concentration. The charge density of the fibres was determined by conductometric titration with N a O H [ 12] after the carboxylic acid groups of the fibres had been converted to the hydrogen form by treatment with 0.01 M HC1. Prior to the experiments, the fibres were washed with 0.01 M HC1 to remove sorbed metal ions and then washed with deionized water until the pH of the filtrate was higher than 4.5. The fibres were then converted to the sodium form by treatment with 0.001 M NaHCO3 and N a O H to pH 9. The fibres were then washed with deionized water to a conductivity of less than 0.5 mS m -1. The fibres were stored in a refrigerator before use. The cationic flocculants used were copolymers of acrylamide and the cationic monomer trimethyl(2-acryloxy-ethyl)-ammonium chloride, hereafter called C-PAM (Allied Colloids Ltd., U K ) . The C-PAM polymers all had molecular weights of (4-5) x I06 (weight average) according to sizeexclusion chromatography measurements [ 13 ], but different degrees of substitution (mole percent), 0.02, 0.04, 0.14 and 0.27. These values correspond to charge densities of 0.26, 0.52, 1.6 and 2.6 meq g - 1 respectively.

2.2. Methods Rheological measurements were made in a Bohlin VOR rheometer (Bohlin Instruments, Sweden) in oscillatory shear using a Couette cell with a 6.7 mm gap and an inner cylinder with a diameter of 14 mm. The surfaces were blasted to prevent wall slip. Small sinusoidal strains were applied on the outer cylinder and the torque on the inner cylinder was measured. The shear modulus is given by G*=U~, where G* is the complex

281

shear modulus, and f and ~7 are the sinusoidal stress and strain respectively. G* is divided into its real and imaginary parts, G * = G ' + i G " ( i = ~ / ~ - i ) , where G'=lG*[cos6 is the storage (elastic) modulus and G"=IG*[ sin ~5 is the loss (viscous) modulus. 6 is the phase angle shift. The strain reported is a dimensionless average strain defined as the straining amplitude divided by the width of the measuring gap. In one set of experiments, a Pulse Shearometer [14, 15] (Stevens Servicing Ltd., U K ) was used to measure the high frequency limit of the shear modulus G~. The measurement is based on the transmission of a pulse of small-amplitude sound waves (21 ms, 200 Hz) through the sample. The sound waves were generated by a piezoelectric crystal connected to a metal plate which made contact with the sample. The shear modulus is calculated from the relationship Go~=uZp, where u/m s -1 is the velocity of the shear wave and p/kg m - 3 the density of the sample. By measuring the propagation time at different distances of separation between the transmitting and receiving plates, the propagation velocity is obtained as the slope of plate separation vs. propagation time. The value used for the density of the fibre suspensions was 1000 kg m-3. The shear applied to the sample is small enough to allow repeated measurements on the same sample with the network structure still intact [ 15]. Fibres were dispersed in deionized water and the suspension was deaerated after disintegration. The pH of the suspensions was 7.5-8.0. Samples of the suspensions were transferred to a baffled dynamic drainage jar [16] equipped with a propeller stirrer. A solid plastic bottom was inserted instead of a screen. The propeller speed was 300 rev rain -1. Flocculant was added and, after the fibre suspension had been stirred for 10 s, samples were withdrawn using a wide pipette and transferred to the rheometer cell. In one set of experiments, the stirring time was varied between 10 s and 5 rain. The pipette used was a graduated 20 ml measuring pipette with 10 mm inner diameter. The tip was cut so that the diameter of the orifice was 7mm. After each measurement, the weight

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concentration of the samples in the rheometer cell was determined gravimetrically after drying. The rheometer was adjusted to a negligible torque during a period of 1 min after the sample was withdrawn from the flocculation jar and strain sweep or frequency sweep measurements were made after a further waiting period of 1 rain. If the zero adjustment could not be achieved within 1 min, this indicated that stresses remained in flocs or in the fibre network and the sample was discarded. All experiments were carried out at room temperature, 22 _+2°C. It was vital to keep all waiting times fixed and, of course, to prepare the sample in the same way each time. Using this procedure, the rheological measurements could be made with good repeatability. A withdrawn sample reflocculates and the rheological measurement gives the viscoelastic properties of this reflocculated structure. An alternative would be to add flocculants and to shear the flocculated suspension in the rheometer. This technique was not used because turbulent shear, which is the relevant hydrodynamic condition for papermaking suspensions, could not be applied to the suspensions in the rheometer used. The fibre concentration in the total sample varies between experiments and, to determine the exact amount of polymer on the fibres in the measured sample, the fibres remaining in the flocculation jar were filtered and weighed after being dried. A difference of +__5% from the desired level of added polymer was tolerated, otherwise the measurement was discarded. To obtain the elastic shear modulus as a function of added amount of polymer, curves of the elastic shear modulus G'o in the linear viscoelastic region vs. fibre concentration were first constructed. Values were interpolated at certain fibre concentrations and curves of G'o vs. amount of polymer plotted. A regression analysis of the fitted power functions to the experimental points of G'o vs. fibre concentration showed that the error due to interpolation of the interpolated values was about 10%. The coefficients of determination r z of the fitted curves were in the range 0.92-0.99. The sediment concentration csed of the softwood pulp fibres was determined by disintegration and deaeration of a 0.5 g 1-1 suspension. The suspen-

sion was poured into a graduated 1000 ml glass cylinder of 6 cm width. The suspension was stirred gently by a perforated circular plate and was then allowed to settle for about 16 h. The volume of the sediment was noted and the amount of fibres was determined gravimetrically after drying. Values reported are averages of three measurements. The water retention value, WRV, was calculated after determining the wet and dry weights of a fibre sample after centrifugation at 3000g for 15 min [17]. The polymer solutions were prepared at a concentration of 0.5 g 1 -1 after the dry polymer beads had been wetted with a few millilitres of ethanol and dissolved in deionized water during 2 h with magnetic stirring and left without stirring for 12 h. The solutions were stored in a refrigerator and used during a period of from 2 days up to 1 week after preparation.

