Colloids and Surfaces, 21 (1987) 29-42 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

29

Kinetics of Polymer-Induced Flocculation of Cellulosic Fibers in Turbulent Flow

LARS WAGBERG and TOM LINDSTRGM

Department of Paper Technology, Swedish Pulp and Paper Research Institute, Stockholm (Sweden)

(Received 10 October 1986; accepted in final form 27 February 19871

ABSTRACT

The kinetics of polymer-induced flocculation in turbulent suspensions of cellulosic fibers were investigated. To measure the degree of flocculation a measuring principle based on frequency analysis of back-scattered laser light was used. The degree of flocculation, given as a flocculation index and an average diameter of the floes formed, is defined from a wavelength power spectrum.

Experiments show that the flocculation process is very rapid and that almost all the flocculation is completed in less than two seconds. Results obtained with polyethyleneoxide and a phenolic resin are discussed in terms of a network flocculation mechanism. Experiments with a dual poly- mer system, anionic polyacrylamide and a cationic polycondensate between a dimethylamine and epichlorohydrin, indicate that polymer complex formation is the most probable flocculation mech- anism and that the cationic polymer has to be pre-adsorbed onto the cellulosic fibers to give maximum flocculation at a given addition level. The third flocculation system investigated, a high- molecular-mass cationic polyacrylamide (M, _ 10’1, also shows rapid flocculation, suggesting very rapid polymer adsorption.

Theoretical values for both the macroscale and the microscale of turbulence are calculated and it is suggested that turbulent eddies may affect both fiber flocculation and floe rupture. It is also suggested that turbulence may markedly increase the rate of polymer adsorption.

INTRODUCTION

Synthetic water-soluble polymers, mainly polyelectrolytes, have for many years been used in industrial applications as dispersants or flocculants. They are, for example, used to increase the efficiency of waste-water treatment plants, to treat drilling muds and as retention aids to increase the retention of fine material from cellulosic fibers and added clay fillers in the paper sheet during paper manufacture. Despite the fact that most industrial applications are per- formed under turbulent flow conditions, few investigations [l-6] have been focused on the connection between flocculation and turbulence.

Polymers are used in paper manufacture to retain fine materials in the paper web. This is often accompanied by an unwanted flocculation of the cellulosic

0166-6622/87/$03.50 0 1987 Elsevier Science Publishers B.V.

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U p-l_ 0

-------

B------F D

C

A

s

G

E

Fig. 1. Schematic picture of the circulation system: 1, stirrer (plastic paddle); 2, 250 1 tank; 3, pump with all parts in contact with suspension made of plastic material; 4, magnetic valve; 5, plunger for polymer dosage; 6, step motor, driven and controlled by the microcomputer unit 10; 7, polymer solution; 8, He-Ne laser (632.8 nm); 9, phototransistor with amplifier; 10, microcomputer unit (ABC-80) ; 11, frequency analyzer; 12, plotter for presenting wavelength power spectra; 13, magnetic valve; 14, glass pipe section.

Fig. 2. Diagram of the optical set-up: A, plane mirror; B,C, plano-convex lenses #=25.5 mm, f= 25.4 mm; D, pinhole with opening $=0.3 mm, E, pipe with streaming pulp suspension; F, phototransistor; G, measuring volume.

fibers, which leads to a substantial decrease in paper basis weight uniformity. Since most of the polymers are added less than ten seconds before the fiber suspension is dewatered to produce a sheet, it is very important for the opti- mization of paper quality to clarify the connection between fiber flocculation and turbulence and the kinetics of the fiber flocculation process within the first ten seconds after polymer addition.

This paper gives a short description of the equipment designed for measur- ing polymer-induced flocculation of turbulent fiber suspensions over the first five seconds after polymer addition. Results of flocculation experiments are discussed in $erms of different flocculation mechanisms, and the effect of tur- bulence on polymer adsorption and stable floe sizes is discussed.

