dynamics of polymer-induced hetero-flocculation of wood fibres and fines

Colloids and Surfaces

A: Physicochemical and Engineering Aspects 174 (2000) 297–306

Dynamics of polymer-induced hetero-flocculation of woodfibres and fines

Tom Asselman, Gil Garnier *Department of Chemical Engineering and Paprican, Pulp and Paper Research Centre, McGill Uni6ersity, 3420 Uni6ersity Street,

Montreal, Quebec, Canada H3A 2A7

Received 30 August 1999; accepted 27 April 2000

Abstract

The kinetics of polymer-induced hetero-flocculation of wood fibres and fines was investigated. A polymer layer(cationic poly(acrylamide)) was deposited on either the fibres or the fines, and the fines concentration was followedafter mixing both components. It is shown that the flocculation state is only transient. This is explained by aredistribution of polymer between surfaces upon particle detachment, which leads to a re-stabilisation of the system.Simultaneous particle deposition, particle detachment and polymer transfer determine the apparent particle detach-ment rate. The detachment rate is strongly shear-dependent, and the resulting polymer layers after redistribution havea reduced bridging ability compared to the fresh layers. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Hetero-flocculation; Cationic poly(acrylamide); Polymer transfer; Flocculation dynamics

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1. Introduction

Polymeric flocculants are widely used in manyindustrial processes. These are typically high molec-ular weight neutral polymers, such as poly(ethyle-neoxide) (PEO), or polyelectrolytes, such aspoly(acryamide) (PAM) and poly(ethyleneimine)(PEI). High molecular weight water-soluble poly-mers are also extensively used in papermaking toimprove the retention of several process colloidsinto the wet paper-web, which eventually becomesthe paper sheet. These colloids mainly consist of

fibre fragments called fines, inorganic filler particles(CaCO3, TiO2) and polymer-stabilised hydropho-bic waxes (size); they are highly valuable as theygovern the paper properties and the process eco-nomics. The retention efficiency of these colloids istypically of the order of 10%; addition of thesewater-soluble polymers–referred to as retentionaids–can increase this efficiency by a factor of 5–8.This study is focused on wood fines.

Newsprint is typically made entirely of a mechan-ically produced pulp, which consists of about 30%fines. These fines are crucial as they increase boththe opacity and the mechanical strength of thepaper sheet. A sound understanding of the mecha-nism of wood fibres and fines co-flocculation istherefore vital for the paper industry.

* Corresponding author. Tel.: +1-514-3981367; fax: +1-514-3988254.

E-mail address: [email protected] (G. Garnier).

0927-7757/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S0927 -7757 (00 )00626 -9

T. Asselman, G. Garnier / Colloids and Surfaces A: Physicochem. Eng. Aspects 174 (2000) 297–306298

An adsorbing polymer can promote floccula-tion in two ways: it can locally alter the charge orit can link two surfaces by forming a ‘bridge’. Thedynamics of this bridging flocculation process israther complex, since several phenomena occurconcurrently and sequentially [1]. At first, thepolymer adsorbs on the solid surface in its solu-tion state. This is a very rapid process that occurs,for common shear rates, on a time scale of ap-proximately 0.1 s [2,3]. Depending on the surfacecoverage, the polymer then tends to adopt a flat-ter configuration on the surface [4,5], while thenumber of bonds increases and its layer thicknessdecreases. This process can take place within sec-onds. Meanwhile, the adsorbed polymer chain cancollide with another surface and adsorb onceagain, forming a bridge. This bridging mechanismcan only take place if the polymer coil protrudessufficiently far from the surface to overcome elec-trostatic repulsion forces between the two sur-faces. Stated otherwise, the polymerhydrodynamic layer thickness should be higherthan the Debye length to allow bridging [6]. Poly-mer transfer between the two surfaces [7–9] canalso occur. This transfer process takes place attime scales ranging from seconds to minutes. Ulti-mately, a polyelectrolyte will be distributed be-tween the surfaces in proportion to the surfacecharge. The transferred polymer layer was re-ported to be of a lower molecular weight than theoriginal one, indicating the preferential transfer ofsmall chains, or the cleavage of the polymer chainduring break up of the aggregate [10]. When anexcess of polydisperse polymer is available in so-lution, small adsorbed chains are exchanged forthermodynamically more favourable larger chains[11–13], on a time scale of hours to days. Woodfibres being a porous material, polymer chains candiffuse inside the pores and cover the internalsurfaces to some extent, depending on the coilsize, affinity and time scale [14].