3. Results The fibre concentration is here given as weight concentration, although the key variable for the formation of a fibre network is the volumetric concentration or the volume fraction. The weight concentration is used not only for convenience; it is the concentration measure normally used among papermakers. The volume fraction of cellulosic fibres is difficult to determine correctly because cellulosic fibres do not have a uniform length and shape, fibres have rough surfaces and fibres swell. However, in order to compare the present results with network models, a conversion to volume fibre concentration is needed. A relation between the weight concentration c and the volume concentration Cv has been derived by Bennington et al. [18]. According to this relation, Cv~2.1c for the softwood pulp fibres and cv~ 1.8c for the hardwood pulp fibres used in this study. 3.1. Effect o f straining frequency

Fig. 1 shows the elastic (G') and viscous (G") shear moduli together with the mechanical loss tangent, tan 6 (= G"/G') as a function of straining frequency (0.001-5 Hz) for softwood pulp fibre

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279~94 Shear modulus (Pa)

0.3 0.2

3.2. Effect o f straining amplitude

0.4

150

100

concentration. At this low amount of added C-PAM, all of the polymer was adsorbed onto the fibres and the viscosity of the surrounding solution was not affected by the added polymer. In the following, viscoelastic measurements were made at a straining frequency of 1 Hz.

tan 5 ,, 0.5

200

283

-

50

0

0.001

0.1

,

, ...... I

,

,,

..... I

,

I r ..... I

0.01 0.1 1 Straining frequency (Hz)

......

0

10

Fig. 1. Elastic shear modulus G'(©, • ) , viscous shear modulus, G" (;q, i), and mechanical loss tangent, tan 6 = G"/G' (A, A), as a function of oscillatory straining frequency for softwood pulp fibre suspensions at 6.7 g kg 1 concentration. Open symbols, without C-PAM; closed symbolswith addition of 0.5 mg C-PAM (DS=0.14) per gram of fibre. The oscillatory strain was 0.0005, i.e. in the linear viscoelastic region. suspensions of 6.7 g kg 1 concentration with and without the addition of a cationic polyacrylamide (degree of substitution (DS) 0.14, contact time 10 s). In these measurements, the strain was 0.0005. The low straining amplitude assured that the samples were strained in the linear viscoelastic regime. It is seen that in the frequency interval investigated, the elastic character increased with increasing straining frequency. The elastic character dominated and G' was an order of magnitude higher than G" at straining frequencies of 0.1 Hz and above. The shear modulus of the fibre network in a cellulosic fibre suspension according to the network model [1] is a function of the elastic modulus of the individual cellulosic fibres [19]. The viscous modulus was almost constant, independent of the straining frequency in the interval 0.001-5 Hz. The elastic modulus increased in the frequency interval investigated, hence the viscous character is more pronounced at low frequencies. The effect of a chemical flocculant on the shear moduli was large; both the elastic and the viscous modulus increased. Generally, the effect of chemicals appeared to be similar to an increase in fibre

Fig. 2 shows the elastic and viscous shear moduli and the mechanical loss tangent as a function of straining amplitude ~ for softwood pulp fibre suspensions of 6.9 g k g - t concentration with and without addition of 0.5 mg g-1 of a C-PAM (DS = 0.14, contact time 10s). This amount gave the greatest increase in shear strength for this particular C-PAM. The elasticity dominated at low strains, and there was a linear viscoelastic region in which the elastic modulus was independent of the strain. In these measurements, the linear region was rather short, because strains lower than 0.0002 could not be applied in the rheometer set-up used. With C-PAM added, the fibre network displayed a higher shear modulus: both the elastic and the

200

Shear modulus (Pa) ........ ' ........

150

--'.'......

,

tan 8 'zx . . . . . . . 1 A

08

"-...

,, OootA

100

-

AA~O0

~°°°oo~,

AA

0.4

.,~t..A

50

0 0.0001

-

........

I 0.001

0.6

....... I 0.01

........

0.2

0 0.1

Strain, ~,

Fig. 2. Elastic shear modulus, G' ( @,•), viscousshear modulus, G" (2q,i), and tan 5 (±, A) as a function of oscillatory strain for softwood pulp fibre suspensions at a concentration of 6.9 g kg 1. Open symbols, without C-PAM; closed symbols with addition of 0.5 mg C-PAM (DS = 0.14) per gram of fibre. The straining frequencywas 1.0 Hz. The horizontal lines denote the linear viscoelastic regions at low strain.

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A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294

viscous moduli increased. A critical strain °/c was observed above which G' started to decrease. The critical strain marks the onset of a structural breakage in the suspension and 7c was somewhat higher when C-PAM was added. It was previously shown [20] that non-linear effects in the viscoelasticity of cellulosic fibre suspensions appear above the critical strain. In the present investigation, the critical strain was evaluated as the strain at which G' had decreased to 90% of its value in the linear viscoelastic region. The plateau value of G' in this region is denoted. The critical strain was 0.0007 without C-PAM and 0.0009 with C-PAM. The effect of flocculant on the shear strength was also seen in the mechanical loss tangent, tan 6 (= G"/G'), which increased rapidly with increasing strain for the suspension without flocculant. Fibre suspensions yield much more easily if they are not flocculated by C-PAM.

70

Elastic shear modulus, G' (Pa) 0 , , , , , , ,

60

0 mg/g 0.5 mg/g

=

,/

/ el

•

_ /

40 30 20

....~J

..~"

-

10 0

I

1

2

3

4

5

6

Fibre concentration

(g/kg)

Fig. 3. Elastic shear modulus G~ (plateau value in the linear viscoelastic region) as a function of fibre concentration for softwood pulp fibre suspensions at different levels of addition of C-PAM (DS=0.14). Straining frequency 1.0 Hz.