EXPERIMENTAL

Equipment and procedures

The flocculation detection equipment has been described previously in detail [ 71. The system is built around a circulation system, Fig. 1, where flocculation is monitored with a laser-optical device shown schematically in Fig. 2. The

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Wavelength A mm

Fig. 3. Two wavelength power spectra from a bleached decrilled softwood pulp showing the effect of addition of a cationic polyacrylamide. Curve A with and curve B without polymer addition. Curve C shows the ratio between the two spectra.

electrical signal from the phototransistor in Fig. 2 is transferred to a frequency analyzer, General Radio 1926 Multichannel RMS detector and 1925 multifil- ter, one third octave, 3.15 Hz430KHz. RMS-values from the different band- pass filters of the analyzer are subsequently used to calculate the wavelength power spectrum of the signal [ 71. By comparing the wavelength power spec- trum with (curve A in Fig. 3 ) and without (curve B in Fig. 3 ) polymer addition it is possible to define a size of the fiber floes formed. The size range of the floes formed is readily determined by calculating the ratio between the two spectra (curve C in Fig. 3 ) and the size of the floes may then be read from the abscissa. Due to the principle of the analysis the value read on the abscissa must be divided by two to give the floe size. Measurements at several positions downstream from the point of polymer addition enable the kinetics of the poly- mer-induced fiber flocculation to be determined.

Polymer solutions can be added to the fiber suspension in a constriction in the pipe by means of a step-motor driven burette, 5 in Fig. 1, with an accuracy of 5*10-* ml. In experiments with dual polymer systems one of the polymers is added to the tank, 2 in Fig. 1, and the other in the constriction. When poly- mer is added in the constriction of the pipe, the fiber suspension is pumped into the sewer.

In the present experiments, the flow was 0.59 dm3 s-’ corresponding to an

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average velocity of 1.12 m s-l in the pipe. The focusing depth of the laser beam was 7 mm. Since the pipe diameter is 26 mm this gives a signal which is rep- resentative of the bulk suspension.

Definition of flocculation index and average diameter of the floes formed

In Ref. [ 71 it was concluded that the coefficient of variation, V%, of the signal from the phototransistor (see Fig. 1) can be used as a measure of the degree of flocculation of the fiber suspension. To characterize the polymer- induced fiber flocculation, the coefficient of variation of the signal with, V,%, and without, VI%, added polymer are used to calculate a flocculation index according to the equation:

F=J(v,%)2-(v1%)2

V,% (1)

which makes it possible to summarize the flocculation information contained in Fig. 3 in a single quantity.

The great advantage of using a power spectrum is that it gives both the degree of flocculation and information as to how this flocculation is distributed over different floe sizes. This latter information is evaluated as an average floe diameter from the function S, which corresponds to the dashed area in Fig. 3:

s= i (E2(1) -El(l))dZ l=a

(2)

where 1 is the wavelength (mm) corresponding to a certain band-pass filter of the frequency analyzer; E2 (1) is the spectral density for wavelength 1, with added polymer; El (1) is the spectral density for wavelength 1, without added polymer; dl is the bandwidth of band-pass filter with centre wavelength 1; a is the wavelength (mm) corresponding to the diameter of the measuring volume in the pipe (cf. Fig. 2, symbol G) ; k is the wavelength (mm) corresponding to the diameter of the pipe.

A typical S-function is shown in Fig. 4. The average diameter of the floes formed, d, is defined by the position in the diagram where the value of the S- function has reached 50% of its final value. Experiments with synthetic fiber floes [ 71 have shown that this is a value which corresponds to physically meas- ured dimensions.

By determining F and d at different positions downstream from the point of polymer addition it is possible to follow both how the degree of flocculation changes and how the average diameter of the floes develops.

The number of experiments which can be performed with a reasonable effort does not allow a formal statistical treatment of the data. However, duplicate experiments were often performed and the scatter was always smaller than 2-3% both in flocculation index and average diameter of formed floes.