There are numerous studies on the use of poly-meric flocculants in papermaking suspensions.Most deal with the homo-flocculation of fibres orfines, at short time scales. The present study aimsat elucidating the hetero-flocculation mechanismof wood fibres and fines using a bridging polymer.The objective is to investigate the flocculation

kinetics as a function of shear, polymer adsorp-tion time and type of flocculation. A typical me-chanical pulp was separated into a fibre fractionand a fines fraction. One fraction was fully cov-ered with a cationic poly(acrylamide) copolymer(PAM) and mixed with the other fraction. Theflocculation kinetics was followed by the finesconcentration in the supernatant.

2. Experimental

Dried unbleached thermo-mechanical pulp(Black Spruce) was soaked for 24 h and disinte-grated. The pulp was separated over a 200-meshscreen, resulting in a long fibre fraction and afines suspension (float-wash apparatus). Acationic poly(acrylamide) (Allied Colloids, Percol292) with medium molecular weight (:5×106)and a degree of substitution of 25% was used asreceived. Solutions of 1 g l−1 were prepared byfirst wetting the polymer with 5 ml g−1 of ethanoland mixing with de-ionised water. This stock solu-tion was stirred for 30 min before mixing withfibres or fines.

Full polymer coverage on the fibres wasachieved by stirring these in a polymer solutionfor 5 min at a ratio of 50 mg of polymer per gramof fibre. The suspension was then filtered over a200-mesh screen, and the fibres were washed twicewith distilled water in order to remove the excesspolymer. When required, fines were covered byadding 100 mg of polymer per gram of fines andstirred for 5 min. The suspension was then cen-trifuged for 5 min at 4000 rpm, and the superna-tant was discarded. The fines were re-diluted andthe separation process was repeated twice.

The hetero-flocculation kinetics was studied byadding fibres to a stirred fines suspension (pH:6.5) in distilled water. In these experiments, one ofthe two components was previously fully coatedwith polymer according to the procedure de-scribed above. Since all excess polymer waswashed off, no polymer is present in solutionduring the experiment. The fines concentrationwas determined by continuously pumping a finesflow via a 200-mesh filter using a peristaltic pumpthrough a spectrophotometer cell (Varian CARY

T. Asselman, G. Garnier / Colloids and Surfaces A: Physicochem. Eng. Aspects 174 (2000) 297–306 299

1E UV/VIS spectrophotometer), measuring theabsorbance at 300 nm. The experimental set-up isillustrated in Fig. 1. The ‘standard experiment’consisted of mixing 2 g of fibres with 0.28 g offines at a stirring rate of 200 rpm. The elec-trophoretic mobility of fines was measured in aRank Bros particle electrophoresis apparatus(Cambridge, UK) equipped with a flat cell.

The effect of polymer adsorption and relax-ation time on the flocculation kinetics was studiedin two types of experiments. In the first, fibreswere coated in an excess polymer solution forperiods ranging from 10 s to 1 h. In the second,fibres were first mixed for 5 min with polymer.The excess polymer was then washed off, and theadsorbed layer on the fibres were allowed to relaxand rearrange in distilled water for periods up to1 h. The standard experiment was then performedwith these fibres.