3.3. Effect of added amount and charge density of cationic polyacrylamide High molecular weight charged polymers induce flocculation mainly by a bridging action. The degree of flocculation depends on the added amount and on the charge density of the polymer. These effects have been investigated for cellulosic fibre suspensions [21] where it was concluded that there is an optimum charge density for cationic polyacrylamides in the bridging flocculation of fibre suspensions. At a lower than optimum charge density there are probably too few polymer segments attached to the fibre surfaces, whereas at a higher than optimum charge density the interaction between polymer and surface sites is so strong that the polymer is adsorbed in a flat configuration. The effects of polymer charge density and added amount were investigated by measuring the fibre network strength. Fig. 3 shows G; as a function of softwood pulp fibre concentration at different levels of added C-PAM ( D S = 0 . 1 4 ) . G; increased strongly with increasing fibre concentration and power functions were fitted to the experimental points. The effect of C-PAM addition was large and depended on the added amount. At an addition of 2 mg g-~, the fibres have apparently been recharged by

adsorbed polymer. The flocculation, and hence the shear strength, decreased in relation to that achieved with 0.5 mg g-1. To evaluate results of experiments with C-PAMs of different DS, values were interpolated to a fibre concentration of 5 g k g -1. Fig. 4 gives the interpolated G; values as a function of added amount of C-PAM for different DS values. In the absence of C-PAM, G; was less than 30 Pa and increased to values of above 60 Pa when C-PAM was added. The maximum in the shear strength was found at different levels of addition depending on the DS. For the C-PAMs of higher charge density, there was a rather sharp maximum at 0.5 mg g-a. For the lower DS polymers, the maxima were more extended. The maximum shear strength reached was roughly independent of the DS but appeared to be highest for DS = 0.04. A high molecular weight C-PAM adsorbs only onto external fibre surfaces. Adsorption data [22] show that the adsorbed polymer charges of C-PAM corresponded to about 2% of the total charge of the fibre material when the adsorption time was 10 s and to about 4% of the total fibre charge at an adsorption time of 30 min. The shear conditions

A. Swerin / Colloids Surfaces A: Physicoehem. Eng. Aspects 133 (1998) 279-294

Elastic shear modulus, G' (Pa)

Threshold concentration, c* (g/kg)

0

801

,

,

j

,

285

,

,

4

'

I

I

I

'

I

I

DS=O.02

_ _ ~ DS=O.04 DS=O.14

60 3

"

DS=0.27

40

20

T

2

1

1

2

3

4

5

6

I

0

Added amount of C-PAM (mg/g)

,

I

1

,

I

,

I

,

I

,

I

,

I

2 3 4 5 6 Added amount of C-PAM (mg/g)

Fig. 4. Elastic shear modulus G; as a function of added amount of C-PAM for different DS levels for softwood pulp fibre suspensions. Straining frequency 1.0 Hz. Values interpolated to a fibre concentration of 5 g kg 1.

Fig. 5. Threshold concentration c* for measurable shear strength as a function of added amount of C-PAM of different DS for softwood pulp fibre suspensions. Straining frequency

using a propeller stirrer were about the same as in the present study. If flocculation occurs according to a bridging mechanism, a maximum in the shear strength should occur when a fraction of the surface charges on the fibres have been neutralized by adsorbed polymer charges. The amounts of added C-PAM charges at the maximum shear strength corresponded to 1-4% of the fibre charge, depending on the charge density of the C-PAM. These results are in agreement with results on the flocculation of fibre suspensions by C-PAMs of different charge densities [ 11,21,23]. It can be seen in Fig. 3 that there was a measurable shear strength at a lower fibre concentration when flocculant had been added. Wahren [ 1] found that the limiting fibre concentration for measurable shear strength coincided with the sediment concentration, i.e. the concentration in the sediment formed from a dilute fibre suspension which is left to sediment after disintegration. For the softwood pulp fibres used in the present study, the sediment concentration was 3.2 g 1-1. In Fig. 3, it is seen that G; is not quite zero at 3.2 g kg-a; an interpolated value is 8 Pa. This value of G; was chosen as the limit for measurable shear strength. Fig. 5 gives the threshold concentration c*, i.e. the fibre

concentration at a shear strength of 8 Pa, as a function of the added amount of C-PAM. The value for c* without C-PAM is the sediment concentration. The curves showed minima at different levels of addition depending on the DS of the C-PAM. There is a strong similarity with the results in Fig. 4 in this respect. When the shear strength is at a maximum, the threshold concentration is at a minimum. The critical strain was evaluated as the strain at which G' decreased to 90% of its plateau value in the linear viscoelastic region. Fig. 6 shows Vc as a function of added amount of C-PAM at two different DS levels. The critical strain Vo was found to be almost independent of fibre concentration; the arithmetic mean values with 95% confidence limits from measurements at different fibre concentrations are given in Fig. 6. The scatter was large, but the data indicated that there was a slight increase in Vc with increasing fibre flocculation by added C-PAM. An interpretation of Vc in relation to the fibre dimensions is given in the discussion below. Fig. 7 shows results for hardwood pulp fibre suspensions in experiments with and without the

1.0

Hz.

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294

286

Critical

strain

9

0.002

Threshold

~

fibre c o n c e n t r a t i o n , I

I

I

I

c* (g/kg) I

Hardwood pulp fibres 1 mg C-PAM/g -

8 0.0015

7 0.001 5

0.0005

4

0

1

2 3 4 5 6 Added amount of C-PAM (mg/g)

3

I

0

0.5

1

I

[

L

I

1

1.5

2

2.5

3

3.5

Added a m o u n t of C-PAM (mg/g) Fig. 6. Critical strain )'c as a function of added amount of C-PAM of different DS for softwood pulp fibre suspensions. Straining frequency 1.0 Hz.

Elastic shear modulus, G' (Pa) 0 i i J i i i 9,, Hardwood pulp fibres 100 [ \ ~ 10 g/kg 120

-

80

~

-

60 40

Fig. 8. Threshold concentration c* for measurable shear strength as a function of added a m o u n t of C-PAM of DS = 0.14 for hardwood pulp fibre suspensions. Straining frequency 1.0 Hz.

strength (1 mg g-1 of C-PAM). In the case of softwood pulp fibres the maximum occurred at 0.5 mg g-1 with the same C-PAM. The difference in behaviour can be attributed to the higher charge density of the hardwood pulp fibres. Fig. 8 shows the threshold concentration c* as a function of added amount of C-PAM. As with softwood pulp fibres, there was a minimum in c* which corresponds to the point of maximum shear strength.