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0.1 0.2 0.4 1 2 4 10 20 40 100 2

Wavelength 1 (mm)

0

Fig. 4. S-function from the experiments shown in Fig. 3, calculated according to Eqn (2)) a and k indicate the summation limits used throughout the experiments.

Materials

The cellulosic fibers used in the experiments were decrilled softwood fibers from a dried, fully bleached kraft pulp (Imperial Anchor, Iggesund, Sweden) free of small fiber fragments (fines). After disintegration, the pulp was beaten in a Valley beater [ 81 and the fiber fines were removed by repeated filtering on a Celleco laboratory filter with a mesh size of 100 pm. Only the coarse fiber fraction was collected. These fibers were washed with lop2 M HCl and then again washed with deionized water to pH 5.

The water used in the experiments was deionized in a two-bed ion-exchange equipment from Culligan Teko giving a conductivity of less than 3 PS cm-‘. The pH of the water was between 6.2 and 7 and, together with the washed fibers, this produced a fiber-water mixture with a pH between 5.8 and 6. The temperature of the fiber suspension was 20 2 4 o C.

Three different polymer systems were used, two dual and one single com- ponent system. These were:

(a) Polyethyleneoxide (PEO), from BDH Chemical Ltd, England, with a molecular mass of w 4 million and a phenol formaldehyde resin (FPR) , FP 1563 from Casco AB, Sweden.

(b) Anionic polyacrylamide (A-PAM), with an anionic molar monomer content of 15.8% and with a molecular mass of w 10 million together with a low-molecular-mass polycondensate between a dimethylamine and epichloro- hydrin (PAE) , Percoll597. The charge density of this cationic polymer was 7

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3.0

4 2.0 .c

s ‘G a 2 $ 1.0 Ii

1 2 3 L

Time after polymer addition (s)

Fig. 5. Flocculation index ( t ) and average diameter of the floes formed ( -o ) in experiments with PEO and phenolic resin. Phenolic resin was added to the circulating fiber suspension and PEO in the constriction of the pipe. Levels of addition were 0.47% for both polymers.

meq gg ’ as determined by colloid titrations [ 91. Both polymers were supplied by Allied Colloids U.K.

(c ) A cationic copolymer (C-PAM) of acrylamide and N,N- (diethylamino- ethyl) acrylate quaternized with methyl chloride. The molecular mass was approximately 10 million and the polymer was of a low charge density with a cationic molar monomer content of 1.8%. This polymer was also kindly sup- plied by Allied Colloids U.K.

All polymers were used as supplied without further purification. The poly- mers received as powders were dissolved in water at a concentration of 0.25 g 1-l on a magnetic stirrer for approximately 12 hours, except for the PEO which was carefully dissolved during no more than four hours, to prevent polymer degradation. Polymers received as solutions were diluted to the desired con- centration less than one hour before use.

RESULTS AND DISCUSSION

Polyethyleneoxide (PEO) -phenolic resin (FPR)

In these experiments, 0.47% phenolic resin, based on the dry mass of the fibers, was added to the circulating fiber suspension and allowed to mix for ten minutes before the addition of 0.47% PEO was started. Figure 5 shows the flocculation index and average diameter of the floes formed as a function of time after polymer addition.

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Time after polymer addition (s)

Fig. 6. Flocculation index ( t ) and average diameter of the floes formed ( -a ) in experiments with A-PAM and PAE. A-PAM was added to the circulating fiber suspension and PAE in the constriction of the pipe. Levels of addition for A-PAM and PAE were 0.06% and 0.15%, respectively.

Clearly, some time f 2 s ) has to elapse before the flocculation index reaches a plateau level. The floe size increases slowly during the first two seconds whereas a more rapid increase is evident towards the end of the detection period. This behaviour may be understood in terms of a network flocculation mecha- nism described by Lindstr~m and Glad-Nor~ark f lo] where it is postulated that PEO and phenolic resin form a polymer network in solution. The slow increase in floculation during the first few seconds is probably due to an almost undisrupted polymer network. When the polymer network starts to disrupt, due to the turbulent eddies in the suspension, the cellulosic fibers are entrained in fragments of the polymer network so that small discrete fiber networks, floes, are formed. The strength of the fra~ents of the polymer network pre- sumably combines with the inherent network strength of the fiber floes to make the fiber floes resistant to disintegration.