Reproducible modified polymer layers, referredto as ‘depleted’ and ‘transferred’, were preparedon fibres and fines as follows. The standard exper-iment was first carried out with fibres coatedaccording to the procedure described above,which were mixed with bare fines. After 40 min,once the system was completely re-stabilised, thefines were separated again from the fibres. Theresulting fines fraction is denoted as [fines+ trans-ferred], indicating that a polymer layer was trans-ferred onto their surface. The resulting fibrefraction is denoted as [fibres+depleted], whichimplies that polymer is transferred from this pre-viously fully coated surface. The standard experi-ment was carried out also with polymer-coated

fines according to the same procedure. This re-sulted in a fibre fraction coated with a transferredlayer, denoted as [fibre+ transferred] and a finesfraction coated with a depleted layer, denoted as[fines+depleted]. These four fractions were sta-ble. In a second step, each of those four coatedfractions were individually mixed with their barecounterpart, according to the conditions in thestandard experiment.

3. Theory

The collision rate J (m3 s)−1 between twofamilies of particles i and j is given by:

J=k1ni nj (1)

with k1 the collision rate constant (m3 s−1), whileni and nj represent the number concentrations ofspecies i and j (m−3), respectively. For shear-in-duced collisions, the collision rate constant can becalculated from the Smoluchowski theory:

k1=1/6 G(di+dj)3 (2)

with G the shear rate (s−1), while di and dj are theequivalent spherical particle diameters (m). Thehetero-flocculation rate, or initial deposition ratein the case of a mixture of a small particle familyi and a large particle family j then becomes:

dni

dt= −ak1ni nj (3)

with a the capture efficiency. Eq. (3) is only validfor low particle coverage on family j. As thecoverage increases, both the reduced availablespace on particle family j and the detachment ratehave to be taken into account. The depositionkinetics can be described by the Langmuir equa-tion, where the particle coverage of i on j isexpressed by [15]:

du

dt=ak1nj(n0−u)(1−u)−k2u (4)

with u the surface coverage of i on j, k2 thedetachment rate constant (s−1) and n0 the ratio ofavailable particles of family i compared to themaximum coverage on family j, given by:

Fig. 1. Experimental set-up. It consists of a beaker, stirrer,filter, pump and spectrophotometer.


Fig. 2. Typical fines concentration curve.

at a stirring rate of 200 rpm. According to Eq. (1),the deposition rate constant can be derived fromthe following expression:

katt=J0

CFC0, f

(6)

with C0, f the initial fines concentration (g l−1), CF

the fibre concentration (g l−1) and katt the deposi-tion rate constant (l g−1 min−1). J0 is the initialdeposition rate (g min−1 l−1) defined as:

J0= −�dCf

dtn

t=0

(7)

with Cf the fines concentration (g l−1). J0 can bedetermined from the initial slope of the finesconcentration drop. This apparent deposition rateconstant relates to the theoretical collision rate asfollows:

katt=ak1nF

CF

(8)

with nF the number fibre concentration (m−3). Byfitting the concentration curve to an exponentialfunction (first order kinetics) after the minimum,an apparent detachment rate constant can bedefined as follows:

Cf=C0, f(1−e−kdett) (9)

with kdet the apparent detachment rate constant(min−1).

This transient hetero-flocculation phenomenonwas reported previously for the flocculation offibres using PAM [16], with approximately thesame time scales as the ones observed here. Thisattachment–detachment sequence was observedfor several polymers, such as PAM, PEI andPEO-cofactor systems. The influence of polymerchemistry on the flocculation dynamics is dis-cussed elsewhere [17].

4.2. Initial deposition

The effect of fibre concentration on the deposi-tion rate J0, for the hetero-flocculation of poly-mer-coated fibres with bare fines, is shown in Fig.3. The observed linear relation is predicted by Eq.(3). From Eq. (2), we can estimate a theoreticalcollision rate constant (k1). Assuming a fibre

Fig. 3. Influence of fibre concentration (g l−1) on the apparentdeposition rate J0 (g l−1.min). PAM-coated fibres, stirring rate200 rpm. Bare fines (0.28 g l−1).

n0=n0, i

Gmaxnj

(5)

with n0, i the initial concentration of family i(m−3) and Gmax the maximal coverage of family ion family j.