20 3.4. o

_

0

Effect of turbulent shear

-

0.5

1 1.5 2 2.5 3 3.5 Added amount of C-PAM (mg/g)

Fig. 7. Elastic shear modulus G~ as a function of added a m o u n t of C-PAM of D S = 0 . 1 4 for hardwood pulp fibre suspensions. Straining frequency 1.0Hz. Values interpolated to fibre concentrations of 5 and 10 g kg -1.

addition of C-PAM (DS = 0.14, contact time 10 s). The hardwood pulp fibres are much shorter and no network was formed at 5 g kg 1. When C-PAM was added, the network had a slight shear strength but it was only about 25% of the shear strength in a softwood pulp fibre suspension at 5 g kg 1. At a fibre concentration of 10 g kg -1, there was a tenfold increase in G; at the maximum shear

During papermaking, the fibrous suspension flocculated by chemical additives, such as cationic polyacrylamide, is subjected to turbulent shear in e.g. pumps and pipe constrictions. To investigate the effect of turbulent shear on the rheological properties of flocculated fibre suspensions, samples were measured after a shearing at 300 rev min-1 in the dynamic drainage jar for different times before measurement. Fig. 9 shows the elastic modulus as a function of stirring time for softwood pulp fibre suspensions at concentrations of 5 g kg-1 and for hardwood pulp fibres at 5 and 10 g kg -1. The values given at zero stirring time are with no C-PAM added. The shear modulus decreased with increasing

A. Swerin / Colloids Surfaces A: Physieochem. Eng, Aspects 133 (1998) 279-294 Elastic shear modulus, G' (Pa) o

120

i

i

o

100

i

~ "~

.

~.

~--'CI

i

i

i

HW pulp fibres, 10 g/kg HW pulp fibres, 5 g/kg

I SW pulp fibres, 5 g/kg

80 60 40 20 0

--

E

0

50

~

I i--~-~-~l

100

150

I

i

[

I

|

]

200 250 300 350 Stirring time (s)

Fig. 9. G~ as a function of stirring time in turbulent shear for softwood (SW) and hardwood ( H W ) pulp fibre suspensions flocculated by C-PAM of DS=0.14. The added amounts of C-PAM were 0 . 5 m g g -1 for SW pulp fibres and 1 m g g i for H W pulp fibres. Points at zero stirring time are experiments without C-PAM added. Lines are fitted exponential functions. Straining frequency 1.0 Hz.

stirring time. The lines are exponential functions fitted to the experimental points. The decrease is due to the floc breakage by hydrodynamic shear. The effect of shear is related both to the initial network strength and to the ease with which broken flocs reflocculate to form a network structure.

4. Discussion

4.1. Rheological measurements offlocculated fibre suspensions The results of theological measurements on flocculated suspensions depend on the state of flocculation, and are thus affected by the shear history, sample handling and the rheometer set-up. This is mainly a result of the fact that flocculation by polymers gives a non-equilibrium structure. Direct comparisons between different investigations in which different measuring techniques have been used are, therefore, difficult. The experimental procedure used in the present study enables the viscoelastic properties of a reflocculated fibre sus-

287

pension to be measured. Cellulosic fibre suspensions form flocs (network fragments), even without the addition of a chemical flocculant, due to mechanical entanglement of the flexible cellulosic fibres. As the fibres are long enough to bridge the gap between the inner and outer cylinder in an ordinary Couette rheometer cell, the gap has to be increased. However, a compromise is necessary so that the approximation can be made that the shear is independent of the radial position and so that fairly high strains can be applied. Fibre suspensions under flow form a fibre-free region near a wall. To prevent this in the present study, the surfaces of the measuring cylinders were blasted to increase the surface roughness. However, the same results were obtained with smooth surfaces. The conclusion is that during these oscillatory measurements the shear is too small for wall-slip to occur. When a chemical flocculant was added, there was a certain adhesion of cellulosic fibres to the metal surfaces. To investigate whether this influenced the rheological measurements, the measuring surfaces were treated with Teflon spray. No fibres adhered to the Teflon-treated surfaces, but the same shear moduli values were obtained as with untreated surfaces. To verify further the effects of chemical flocculants on the rheological properties of fibre suspensions, an independent measuring technique was used. Measurements were made with a Pulse Shearometer [14, 15] (see also Section 2.2). These measurements give the high frequency limit of the elastic shear modulus G~. Fig. 10 shows Go~ as a function of fibre concentration with and without cationic polyacrylamide added. The scatter in the experimental points was high. One important reason for this was the difficulty of controlling the fibre concentration between the plates in the shearometer. The experiments clearly verified, however, that C-PAM increased the shear strength of the cellulosic fibre suspension. The increase in fibre network strength can be due to two main effects: an increase in the number of fibres which are active in the network, and an increase in the bonding strength in the fibre-fibre contact points. It was not possible in the present study to determine quantitatively the relative

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294

288

Shear modulus, G (Pa) 500 400

i

o •

i

no C-PAM C-PAM, 1 mg/g

300 0

200

0

100

•

0

0 0

0 7.5

O0 0

0

8 8.5 9 Fibre concentration (g/kg)

Fig. 10. The limiting shear modulus Go from pulse shearometry as a function of fibre concentration (O) with and (©) without the addition of C-PAM (DS=0.02).

importance of these two factors. The lower threshold concentration for a flocculated sample in the presence of C-PAM suggests that, in the low concentration regime below the sediment concentration, the increase in the number of active fibres must be important. At a somewhat higher fibre concentration, where the number of contact points per fibre is high, a contribution due to an increase in the bonding strength in the fibre-fibre contact points is very likely.