Results of two experiments with A-PAM and PAE are shown in Figs 6 and 7, the only difference being the order of addition of the polymers. The first component was added to the suspension and allowed to mix ten minutes before the other component was added in the constriction. Levels of addition of A- PAM and PAE were 0.06% and0.15%, respectively. Figure 6 shows the effect of adding A-PAM to the circulating fiber suspension and PAE in the constrie- tion of the pipe and Fig. ‘7 shows the effect when the order of addition is reversed.

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3 - $

> 1.0 E -3 E 2 0.8- 5 0

%I

0.6 - %

> :,2 h I I I 1 1 2 3 4

Time after polymer addition 1s)

Fig. 7. Flocculation index ( -o ) and average diameter of the floes formed ( -o ) in experiments with A-PAM and PAE. PAE was added to the circulating fiber suspension and A-PAM in the constriction of the pipe. Levels of addition for A-PAM and PAE were 0.06% and 0.15%, respectively.

It is clear that both flocculation index and average diameter of the floes formed are very dependent on the order of addition of the polymers.

The mechanism most probably responsible for the flocculation detected in Fig. 6 is known as complex flocculation where the formation of an insoluble polymer complex between A-PAM and PAE causes a simultaneous formation of fiber floes. This type of flocculation has been described by several authors [ 11,121.

The results of Fig. 7 are most readily understood as being due to a polymer bridging mechanism [ 13,141. When the PAE molecules are adsorbed onto the fiber surface, positively charged patches are formed [ 15,16 ] and, when added to the suspension, the A-PAM molecules form polymer bridges between posi- tively charged patches on different fibers resulting in a rather extensive fiber flocculation.

Despite the difference in magnitude of the flocculation in Figs 6 and 7, a very rapid flocculation is detected in both experiments. This is in agreement with polymer complex formation studies [ 171 which show that complex formation between two polyelectrolytes even in dilute solutions is a very rapid process, taking place in much less than one second.

The more extensive flocculation detected in Fig. 7, when the cationic poly- mer is pre-adsorbed onto the fiber surface may be explained in terms of an adsorption sensitized bridging mechanism. When the order of addition is reversed the poly-mer complex formation takes place in the entire solution and

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1 2 3 L

Time after polymer addition (s)

Fig. 8. Flocculation index ( t ) and average diameter of the floes formed ( -o ) in experiments with C-PAM. Level of addition was 0.1%.

is hence no longer specifically located to the fibers. It may thus be concluded that this latter mode of addition gives a less efficient utilization of the added polymers.

Cationic polyacrylumide (C-PAM)

Figure 8 shows an interesting result from experiments with 0.1% C-PAM added. There is a very rapid increase in both flocculation index and average diameter of the floes formed, with a plateau level reached as early as 0.5 s after polymer addition.

Since C-PAM polymers are believed [ 181 to induce flocculation by means of a polymer bridging mechanism [ 141, the results shown in Fig. 8 indicate a very rapid polymer adsorption. This is in contrast to earlier reports [ 51 where the polymer adsorption was found to be a rather slow process. There may be several explanations of this discrepancy, since there is a large difference between the experimental conditions and materials used. If the polymer adsorption is considered to be a collision process [ 191 between polymers and fibers, it could certainly be affected by turbulent eddies in the suspension. This has been dis- cussed by Argaman and Kaufman [ 201, who calculated turbulent diffusion coefficients from turbulence energy spectra. It was shown that there is a large difference between Brownian and turbulent diffusion coefficients. If it is assumed that the turbulence affects the transport of polymer molecules towards the fibers, adsorption times of less than a second are expected and hence it is reasonable to suggest the bridging-type flocculation mechanism for the C-PAM.