4. Results and discussion

4.1. Characterisation of the flocculation kinetics

Fig. 2 shows a typical fines concentration curveas a function of time, after mixing polymer-cov-ered fibres with fines. After an initial drop, thefines concentration in solution slowly rises againto the initial level. This typically takes 5–10 min


length of 2 mm and a diameter of 30 mm, anequivalent spherical diameter (based on volume)of 140 mm can be calculated [15]. A fines diameterof 50 mm is assumed. For the standard experimentwith a fibre concentration of 2 g l−1, approxi-mately 1×1010 fibres per m3 (nF) are present inthe suspension. An effective shear rate of 50 s−1

was estimated for a stirring rate of 200 rpm. FromEq. (2), the theoretical collision rate constant (k1)is 5.7×10−11 (m3 s)−1. The observed depositionrates J0 for bare fines on polymer-covered fibresand for polymer-covered fines on bare fibres were7.1 and 12.8 l g−1 min−1, respectively. The corre-sponding deposition rate constants (ak1) can becalculated according to Eq. (8). This yields 2.4×10−11 and 4.3×10−11 (m3 s)−1 for both respec-tive cases. Consequently, these rates are consistentwith the calculated theoretical collision rates, withcapture efficiencies (a) of 0.42 and 0.75, respec-tively. This is somewhat high, but it should benoted that the calculations are based on approxi-mate sizes for both fibres and fines, and assumemonodisperse cylinders; fibres and fines areknown to be very polydisperse. It is interesting tonote that the deposition rate depends on whetherthe fibres or the fines are initially coated withpolymer. The higher deposition rate for coveredfines (12.8 compared with 7.1 l g−1 min−1) in thestandard experiment can be explained by the factthat the fines were flocculated to a certain extentbefore the fibres were added. In such a case, the

capture efficiency increases [18,19]. The increasein the collision rate constant (because of the sizeincrease) is cancelled out by a decrease in thenumber of individual particles, and consequentlydoes not affect the deposition rate.

Fig. 4 shows the influence of stirring rate on thedeposition rate for the hetero-flocculation of poly-mer-coated fibres with bare fines (standard condi-tions). The relation between the shear rate and thestirring rate can be approximated by [20]:

G=KV0.8 (10)

with G the shear rate (s−1), K a constant and Vthe stirring rate (rpm). This relation can be con-sidered linear in this interval. The observed linearrelation corresponds therefore with the theoreticalprediction of Eq. (2)

4.3. Apparent detachment

4.3.1. MechanismThe apparent kinetics of this hetero-flocculation

process is clearly more complex than predicted bythe Langmuir kinetics (Eq. (4)). Indeed, if thedeposition and detachment rate constants (asdefined by the Langmuir theory) remain constantin time, the fines coverage should reach a steadystate without reaching a maximum. This is evi-dently not the case (Fig. 2). Consequently, othereffects have to be considered to elucidate thebehaviour. A plausible explanation is that anelectrostatic and steric barrier is created due topolymer transfer during particle detachment.Polymer originally present on one surface can betransferred to the opposite (bridged) surface.Upon particle detachment, the originally bare sur-face becomes partially coated with polymer. Thefraction of the surface coated with transferredpolymer layer can no longer interact with theoriginally coated surface. Furthermore, the trans-ferred polymer influences both particle depositionand detachment by decreasing both capture effi-ciency and bond strength due to electrostatic andsteric repulsion. Consequently, three interdepen-dent phenomena take place simultaneously duringthe ‘detachment’ phase of this experiment: (1)particle deposition, (2) particle detachment and(3) polymer transfer. The occurrence of polymer

Fig. 4. Influence of stirring rate (rpm) on deposition rateconstant (l g−1.min). PAM-coated fibres (2 g l−1) with barefines (0.28 g l−1).


Fig. 5. Time-dependence of the electrophoretic mobility offines (m2 V−1 s−1) upon mixing with polymer-coated fibres.Standard experiment.