4.2. Influence of critical strain The critical strain increased when a fibre suspension was flocculated. The increase was rather small and the scatter in the values was high. The effect is related to the increase in the strength of the network as seen in Figs. 4 and 6. The influence on 7¢ of the fibre concentration and type of fibre was negligible. In rheological studies of other flocculated systems, silica suspensions [24] or kaolin clay suspensions [25], 7~ was found to decrease with increasing flocculation. We attribute the observed increase in 7c to an increase in the number of fibres that actively participate in the fibre network. This implies that, with increasing flocculation, a larger number of contact points per

fibre has to be broken in order to break the network. In an earlier investigation [20], 7° was found to be almost independent of fibre concentration in the interval of 30 80 g kg 1. In that study [20] ~/c corresponded to straining amplitudes of 25-45 gm. In the present study a different way of evaluating 7o was used so that the values are somewhat lower; but, if the same procedure was used [ 11 ] "/c was in the range of 20-35 lam. When the fibre network is strained to the critical strain, the network starts to disrupt because fibre-fibre contact points are disconnected due to the shear applied. The distance required to disrupt a fibre-fibre contact is probably a function of the shortest dimension of the fibre, i.e. the fibre width. As seen from Table 1, fibre widths for softwood and hardwood pulp fibres are almost the same, i.e. 24 gm for softwood and 20 tam for hardwood pulp fibres. This is probably why no significant difference was found between the different types of fibre.

4.3. Influence of hydrodynamic shear The influence of hydrodynamic shear on the shear strength of cellulosic fibre suspensions flocculated by cationic polyacrylamide has not been investigated in detail. Fig. 9 gives some experimental results, showing that there is an exponential decay in the shear strength with increasing stirring time. When flocs are first formed, many adsorbed polymers are locked in a looped configuration giving a strong bridging flocculation. When flocs are broken, adsorbed polymers have the opportunity to reconform towards a flatter configuration on the fibre surfaces. When flocs are reformed after shear deflocculation, a smaller number of bridging polymer chains are available [26,27]. The bridging capability is, therefore, reduced and the re-formed fibre network is weaker. Polymer chains may also be broken during floc breakage [28-30], and this limits the possibility of reflocculation by bridging. The relative importance of shear strength due to mechanical entanglement and due to bridging flocculation is likely to depend on the type of fibre. At a fibre concentration of 5 g kg- 1, the softwood pulp fibre suspension has a certain shear strength

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294

due to both mechanical entanglement and bridging flocculation, whereas the hardwood pulp fibre suspension showed some shear strength only because of bridging flocculation. The bridging flocculation was rather easily disrupted, and the degree of reflocculation was lower because of the reduced bridging ability after floc breakage. The degree of reflocculation due to mechanical entanglement is high and it is not affected by the adsorption kinetics. This explains the slow decay for the softwood pulp fibre suspension. In the case of the hardwood pulp fibre suspension, there seemed to be a slower decay in the shear strength at high fibre concentration; this was possibly because a larger number of fibre-fibre contact points, formed by the addition of flocculant, have to be broken at the higher fibre concentration. It should also be possible to scale the influence of shear on the fibre network strength; see below. The experimental data in the present study, however, are too few to allow a detailed analysis. The type of shear and the shear intensity should, of course, also be better controlled if it is desired for quantitative studies. 4.4. Scaling relationship Power functions for the elastic shear modulus as a function of fibre concentration were found to give a good fit to the experimental data, in agreement with results from other researchers [18,31], i.e. G'o =ac b

(1)

A total of 26 curves of G~ as a function of fibre concentration for different added amounts of C-PAMs of different DS were fitted to Eq. (1). The exponent b was fairly constant, b = 2.2 + 0.19, while the value of a depended on the added amount of C-PAM. Thal6n and Wahren [31] also arrived at an exponent of 2.2 in rheological measurements using different types of papermaking fibres. A more general relation, giving a better fit, is given by G=a(c-e*) b

(2)

where G is the shear modulus, c the fibre concentration, c* the threshold concentration for measurable shear strength and a and b are constants. The

289

Elastic shear modulus, G' (Pa) 200

o

i

[

i

I

[

i

SW pulp fibres C-PAM, DS=O.14

[]

150 0

100

0~

O0

•

50

o ~--9 ~°'0 1

' 2

I

I

I

I

3

4

5

6

c-c*

7

(g/kg)

Fig. 11. Elastic shear modulus G6 as a function of the fibre concentration in excess of the threshold concentration, c-c*, for softwood pulp fibre suspensions at different amounts of added C-PAM of DS=0.14: © = 0 ; 0=0.05; D=0.1; • =0.25; A =0.5; • =0.75; ~ = 1.0; ~ =2.0; Q = 3 . 0 m g g -~.

threshold concentration depends on the fibre dimensions. Shorter fibres have a higher c*. The threshold concentration also depended on the addition of chemical flocculants. When the experimental points were plotted according to Eq. (2), all the curves coincided within the experimental error, and a value of b = 1.6 gave the best fit (coefficient of determination, r2=0.96). As an example, Fig. 11 shows G; as a function of ( c - c * ) for softwood pulp fibre suspensions at different levels of added C-PAM of DS = 0.14. In order to obtain a zero value for the shear modulus at zero fibre concentration, the G~ value at the sediment concentration was here subtracted from the G; values (8 Pa for the softwood pulp fibres). It should also be possible to scale the influence of the type of fibre. The shear modulus of a fibre network depends on the fibre length, but nonadditive effects on the shear strength have been found when fibres of different fibre lengths are mixed [32]. This indicates that the fibre length distribution is also important. In a semi-empirical formula [33] based on experiments on different types of fibre and on a mathematical model for the shear strength of fibre networks [34], there is

A. Swerin/ ColloidsSurfacesA: Physicochem.Eng. Aspects133 (1998) 279-294

290

concentration for network formation thus defined [34] can be calculated from the expression

