Colloids and Surfaces, 31 (1988) 231-253 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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Polymer Ad~rption and ~~~cu~ation in Sheared Suspensions

JOHN GREGORY

Department of Civil and Municipal Engineering, iJniversity,College London, Gower Street, London WClE 632” (United Ki~dom~

(Received 8 April 1987; accepted in final form 11 May 1987)

ABSTRACT

Dynamic aspects of polymer adsorption and flocculation are considered and their relevance to the testing of polymeric flocculants is emphasised. In particuler, the adsorption of polymer on particles can be slow compared to the vacation rate in sheared stations and this can lead to some uncertainties in the interpretation of results from continuous tests. Results using a newly- developed flocculation monitor are presented, with a variety of suspensions and polymers, which illustrate some of the important points.

INTRODUCTION

Almost all applications of polymeric flocculants are under conditions where a suspension is subjected to shear. When flocculation occurs by bridging or charge neutralisation mechanisms, then adsorption of polymer chains on par- ticles is an essential step in the process and this may be considerably influ- enced by the applied shear. At present there is little fundamental understanding of polymer adsorption and flocculation under dynamic conditions and most e~rimen~l studies have paid little or no attention to dynamic aspects. Newly- developed methods for monitoring particle aggregates in flowing suspensions have made dynamic- testing of flocculants rather more straightforward than before.

ADSORPTION AND FLOCCULATION KINETICS

When a polymer solution is added to a stable suspension in an amount suf- ficient to destabilise the particles, several processes are initiated [ 11, the rates of which could have significant effects on the overall flocculation process. The following steps, illustrated schematically in Fig. 1, need to be considered:

(a) Mixing of the polymer molecules among the particles. (b ) Adsorption of polymer chains on the particles.

0166-6622/~/$03.50 0 1988 Elsevier Science Publishers B.V.

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Fig. 1. Schematic diagram showing mixing, adsorption and flocculation when a polymeric floc- culant is added to a suspension.

(c ) Re-arrangement (re-conformation) of the adsorbed chains from their initial state to an eventual equilibrium configuration.

(d) Collisions between particles having adsorbed polymer to form aggre- gates ( floes) , either by bridging or by charge effects.

(e) Break-up of floes. In practice, these processes do not simply occur in sequence but simulta-

neously, at rates which depend on a number of factors, making the whole pro- cess difficult to analyse in a straightforward manner. In some studies initial conditions have been arranged so that steps (a) - ( c ) above occur without floc- culation, and then flocculation is initiated by changing the conditions. For instance, Fleer and Lyklema [ 21 added an excess of polymer to one portion of suspension and allowed time for adsorption and re-conformation to occur. On adding a second portion of suspension, flocculation between coated and un- coated particles was observed. Alternatively, polymer can be added to a sus- pension at low ionic strength, where no flocculation occurs, and then flocculation can be induced by adding salt [ 31. However, these procedures are not normally applicable and the complexity of the overall process has to be recognised. Nevertheless, it is convenient to consider the various steps separately.

Mixing

Polymeric flocculants are often added as fairly concentrated stock solutions (0.1-l% ,by weight), which may be very viscous. Mixing a small amount of such solution into a large volume of suspension may take some time, during which some particles are subjected to a local overdose and may become resta- bilised. This effect is thought to be the origin of residual haze and poor filtra- bility in some flocculated suspensions [ 41. If the droplets of added polymer solution are not rapidly dispersed, they may act as ‘nuclei’ for floe formation.

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In the following, we shall assume that complete mixing has been rapidly achieved and only consider steps (b )-(e) in Fig. 1.

Adsorption rate

There is little information available on the kinetics of polymer adsorption on dispersed particles, but it seems reasonable to consider the process as trans- port-limited, at least in the early stages of the process, where surface coverage is still quite low. Under these conditions, the adsorption rate will depend on the rate of arrival of polymer molecules at a particle surface. As particle sur- faces become more fully covered by adsorbed polymer, then the rate of further adsorption will be reduced since there are fewer adsorption sites. However, since optimum flocculation usually occurs at considerably less than complete surface coverage, the assumption of a transport-limited rate should not be too bad.

If there are initially N1 particles and Nz polymer molecules per unit volume, then the number of particle-polymer encounters occurring in unit volume per unit time, J12, will be given by:

(1)

where klz is a rate constant. A similar expression, with N1 = N,, applies to the rate of flocculation.