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As for the PEO-phenolic resin system, it may also be suggested that it is a combination of the inherent network strength of the fiber floes and the strength given by the polymer bridges that makes the floes resistant to break up in the turbulent shear field in the pipe.

Different scales of turbulent eddies and their effect on flocculation and floe rupture

Argaman and Kaufman have in several publications [ 1,20,21] discussed the formation and break-up of floes in turbulent flow. The same type of investi- gation has also been carried out by Thomas [ 221. Their theories are all based mainly on the assumption that the turbulence consists of a large variety of eddies with different sizes and different intensities and that these eddies may affect flocculation in different ways. From the geometry of the flocculation equipment, a large scale motion, the macroscale of turbulence, L, is obtained. These eddies contain almost all the energy and are responsible for the energy transport through the solution. Energy is transferred from these large scale motions to smaller scale motions until the viscous forces begin to have a dom- inating effect on the motion of the fluid [ 231. The energy from these small scale motions, the microscale of turbulence, is converted to heat. The size of these eddies is uniquely determined by the energy dissipation into the solution and the kinematic viscosity of the liquid [ 231, according to Eqn (3)

/2= ( Y3/W (3)

where: E is the energy dissipation/unit mass ( m2 se3), v is the kinematic vis- cosity ( m2 s- ’ ) , and A is the microscale of turbulence ( m ) .

Since the floes formed by the cellulosic fibers cover a wide size range it is obvious that they may be affected by a spectrum of different eddies. It has also been suggested [ 22,241 that the large scale motions, L, may tend to give the floes “stretched out filamentous shapes” and that if the intensity is large enough, these eddies may finally disrupt the floes. Normally, eddies with sizes comparable to the size of the fiber floes are considered to cause disruption of the floes.

Smaller eddies are not capable of disrupting complete fiber floes but may still affect fiber floes through surface erosion [ 221 of single fibers from the surface of the floe.

Apart from floe rupture, turbulence naturally also causes collisions between fibers which are essential for flocculation, and Hubley et al. [ 251 have sug- gested that flocculation in turbulent flow of dilute fiber suspensions is a dynamic equilibrium between the formation and destruction of floes. As in the case of floe disruption, different eddies may be important for flocculation, provided they are of the appropriate size.

To clarify the importance of turbulent eddies for fiber flocculation, the sizes

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of both the macroscale and microscale of the turbulence must be known. These may be estimated from flow measurements using common turbulence defini- tions of the macro- and microscale of the turbulence. According to Powe and Townes [ 261, the longitudinal macroscale, L, is determined by the empirical relationship:

L=O.ll.D

where D is the pipe diameter,

(4)

The microscale of turbulence is somewhat more difficult to estimate since it is commonly recognized that fibers considerably affect the energy dissipation into the solution. The problem may however be solved by combining work done by Lee [ 271 and Laufer [ 281. Through integration of Laufer’s data, it is found that the energy dissipation into the solution may be calculated by the equations

28.4.~~ E=L

D (5)

and

u, =u.@‘2 (6)

where u, is the frictional velocity (m s- ’ ) , z.i the average velocity in the pipe (m s-l), and @ the friction factor.

The friction factor for the fiber suspension must also be evaluated. For fully bleached kraft fibers, Lee found that the friction factor is uniquely determined by the equation:

@-l/2 =+n&.@1/2 + (14-g)

U-D Re=-

V

K=O 4-o 111*c”.584 . . (9)

where K is the apparent von Karman constant, and c the fiber concentration

(%). For the present experiments, D=26 mm, c=O.l% and ti=1.12 m s-‘. By

inserting these values into Eqns (9) and (8)) Eqn (7) may be solved by an iterative procedure. The friction factor is then used with Eqns (3)) (5) and (6) to give a microscale of turbulence of 45.6 pm. From Eqn (4)) the macro- scale of the turbulence is found to be 2.9 mm.