Elastic shear modulus, G' (Pa) o

120

'o SW pulp fibres e_ HiWePUlPcufibres

100

'

o'/o'

16nL

/

Cv =

(4)

[2L/nd + n/(n + 1)]3 (n - 1) d

80 60 40 20

o~o

~ ~"~,

0 0

o

~

i

0.0002

I

r

,

0.0005 0.0007 ~LW(Lw/L )(c-c*)

Fig. 12. Elastic shear modulus G6 as a function of the quantity

~w([w/E,)(c-e* ) for softwood (SW) and hardwood (HW) pulp fibre suspensions. The fitted curve has a proportionality constant, kl = 1.47 x 1 0 9 and an exponent k2=2.2. The G6value at the sediment concentration, 8 Pa and 5 Pa for the SW and HW pulp fibres respectively, was subtracted from the values. a square-root dependence on the weight-average fibre length /2w and a linear dependence on the width of the fibre length distribution given by Lw/Ln. In accordance with this, Eq. (2) would become G; = kx ~ww (Ew//~n) (C -- C*)k2

(3)

Fig. 12 shows the data for softwood and hardwood pulp fibres plotted according to Eq. (3). The fibre concentration is in this case given as a weight fraction. The fitted curve had a proportionality factor kx = 1.47 x 10 9 and an exponent k 2 =2.2.

4.5. Number of contaet points between fibres In a mathematical model presented by Meyer and Wahren [34] for the calculation of the shear modulus at small deformations, the network strength is a function of the volumetric fibre concentration. Furthermore, the fibre length-todiameter ratio was shown to be the primary parameter determining the threshold concentration. According to the model, for networks formed only due to mechanical entanglement, three contact points between four fibres are enough for a continuous network to be built up. The threshold

where cv is the volumetric fibre concentration, L/m the average fibre length, n the number of contact points per fibre and dim the average fibre diameter. For fibres with a large length-to-diameter ratio, n/(n+l)<
1 +Xw(pf/pw) Cv =

(5)

1 + [( 1 -- c)/c](pf/pw)

where xw/kg HzO/kg fibre is the degree of fibre swelling, pf/kg m -3 the fibre density (a value of 1500 is used) and pw/kg m -3 the density of water. For network formation by mechanical entanglement, a minimum of n = 3 is required, whereas the lowest number of contact points to give an interconnected fibre network is n = 2. Table 2 gives values of c* according to Eqs. (4) and (5). When the calculated values are compared with the experimental results, the agreement is quite satisfactory for the softwood pulp fibres. The sediment concentration, csed=3.2gl 1, is the threshold concentration for mechanical entanglement, and the data in Fig. 5 give a c * ~ 1.8 g kg -1 when C-PAM is added as flocculant.

Table 2 Calculated threshold fibre concentration c* for different numbers of contact points per fibre according to the Meyer and Wahren network model [34] Type of fibre

Softwood pulp Hardwood pulp

Calculated threshold concentration, c* (g kg-1) n=3

n=2

2.9 21

1.8 13

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294

For the shorter hardwood pulp fibres, the calculated values are much too high, since csed= 8.8 g 1 1, and the minimum c* when C-PAM is added is about 2.3 g kg -1 (Fig. 8). Another way of calculating the number of contact points in a fibre assembly has been derived by Komori and Makishima [35]. For random threedimensional networks their expression reduces to

gations on the fibre flocculation by chemical flocculants. The possibility of using site percolation theory to describe mechanical entanglement and bond percolation theory to describe bridging flocculation was investigated, see Appendix A.

Acknowledgment

(6)

n = ~zdNfL2/2

where Nf is the number of fibres per unit volume and L is the fibre length. Nf can be calculated from the coarseness value [36] and Eq. (6) can be expressed as a function of the fibre concentration: n : ~ d E 2 c/2 C L

291

n

The author is indebted to Ms. G. Risinger for skilful experimental assistance and to Professor L. Odberg for valuable comments on the manuscript. Dr. J.A. Bristow kindly made a linguistic revision of the manuscript.

(7)

where /~,l is the length-weighted average fibre length, Cling m-1 is the coarseness and/7, n is the number average fibre length. Eq. (4) gives a square-root dependence of n on c, whereas Eq. (7) gives a linear dependence. For softwood pulp fibres, Eqs. (4) and (7) gave almost the same results, but Eq. (7) gave lower values than Eq. (4) for hardwood pulp fibres, c * = 8 g kg -1 for n = 2 and c* = 12 g kg- x for n = 3. To shed some light on whether a linear or a square-root dependence is correct, results from computer simulations of three-dimensional fibre flocs according to a ballistic growth model [37] can be used [38]. Flocs with randomly distributed fibres of uniform length were generated with two to four contact points per fibre. The floc density (grams per litre) showed a square-root dependence on n. At 2 mm fibre length, n = 3 corresponded to 3gl -landn=2to 1.9gl -1

5. Conclusions The shear strength in a cellulosic fibre suspension is increased by the addition of a high molecular weight cationic polyacrylamide. This increase in shear strength is a combination of an increase in the number of active fibres in the network and an increase in the binding strength in the contact points between fibres. The infuence of cationic polyacrylamide flocculants on the rheological properties is in agreement with results from investi-

Appendix A. Percolation behaviour in pulp fibre suspensions In this appendix, an attempt is made to understand fibre network strength in cellulosic fibre suspensions in relation to a percolation theory. There is a threshold value of fibre concentration above which a measurable elastic shear strength appears. At higher concentrations, the fibre suspension is capable of taking up load and transmitting shear stress through the sample. In order for this to occur, an interconnected network must span the sample. A fibre network thus shows an elastic percolation behaviour. In the absence of flocculant, mechanical frictional forces between fibres gives an interlocking effect and, for this mechanism, three contact points per fibre are required. When a flocculant is added, the threshold is at a lower fibre concentration. This should mean that the average number of contact points per fibre is less than three. The effect of chemical flocculants can be scaled using the limit for measurable shear strength as the percolation threshold. It is also suggested that the effect of type of fibre, i.e. fibre length, shows a scaling behaviour. In the percolation theory, percolation can be related to either bond or site probability, pb or pg respectively [39]. The probability of a site or a bond occurring is proportional to a measurable quantity Q and for the elastic modulus can be