Under normal circumstances, there will be far more polymer molecules than particles and hence the rate of adsorption should be greater than the particle collision rate. However, it will usually be necessary for a substantial fraction of the added polymer to be adsorbed before particles are sufficiently destabi- lised for flocculation to occur. If the polymer acts by a bridging mechanism, then the number of chains adsorbed on particles must provide enough bridges to form floes of adequate strength. Polyelectrolytes which act by charge neu- tralisation need to adsorb sufficiently to overcome electrical repulsion between particles. In both cases the amount of polymer added cannot be much in excess of the amount required to adsorb, otherwise there would be, at best, a wastage of flocculant and, often, an eventual re-stabilisation of the particles as excess polymer is adsorbed. Assuming that the particle number concentration re- mains constant and that the rate constant k12 is independent of surface cov- erage, then the time tA required to adsorb a fraction f of the added polymer can be derived from Eqn (1) simply by integration [ 5 ] :

tA = - In (1 -f) /klP N, (2)

The assumptions leading to Eqn (2) are questionable, since the available surface area will decrease as adsorption occurs, leading to a decrease in k12 and the number of particles N1 will decrease as flocculation occurs. Both of these effects would cause the actual adsorption time to be greater than tA calculated

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from Eqn ( 2). Nevertheless this simple expression can give a useful estimate of the minimum time needed for adsorption of sufficient polymer, provided that a reliable estimate of the rate constant can be made. A very significant feature of Eqn (2) is the inverse dependence of the adsorption time on the number concentration of particles. Thus, slow polymer adsorption is more likely to be observed in dilute suspensions. Statements about the “rate of polymer adsorption” are of little meaning without information on the particle concentration.

Estimates of the adsorption rate constant can be made if the polymer mol- ecules are assumed to behave as equivalent spheres and the particles are also spherical. If the transport is entirely by diffusion, then the Smoluchowski re- sult for perkinetic collision of unequal spheres is appropriate and gives:

k lz= (2kT/Qu) (~1 +~?‘h~z (3)

where k is Boltzmann’s constant, T the absolute temperature andp the viscos- ity. a, and u2 are the radii of the particles and polymer molecules, respectively. (The latter value may be determined by a technique such as photon correlation spectroscopy, in which the diffusion coefficient of the molecule is obtained. The resulting radius should be acceptable for calculating the diffusion-con- trolled adsorption rate.)

In sheared suspensions, provided that the shear is uniform, the Smolu- chowski expression for orthkinetic collisions can be used:

L= (4/3)G(o, +a213 (4)

where G is the velocity gradient or shear rate (s-l). In this case the use of a value for u2 based on diffusion coefficient may not be appropriate and a value closer to the size of the polymer coil in solution (for instance from gel permea- tion chromatography) would be better, since this will be more closely related to the probability of collision. The diffusion coefficient of a polymer molecule in solution usually gives an equivalent “hard-sphere radius” rather less than the radius of gyration and so calculations of orthokinetic collision rates based on the former will tend to underestimate the rate.

Generally, polymeric flocculants are added to suspensions under shear con- ditions which are far from uniform, and the effects of turbulence need to be considered. Polymer molecules can be transported to a particle surface by tur- bulent eddies, depending on the sizes of particles and polymer in relation to the turbulence microscale, which depends, in turn, on the rate of energy dis- sipation. It has been suggested (e.g. Amirtarajah and Trusler [ 61) that the adsorption rate under turbulent conditions passes through a maximum at a certain value of the energy inputrate, although there is very little experimental evidence on this point.

Another relevant aspect of polymer adsorption under conditions of high shear and especially in turbulent flow is the possibility of a reduced adsorption rate

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Fig. 2. Adsorption rate constants, k,,, for diffusion-controlled (perikinetic) and shear-induced (orthokinetic) transport, as a function of polymer radius, u2. Particle radius, a,, = 1 pm; shear rate, G=50 s -I.

and even desorption as a result of shear forces at the particle surface [ 71. At present, quantitative predictions of adsorption rates under such conditions are not possible.

A useful practical compromise for fairly low shear rates is to use an expres- sion like Eqn (4)) but instead of the uniform shear rate G, insert an “effective” value based on the power input to the suspension (e.g. in a stirred vessel). Such an approach has a number of shortcomings [ 81, but is acceptable for order-of-magnitude estimates.