Figures 5-8 show that a macroscale of approximately 3 mm may certainly affect the large fiber floes formed during the experiments since these are in the same size range. Since the cellulosic fibers used in the present investigation

have a diameter of about 30 pm, it may be concluded that surface erosion of the floes due to the microscale of the turbulence is likely to occur.

Turbulent effects on p&mer adsorption

In order to determine appropriate adsorption times, Gregory suggested [ 191 that the polymer adsorption process in a laminar system may, as a first approx- imation, be regarded as a collision process. This approximation was also used by Wigsten and Stratton [ 51 in a turbulent system, but so far there is only a limited understanding of how turbulence may affect polymer adsorption.

When the polymer adsorption is regarded as a collision process in a turbulent system, the turbulence energy spectrum has to be considered, since the eddies may affect the collision process differently depending on their size and inten- sity. Furthermore, Argaman and Kaufman [ 201 suggested that all turbulent eddies with a size equal to or smaller than the distance between the colliding particles contribute to what these authors call a turbulent diffusion coefficient. Once the turbulence energy spectrum is recorded, this coefficient may be calculated.

In the present investigation, the average distance between the fibers was 1 mm since 1 g 1-l corresponds to approximately 1 million fibers per litre. If, at very low levels of polymer addition, the polymersare uniformly distributed among the fibers, the average distance between a polymer molecule and a fiber would be 0.5 mm. According to the preceding section, the scale of turbulence varied between 4.6. lop5 and 2.9. lop3 m. This is of the same order of magni- tude as the distance between the polymers and the fibers. Without going into further details it may thus be suggested that polymer adsorption may be affected by the turbulence.

At “higher” polymer concentrations (1 mg 1-l ) , however, the average dis- tance between the polymer molecules and the physical shape of the fibers have to be considered. The average molecular mass of the polymer is 10 million (C- PAM), which gives an average distance between the molecules of 2.6. lop6 m. When a fiber, with a diameter of 30*10-6 m and a length of 3.0*10-3 m, is added to such a suspension, it immediately collides with a large number of polymer molecules.

The “true” process for polymer adsorption in turbulent dilute suspension of cellulosic fibers is probably a combination of these two model processes.

CONCLUSIONS

Equipment for the detection of polymer-induced flocculation of cellulosic fibers has been described. Experimental results show that, under turbulent conditions in pipe flow, flocculation with both single and dual component poly-

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mer systems is a very rapid process with almost all the flocculation completed in less than two seconds.

The comparatively slow (2 s) flocculation in the PEO-FPR system was interpreted in terms of the stability of the transient network formed by the two components. Experiments with anionic polyacrylamide (A-PAM) and a dimethylamine epicholorhydrin condensate (PAE) show that pre-adsorption of the PAE molecules to the fiber surface is essential for maximum utilization of the flocculating capacity of the polymers. If A-PAM is added before the PAE, both the degree of flocculation (~occulation index) and the average diameter of the floes formed is decreased. From experiments with a cationic polyacryl- amide, C-PAM, of high molecular mass and low charge density where polymer bridging is believed to cause the flocculation, it appears that the polymer adsorption rate is very fast and is influenced by the turbulence in the suspension.

From calculations of the macroscale and microscale of the turbulence, it is concluded that turbulent eddies in the suspension may influence both fiber ~occulation and fiber floe rupture. A rather close correlation was also found between the collision radius between the C-PAM and the cellulosic fibers, and the scale of turbulence, suggesting a turbulence-induced polymer adsorption.

ACKNOWLEDGEMENTS

The authors are indebted to Dr Lars i)dberg, Dr Bo Norman and Dr Lars Winter for valuable suggestions during the work and during the preparation of the manuscript. Colleagues in the Paper Technology Department of the Swed- ish Pulp and Paper Research Institute and in the Paper Technology Depart- ment of the Royal Institute of Technology in Stockholm are also thanked for many stimulating discussions. Dr J.A. Bristow is thanked for linguistic revi- sion of the manuscript.

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