Flocculation was induced in a fines suspensionthat was separated from a standard experimentafter 40 min, in which they were originally bareand mixed with polymer-coated fibres. This floc-culation does not occur with fresh bare fines,which were used for this experiment. Second, theelectrophoretic mobility (EM) of these fines wasmeasured in time throughout the same experi-ment. The EM changes sign from negative topositive during the experiment (Fig. 5). This indi-cates the gradual coating of the fines with cationicpolymer, transferred from the fibres. The mecha-nism is summarised in Fig. 6.

4.3.2. Influence of fibre concentration and shearrate

In Fig. 7, the apparent detachment rate con-stant is compared as a function of fibre concentra-tion for both the hetero-flocculation of coatedfibres with bare fines and for the hetero-floccula-tion of bare fibres with coated fines. The standardexperimental procedure was followed. Whenfibres are coated with polymer, kdet increases lin-early with fibre concentration. On the other hand,when fines are covered with polymer, the fibreconcentration has little effect on the apparentdetachment rate. This can be explained by the factthat, for polymer-covered fibres, more polymer isavailable for transfer when the fibre concentrationincreases. Therefore the polymer transfer is fasterand hence the apparent detachment rate increases.The apparent detachment rate constant is higherwhen the polymer is transferred from polymer-covered fines to fibres, as shown in Fig. 7. This isexpected since the surface area of fines is higherthan for fibres. Consequently, more polymerneeds to be transferred to bare fines to form anelectro-steric barrier, and the apparent detach-ment rate is lower. The polymer-covered finestend to aggregate, which increases both the de-tachment rate and the deposition rate due to thelarger size of the aggregates. Therefore, the poly-mer transfer process occurs faster.

The effect of the stirring rate (shear rate) on theapparent detachment rate is shown in Fig. 8 forthe hetero-flocculation of bare fines and coatedfibres. kdet augments with shear. Increasing shearrate causes two opposite effects on the apparent

Fig. 6. Mechanism of transient flocculation due to polymertransfer. Polymer-coated fibres are mixed with bare fines.Three steps are involved: hetero-flocculation, polymer transferand stabilisation. te denotes the equilibrium time.

Fig. 7. Influence of fibre concentration (g l−1) on the apparentdetachment rate (min−1) for two systems: (1) PAM-coatedfibres with bare fines (0.28 g l−1) (), (2) bare fibres withPAM-coated fines (0.28 g l−1) (�).

transfer was established with two experiments.The first consists of inducing flocculation withbentonite, a highly negatively charged colloid.


detachment rate. First, the deposition rate con-stant increases (Eq. (2)), therefore decreasing theapparent detachment rate. Second, the detach-ment rate constant increases, augmenting the ap-parent detachment rate. For the investigated shearrate range, the second influence clearly dominatesthe first. These results may have important conse-quences in papermaking at industrial shear rates.In our experiments, the shear rate was in theorder of 10–100 s−1, where in modern papermak-ing systems, shear rates of up to 104 s−1 arepresent after polymer addition [21]. The differencein shear rate is expected to reduce the time scaleof fines detachment and polymer transfer.

4.3.3. Influence of polymer adsorption andrelaxation time

The effect of polymer adsorption time and re-laxation on the hetero-flocculation kinetics wasstudied. Two experiments were carried out. In thefirst, the polymer adsorption time on the fibreswas varied from 10 to 3600 s. The standardexperiment was then performed, in which thesecoated fibres were mixed with bare fines. In thesecond experiment, the polymer relaxation timewas controlled. Fibres were stirred for 5 min inthe polymer solution, washed and left in water for10–3600 s. Again, the standard experiment wasperformed by mixing those fibres with bare fines.Fig. 9 presents the apparent detachment rate con-stant as a function of polymer adsorption andrelaxation time on the fibres. No influence on thedeposition rate was observed in both experiments.A decreasing apparent detachment rate is ob-served as a function of polymer adsorption time.This can be attributed to a stronger fines–fibrebond. The bond strengthening can be caused bythree effects. Firstly, a stronger polymer-fibrebond could be formed due to a higher number ofchain segments in contact with the surface(‘trains’). Secondly, the adsorbed amount of poly-mer could increase in time, giving rise to a moreefficient bridging layer. Thirdly, small chains ad-sorbed on the surface could be exchanged bymore effective long chains. The stronger bondpresumably decreases both the detachment rateand the polymer transfer, hence decreasing theapparent detachment rate. The polymer relaxationtime after 5 min of polymer adsorption has noinfluence on either the deposition rate or apparentdetachment rate (Fig. 9). This suggests that poly-mer reconformation has little effect on this timescale, which means that there is no significantincrease in trains over time. Also, it implies thepolymer remains on the surface, rather than pene-trating in the pore structure of the fibre by surfacediffusion, as previously suggested [7]. Possibly,low molecular weight chains have already filledthe available pores during the adsorption time of5 min, or the surface diffusion does not occur atall on this relaxation time scale. Acrylamide-basedcationic copolymers have been reported to hy-drolyse in the pH range between 3.5 and 8.5 and