Returning to Eqn (4)) it is clear that the rate of polymer adsorption as a result of shear should increase as the size of the polymer molecule increases, in contrast to diffusion-controlled adsorption, where an increase in molecular weight leads to a reduced diffusion coefficient and a decrease in adsorption rate. This point is illustrated graphically in Fig. 2, where the adsorption rate constant is plotted against the radius of the polymer molecule, for the cases of perikinetic and orthokinetic transport. For these calculations, the particle ra- dius has been taken as 1 pm and the shear rate as 50 s-l. The dispersion me- dium is assumed to be water at 25 ’ C.

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The rate constants in Fig. 2 show that the diffusion-limited rate exceeds the shear-induced rate only when the polymer molecule is quite small (a, < 50 nm) . As a2 increases, the orthokinetic rate becomes larger and, for molecules of ra- dius 200 nm (corresponding to a molecular weight of several million), diffu- sion would be relatively insignificant as a transport mechanism. These results depend on the choice of values for shear rate and, especially, the particle radius, a,. For lower shear rates and smalles particles, the orthokinetic rate is de- creased and diffusion becomes relatively more important. Nevertheless, the values chosen for the present calculations are appropriate for many practical flocculation processes; in fact, effective shear rates rather greater than 50 s-l are often used, so that orthokinetic transport would be even more significant. The point mentioned previously concerning the appropriate value of a2 to use in the calculations also leads to the conclusion that the results in Fig. 2 may underestimate the contribution of orthokinetic adsorption.

Having values for the adsorption rate constants, it is a simple matter to calculate values of adsorption times from Eqn (2). Assuming a particle num- ber concentration of 10’ cmW3, a shear rate of 50 s-l, a particle radius, a, = 1 pm, polymer radius, a2= 100 nm and that 90% of the added polymer needs to adsorb (f= 0.9)) the required times are: Perikinetic: tA = 62 s Orthokinetic: tA= 26 s.

Thus, in an unstirred suspension, polymer adsorption should take more than twice as long as when gentle agitation (G= 50 s-l) is applied. Of course, these numbers are for arbitrarily chosen values and are based on a rather simplistic model, but they serve to show, at least in a qualitative manner, that polymer adsorption rates can be significantly enhanced in sheared suspensions.

Re-conformation rate

There is very little information on the rate at which adsorbed polymer chains attain their equilibrium configuration. Limited experimental data are avail- able for adsorption on flat surfaces [ 91, which indicate a two-step process, in which the polymer first adsorbs and then undergoes a very slow re-conforma- tion, which may take several hours. However, such results were obtained for polymers approaching saturation adsorption and their relevance to the floc- culation of suspensions is questionable. Under optimum flocculation condi- tions, the adsorbed polymer is at fairly low surface coverage and re- conformation may be much more rapid. Nevertheless, times of the order of several seconds or more may be involved.

If the time required for re-conformation is greater than the average interval between .particle collisions, then particles will collide before their adsorbed polymer chains have attained an equilibrium configuration. In this case the adsorbed polymer will extend further from the particle surface than at equilib-

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rium and, intuitively, this should lead to an enhanced opportunity for polymer bridging and improved flocculation, indicated by the dashed line in Fig. 1. This effect should be more apparent with concentrated suspensions, where the par- ticle collision frequency is high, and may partly explain why high-molecular- weight polymers are especially effective in such systems. When polymeric floc- culants are applied to concentrated suspensions it is unlikely that an equilib- rium adsorbed configuration is ever attained.

Flocculation rate

The frequency of particle collisions depends on the particle number concen- tration and on a collision rate constant, as in Eqn (1) . The flocculation rate is obtained from the collision frequency, together with a collision efficiency fac- tor, a, which is the fraction of collisions leading to permanent aggregates. For a fully-destabiiised suspension, a collision efficiency of unity might be ex- pected, but this is not generally observed because of hydrodynamic or viscous interaction between particles, which can give appreciably lower values. In the perikinetic case, reductions in aggregation rate by a factor of about 2 are typical [ lo]. With sheared suspensions the orthokinetic rate can be reduced by a fac- tor of 5 or more by hydrodynamic effects, although this depends greatly on the particle size and shear rate [ 111.