292

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 2 7 9 - 2 9 4

written as G%c ( Q - Q¢)Y

t "

(8)

where Qo is the value of the quantity at the percolation threshold. If fibres are chains of an infinite network, bond percolation is appropriate. In this case, for any two bonds belonging to the network, it is possible to find a path between them only by passing over occupied bonds. One example is conductivity in a lattice consisting of conducting bonds. On the other hand, site percolation is appropriate if fibres are connected into a network where, for any two sites belonging to the network, they are connected if a path between them does not pass through an absent site. An example of site percolation is gel elasticity. The exponent f depends on the type of percolation, and values given in the literature show higher values for site percolation, than for bond percolation, f ~ 1.8 [4]. We now make an attempt to apply a site/bond percolation concept to a fibre suspension in a manner similar to that which has been used for flocculation in silica suspensions [40,41]. The site probability p~ is the probability for a contact point between fibres, and is proportional to the weight fraction of fibres in the suspension. The bond probability pb is proportional to the degree of flocculation induced by added flocculant. The assumption was made that fibre network formation in the absence of flocculant corresponds to a site percolation and that bridging flocculation can be described by a bond percolation. A change in the exponent f should thus accompany the increased bridging. To model the bridging, the mechanism of interparticle bridging [42] was used. The flocculation efficiency is, according to the bridging mechanism, a function of 0 ( 1 - 0 ) , where 0 is the fractional surface coverage of a fibre. A minimum in the percolation threshold should occur at the optimum ftocculant dosage, i.e. at a fractional surface coverage of 0=0.5. The situation is illustrated as a two-dimensional phase diagram in Fig. 13. The line is the percolation threshold, which corresponds to n =3 without bridging flocculant. With increased bridging, the percolation threshold decreases and passes through a minimum at 0 = 0.5. This point corresponds to n = 2 . For a cellu-

'

I

'

I

E 0.8 O

.~0.6 O) 0.4

-

> O o

¢~ 0.2 cO

~_ o~

no p,erco

percolation

0

'

1

2

3

]

4

'

5

No. of contact points per fibre, n Fig. 13. Percolation threshold line as a function of the fractional surface coverage 0 by bridging polymer, and the number of contact points per fibre n.

losic fibre suspension, the percolation behaviour is probably not purely site or bond percolation because fibre flocs are also formed without added flocculant. Flocs can be the units that build up a network instead of individual fibres. This implies that the system percolates when flocs are connected and not when individual fibres connect. An analysis of flocculated suspensions of anisotropic magnetic particles according to floc percolation has been made by Kanai et al. [4]. To use this approach, values of the floc density are needed. These data were not available for our system. The analysis given in the present study is a first approximation. A theoretical analysis of the transition from site to bond percolation has been given by Mall and Russel [43]. The position of the percolation threshold line in Fig. 13 as a function of fibre concentration depends on the fibre dimensions. The number of contact points per fibre is related to the volumetric fibre concentration cv according to Eq. (4). Fig. 14 shows the percolation phase diagram when the length-to-diameter ratios of softwood and hardwood pulp fibres are inserted in Eqs. (4) and (5) to give c. The experimental results in Figs. 5 and 8, giving the threshold fibre concentration c* for measurable shear strength as a function of added amount of C-PAM, are replotted in Fig. 15 to permit a corn-

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294 ~ l , , , , i , ~ ,

I

, , , ,

1/~

,,

f

E 0.8

f

/ /

O

/

~>" 0.6

I f I

> O c.9 (.~

o~

0.4

\ \ \

0.2

0 5 10 15 20 25 Calc. fibre concentration, c (g/kg)

Fig. 14. Percolation threshold lines as a function of the fractional surface coverage 0 by bridging polymer, and the calculated fibre concentration c for fibres of different length-todiameter ratios: ( ) L/d=ll7 for softwood pulp fibres; G ) L/d=46 for hardwood pulp fibres.

1

m

I

I

I

I

I

I

<

0_

d 0.8

E 0.6 O

E "O

0.4

293

the fibre charges into account, corresponded to 100% fibre coverage. The percolation thresholds are quite different, depending on the aspect ratio o f the fibres and on the added a m o u n t o f bridging flocculant, as predicted in Fig. 14. For the softw o o d pulp fibres flocculated by C - P A M s o f different DS, the curves almost overlapped. The experimental results in Fig. 15 show a qualitative agreement with the percolation diagram in Fig. 14. The analysis o f flocculated fibre suspensions according to the percolation theory indicates a similarity between flocculated fibre suspensions and other flocculated systems. However, regimes with different exponents in the scaling relations depending u p o n the type o f flocculation (mechanical entanglement or polymer-induced) were not observed. This is in contrast to studies o f other flocculated systems [4]. It is possible that this is due to our simplified a p p r o a c h o f applying percolation to fibre contact points instead o f taking into account the percolation t h r o u g h the contact points between flocs o f fibres. It is also possible that the fibre concentration interval investigated here is too n a r r o w to allow a complete site/bond analysis. A n extension o f this investigation to higher fibre concentrations is needed.

!