Fig. 8. Influence of stirring rate (rpm) on the apparent detach-ment rate constant (min−1). PAM-coated fibres (2 g l−1) withbare fines (0.28 g l−1).

Fig. 9. Influence of polymer adsorption time () and relax-ation time (�) on the apparent detachment rate constant(min−1). PAM-coated fibres (2 g l−1) with bare fines (0.28 gl−1).


Fig. 10. Schematic representation of the polymer conforma-tions after stabilisation.

polymer transfer. After re-stabilisation of the sys-tem, the surface originally covered with polymerbecomes ‘depleted’, while the opposite surface isenriched with ‘transferred’ polymer chains. Fourdistinct surfaces can thus be distinguished at equi-librium, upon stabilisation of the system: (1) fibreswith depleted polymer, (2) fines with transferredpolymer, (3) fibres with transferred polymer and(4) fines with depleted polymer. The first two arethe result of mixing polymer-coated fibres withbare fines, where the last two are the product ofmixing bare fibres with polymer-coated fines. Thisterminology is illustrated in Fig. 10. These result-ing polymer layers were characterised by separat-ing fibres and fines after an experiment with freshlayers, and mixing each component with a freshcounterpart to perform a new flocculation experi-ment. This procedure is shown in Fig. 11 and theresults are summarised in Table 1.

The electrophoretic mobility (EM) of fines wasdetermined after the original experiment. Finesfreshly covered with polymer have an EM of8.8×10−9 m2 V−1 s−1; for fines with a trans-ferred polymer layer (Fig. 5), the EM drops toabout 5.3×10−9 m2 V−1 s−1. This means thatthe charge density of the transferred layer isFig. 11. Experimental procedure for characterising the result-

ing polymer layers. Two steps are involved. First, a freshlycoated fraction is mixed with a bare counterpart. After thesystem stabilises, the fines are separated from the fibres, andboth are mixed with a bare counterpart in a standard floccula-tion experiment.

Table 1Kinetic rate constants katt (l min−1 g−1) and kdet (1 min−1) fordifferent polymer layers at a fibre consistency of 2 g l−1 and afines concentration of 0.28 g l−1a

katt kdetMixture(min−1)(l min−1 g−1)

0.3390.05[Fibres+polymer] 7.190.5+[fines]

[Fibres+depleted] 0.573.1+[fines]

0[Fibres] –+[fines+transferred]

[Fibres] 12.8 0.65+[fines+polymer]

5.6 0.93[Fibres+transferred]+[fines]

4.5[Fibres] 0.44+[fines+depleted]

a Square brackets indicate one solid phase.

in the temperature range between 22 and 50°C[22]. The hydrolysis of ester groups cleaves thequaternary amines into carboxylic groups. Posi-tive charges are replaced by negative charges, as afunction of the extent of hydrolysis. The fact thatthe relaxation time does not influence the deposi-tion rate nor the apparent detachment rate confi-rms that the hydrolysis of poly(acrylamide) doesnot affect the polymer layer at the time scale ofthe experiments. This is expected in the investi-gated pH range between 6 and 7 [22].