In polymer flocculation, it has been frequently assumed, following Healy and La Mer [ 121, that the collision efficiency would be proportional to the term 8 (1 - 8)) where 8 is the fraction of the particle surface covered by polymer. This implies that the only successful collisions are those occurring such that coated and uncoated areas of colliding particles come into contact. It follows that the maximum rate of successful collisions will occur when 8 =0.5 ( “half surface coverage”) and that, under these conditions, half of the total collisions will be successful. On this basis, a maximum rate of polymer flocculation just half of that when the particles are fully destabilised by salt would be expected. Hogg [ 131 has considered the case where colliding particles are able to re- orient to give a more favourable interaction, leading to a higher flocculation rate. Intermediate cases can also be envisaged.

However, in view of the conformation of adsorbed polymer molecules, the concept of “surface coverage” is rather imprecise and these approaches to poly- mer flocculation kinetics should not be taken too seriously. None of them pre- dicts a rate faster than that for a fully-destabilised suspension, but there are reasons why a rate enhancement might be expected. For instance, bridging flocculation implies capture of particles by adsorbed polymer which extends some way from the particle surface, which would give an increased collision radius and more rapid flocculation [ 141. There are very few direct measure- ments of polymer flocculation rates, although many qualitative observations indicate enhanced rates.

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Cationic polyelectrolytes are thought to adsorb with a rather flat configu- ration on negative particles and do not greatly enhance flocculation rates, at least in dilute suspensions. Perikinetic rates up to twice the value found for salt destabilisation have been observed with cationic polymers of moderate molecular weight, and can probably be explained by “patchwise” adsorption [151.

Since polymer adsorption can be quite slow, flocculation may not begin im- mediately after adding polymer to a suspension. The time required for a certain fraction of added polymer to adsorb has been considered previously and this needs to be compared with the characteristic flocculation time, tr, which is the time in which the total number of particles is reduced to half of the initial value as a result of aggregate formation. For an initially monodisperse suspension, where all of the particles have radius al, tr can be written in terms of the cor- responding collision rate constant from Eqn (3) or (4) (assuming that every collision is effective ) :

tp = 1/2&N() (5)

where No is the initial number concentration of particles. This gives the following results for perikinetic and orthokinetic flocculation:

Perikinetic: tr = 3p/4N0 kT (6)

Orthokinetic: tr = 3/16GN,& (7)

We can then calculate the flocculation times for the conditions assumed earlier (N,= 10’ cmm3, a 1 = 1 pm, G= 50 s-l) and compare them with the cor- responding adsorption times calculated before (f= 0.9, a2 = 100 nm) : Perikinetic: tA = 62 s; tr = 163 s. Orthokinetic: tA = 26 s; tr = 3.8 s.

These results show, as expected, that flocculation is much more rapid when shear is applied, taking only about l/40 of the time needed for the diffusion- controlled process. An important aspect of these calculations is that, although the absolute adsorption rate is faster in the orthokinetic case, it is considerably slower than the flocculation process. By contrast, under perikinetic conditions, adsorption occurs appreciably faster than flocculation and so would not be rate-limiting. In sheared suspensions it is likely that a given particle would undergo several collisions with other particles before it had acquired enough polymer to allow aggregates to form. This effect can be seen experimentally as a lag time between the addition of polymer and the onset of flocculation (see later ) .

Although these calculations are for a rather arbitrary set of assumptions, and the results would be very different for, say, other values of shear rate and number concentration, the general implications are fairly clear. For particles of around 1 pm in size and greater and shear rates above about 10 s-l, adsorp-

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tion of high-molecular-weight polymers should occur predominantly by fluid motion rather than by diffusion, and the adsorption rate may be fairly slow in relation to the flocculation rate. Such effects have been shown to be important for polymer adsorption and flocculation in turbulent pipe flow [ 161 and in the adsorption of polymers on filter grains [ 171.

Floe break-up

In a sheared suspension, flocculation may initially occur quite rapidly, but the floes eventually reach a limiting size and no further flocculation occurs. This limiting size depends on the applied shear rate and on the strength of the floes. There is very little fundamental information on floe strength and break- up and most observations have been of a rather empirical nature. Polymeric flocculants usually produce stronger floes than simple salts and so the floes are larger under given shear conditions. Polymer bridging produces stronger floes than charge neutralisation, but in the former case, floes broken at high shear rates may not easily re-form. This irreversibility may be a result of re-confor- mation of adsorbed chains during the application of high shear or chain scis- sion [ 181. Floes produced by charge neutralisation appear to re-form readily after breakage and this could be a useful method of distinguishing between the two mechanisms [ 191.