~ 0.2

References

0

z

0

l

1

2

3

4 5 6 7 8 9 Fibre concentration, c (g/kg)

Fig. 15. Experimental percolation threshold lines as a function of normalised amount of C-PAM (added amount of polymer/maximum added amount for the fibre-C-PAM combination) and fibre concentration. Softwood and hardwood pulp fibre suspensions and C-PAMs of different DS. Softwood pulp fibres, DS of C-PAM: Q =0.02, 0=0.04, [~ =0.14, 11=0.27. Hardwood pulp fibres, DS of C-PAM: A =0.14. parison. C - P A M gives a m a x i m u m effect on c* depending on the charge density. Furthermore, the h a r d w o o d pulp fibres have a higher charge density than softwood pulp fibres. To normalise the added a m o u n t o f flocculant, it was assumed that the highest a m o u n t added, which was chosen by taking

[ 1] D. Wahren, On three-dimensional fibre networks, Doctoral Thesis, KTH, Stockholm, 1964. [2] D. Wahren, Proc. Conf. in Paper Science and Technology The Cutting Edge, Institute of Paper Chemistry, Appleton, USA, 1979, p. 112. [3] R. Ritala, M. Huiku, in: C.F. Baker, V.W. Punton (Eds.), Fundamentals of Papermaking, Trans. Ninth Fundam. Res. Symp., Cambridge, Mech. Publ. Eng. Publ. Ltd., London, 1989, p. 195. [4] H. Kanai, R.C. Navarrete, C.W. Macosko, L.E. Scriven, Rheol. Acta 31 (1992) 333. [5] A.A. Ogale, S.F. Wang, Compos. Sci. Technol. 46 (1993) 379. [6] S.F. Wang, A.A. Ogale, Compos. Sci. Technol. 46 (1993) 389. [7]C. Bjellfors, K.-E. Eriksson, F. Johansson, Sven. Papperstidn. 68 (24) (1965) 865. [8] M.Y. Chang, A.A. Robertson, Pulp Pap. Mag. Can. 68 (1967) T438. [9] E. Poppel, in: Rheologie und Elektrokinetische Vorg~inge

294

A. Swerin / Colloids Surfaces A: Physicochem. Eng. Aspects 133 (1998) 279-294

in der Papiertechnologie, VEB Fachbuchverlag, Leipzig, 1977, p. 80. [10] E. Poppel, S. Ciovica, N. Ghiurco, Zellst. Pap. 39 (5/6) (1990) 21. [11] A. Swerin, L. Odberg, Nord. Pulp Pap. Res. J. 8 (1) (1993) 141. [12] S. Katz, R.P. Beatson, A.M. Scallan, Sven. Papperstidn. 87 (6) (1984) R48. [13] A. Swerin, L. Wgtgberg, Nord. Pulp Pap. Res. J. 9 (1) (1994) 18. [14] J.W. Goodwin, A.M. Khidher, in: M. Kerker (Ed.), Colloid and Interface Science, vol. 4, Academic Press, New York, 1976, p. 529. [15] R. Buscall, Colloids Surf. 5 (1982) 269. [16] K.W. Britt, Tappi 56 (3) (1973) 83. [17] T. Lindstr6m, in: J.A. Bristow, P. Kolseth (Eds.), Paper Structure and Properties, Marcel Dekker, New York, 1986, p. 75. [18]C.P.J. Bennington, R.J. Kerekes, J.R. Grace, Can. J. Chem. Eng. 68 (1990) 748. [19] J. Bergman, N. Takamura, Sven. Papperstidn. 68 (20) (1965) 703. [20] A. Swerin, R.L. Powell, L. Odberg, Nord. Pulp Pap. Res. J. 7 (3) (1992) 126. [21] L. W~gberg, T. Lindstr6m, Nord. Pulp Pap. Res. J. 2 (4) (1987) 152. [22] L. Wgtgberg, L. Odberg, T. Lindstr6m, R. Aksberg, J. Colloid Interface Sci. 123 (1) (1988) 287. [23] A. Swerin, U. Sj6din, L. Odberg, Nord. Pulp Pap. Res. J. 8 (4) (1993) 389. [24] Y. Otsubo, K. Watanabe, Colloids Surf. 41 (1989) 303. [25] U. Eriksson, L. J~irnstr6m, G. Engstr6m, M. Rigdahl, in: J. Weigl (Ed.), PTS-Streicherei-Symposium 1991, Manchen, Germany, Deutscher Fachverlag GmbH, 1991, p. 97.

[26] J.E. Unbehend, Tappi 59 (10) (1976) 74. [27] L. Wggberg, L. ()dberg, G. Glad-Nordmark, in: C.F. Baker, V.W. Punton (Eds.), Fundamentals of Papermaking, Trans. Ninth Fundam. Res. Symp., Cambridge, Mech. Eng. Publ. Ltd, London, 1989, p. 413. [28] M.D. Sikora, R.A. Stratton, Tappi 64 (11) (1981) 97. [29] H. Tanaka, A. Swerin, L. Odberg, J. Colloid Interface Sci. 153 (1) (1992) 13. [30] L. Odberg, H. Tanaka, A. Swerin, Nord. Pulp Pap. Res. J. 8 (1) (1993) 6. [31] N. Thal6n, D. Wahren, Sven. Papperstidn. 67 (7) (1964) 259. [32] N. Thaldn, D. Wahren, Sven. Papperstidn. 71 (20) (1968) 744. [33] K.E. Almin, P. Biel, D. Wahren, Sven. Papperstidn. 70 (22) (1967) 772. [34] R. Meyer, D. Wahren, Sven. Papperstidn. 67 (10) (1964) 432. [35] T. Komori, K. Makishima, Textile Res. J. 47 ( 1) (1977) 13. [36] Kajaani FS-200 Manual, Kajaani Electronics, Finland. [37] P. Meakin, Adv. Colloid Interface Sci. 28 (1988) 249. [38] U. Sj6din, in: Theoretical modelling and simulation in colloid and interface science, Bristol, April 18 20, Royal Society of Chemistry--Faraday Division, Colloid and Interface Science Group, 1994. [39] A. Hansen, in: H.J. Herrman, S. Roux (Eds.), Statistical Models for the Fracture of Disordered Media, NorthHolland/Elsevier, Amsterdam, 1990, p. 119. [40] Y. Otsubo, K. Watanabe, J. Colloid Interface Sci. 127 (1) (1989) 214. [41] Y. Otsubo, Langmuir 6 (1) (1990) 114. [42] V.K. La Mer, T.W. Healy, Rev. Pure Appl. Chem. 13 (1963) 112. [43] S. Mall, W.B. Russel, J. Rheol. 31 (8) (1987) 651.