4.4. Depleted and transferred polymer layers

Upon hetero-flocculation of fibres and fines, inwhich polymer is initially present on one of thesurfaces, the system re-stabilises in time due to


lower, indicating either a lower polymer coverageor a different conformation than the originallayer. The observed EM of fines with a depletedlayer was approximately the same as for a freshlayer.

The bridging ability of the surfaces as well asthe ratio between attraction (van der Waals, elec-trostatic) and repulsion (electrostatic) forces, asdescribed by the DLVO theory, determine thedeposition rate constant at constant shear rate.Upon collision, both the density of bridging poly-mer and the magnitude of the resulting attractionforce decide whether a particle deposits or not.

It is clear that the deposition rate constant forboth the transferred and the depleted polymerlayers is significantly reduced (Table 1). This isdue to two effects: a reduction of the polymerbridging ability combined with an increase in theelectrostatic repulsion. For a transferred layer,this could be explained by the fact that the trans-ferred polymer has sufficient space and time torelax into a flatter conformation on the surface,since the time scale is much larger than for poly-mer adsorption from solution. Also, polymercleavage could lead to smaller chains, which againproduce flatter layers. This effect is even morepronounced for the transfer from fibres to fines,where the resulting polymer layer is completelyinactive. For the depleted layer, the bridging abil-ity is presumably impaired because polymerchains that were originally bridging are chieflytransferred. As a result, fewer loops and chainsreach out of the surface, and therefore the densityof potential bridges is reduced. Reconformationof the depleted layer after polymer transfer couldlikewise contribute to this impairment.

The apparent detachment rate, at constantshear and fibre concentration, is determined bythe bond strength and the polymer transfer rate.Stronger bonds slow down the detachment pro-cess. The bond strength is determined by thedensity of bridges that are formed between thesurfaces and by the ratio between attractive vander Waals forces and repulsive electrostatic forces.It is reasonable to assume that polymer transferfrom a depleted layer is slower compared to thepolymer transfer from a fresh layer, because less‘transferable’ polymer is available after the initial

transfer. This effect should decrease the apparentdetachment rate for a depleted layer, compared toa fresh layer. On the other hand, the fact that less‘bridging’ loops and tails are present decreases thebond strength between fibres and fines. Therefore,the apparent detachment rate should increase. Fora depleted layer on fibres, the apparent detach-ment rate increases upon mixing with bare fines,whereas for a depleted layer on fines the apparentdetachment rate decreases after mixing with barefibres. A layer transferred from fines to fibresproduces a higher detachment rate, again pre-sumably due to a reduced bond strength of theflatter layer. A transferred layer on the fines hasno bridging ability at all (Table 1).

These results clearly indicate that the polymertransfer process causes a reduction in the floccula-tion efficiency of the resulting polymer layers.

5. Conclusions

The hetero-flocculation of fibres and fines usingPAM is transient. Both the fines deposition anddetachment rates, as defined by the Langmuirtheory, are time-dependent. This was attributed tothe transfer of polymer layer between surfaces,leading to the creation of an electro-steric barrierthat inhibits deposition and eventually leads to are-stabilised system. The observed initial deposi-tion rates are consistent with Smoluchowski kinet-ics. The apparent detachment rate is determinedby simultaneous particle deposition, particle de-tachment, and polymer transfer. This detachmentrate significantly increases with shear rate. Theresulting depleted and transferred polymer layersposses only limited bridging ability with non-cov-ered surfaces. In an industrial papermaking pro-cess, this could mean that deposited particles willbe quickly dislodged under high shear, causingpolymer transfer and leading to polymer layerswith reduced bridging ability.

Acknowledgements

The authors thank T.G.M. van de Ven, B.Alince and J. Petlicki for inspiring discussions and


valuable advice. Financial contributions fromNSERC for Tom Asselman’s PGS scholarshipand for R&D grant 601-110 1195 are kindlyacknowledged.

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dynamics of polymer-induced hetero-flocculation of wood fibres and fines

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