One difficulty in studying flocculation in stirred vessels is that there are extreme variations in effective shear rate at different locations [ 201. Near the tips of rotating stirrer blades the shear rate can be 10 times greater than the average value over the whole vessel. The limiting floe size will depend on the maximum shear rate, whereas the rate of flocculation will be more closely linked with the average value.

FLOCCULATION MONITORING

A major reason for the rather limited knowledge on dynamic aspects of poly- mer adsorption and flocculation has been the lack of suitable experimental techniques, Most methods of assessing the extent of flocculation have involved sedimentation or filtration methods, which are not sufficiently rapid to give information on the early stages of the process. A recently developed technique [ 21,221, based on measurements of fluctuations in transmitted light intensity with flowing suspensions, gives a very sensitive indication of changes in the state of aggregation and is well suited to on-line measurements. The funda- mental basis of the technique has been discussed previously [ 231 and examples of its use in flocculation and dispersion monitoring have been given [ 241. Bas- ically, the transmitted light intensity is converted, by a sensitive photodetec- tor, into a voltage, which consists of a large dc component and a much smaller fluctuating (ac) component. The root mean square (rms) value of the fluc-

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r--i

’ f ’ *

1 I M r Suspension

I I I I I I I I

(b) Time

--- l --_-_-_--_

(a) t

Fig. 3. (a) Schematic arrangement for batch flocculation testing. (b) Typical responses from the monitor after polymer dosing. ( 1) “Optimum” polymer dose with dilute suspension. (2 ) Higher than optimum dose with dilute suspension. (3) Sub-optimal dose with concentrated suspension.

tuating part of the signal is measured and divided by the dc value to give a ratio, R ( = rms/dc) , which increases as aggregation occurs. In most cases of practical interest, R provides a much more sensitive indication of aggregation than could be obtained by simply measuring the average transmitted light in- tensity (i.e. the dc value). For real aggregating suspensions, with irregular particles and a range of aggregate sizes, it is not possible to derive quantitative information, for instance on the aggregate size distribution, but the ratio value, R, is a very useful empirical index of the degree of flocculation of a suspension and shows up many of the effects discussed previously, such as the slow ad- sorption of polymer and the break-up of floes at high shear rates.

Test procedures

A simple means of studying flocculation in a stirred vessel is shown sche- matically in Fig. 3a. The suspension is stirred at a controlled rate and sampled continuously through a tube which passes to the monitor. For a sampling rate which is not too low and a fairly short length of tubing, the time lag between the stirred vessel and the monitor can be made very short (of the order of a second or so), so that changes occurring to the suspension in the vessel are almost immediately apparent as variations in the monitor output. The shear rate experienced by suspensions in tube flow can be quite high and cause dis- ruption of aggregates, but it is usually possible to ensure that the shear rate in the tube is less than that in the stirred vessel so that break-up would not be a problem. Depending on the quantity of sample, the sampling rate and the du-

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ration of a test, the flow from the monitor can either go to waste or be re- circulated, as shown.

When a polymeric flocculant is added to the suspension, several types of response may ‘be found, and the characteristic features of some of these are shown in Fig. 3b. For fairly dilute suspensions, and for polymer doses around optimum, a distinct lag time can be seen, followed by a sharp rise in the R value. In many cases this rise appears to be linear with time over an appreciable period and, although no theoretical basis for the linearity has yet been found, the slope of the line provides a useful empirical measure of the “flocculation rate”. It seems very likely that the observed lag time is a result of slow polymer adsorption discussed previously. The most rapid flocculation occurs only when the particles have adsorbed sufficient polymer, which may be a substantial fraction of the amount added initially. When excess polymer is added, the lag time can effectively disappear and flocculation begins immediately after add- ing the polymer, at a rate similar to that achieved eventually at the optimum dosage. However, this rapid rate is not maintained and the monitor response soon levels off. Again, this behaviour can be explained in terms of polymer adsorption kinetics, since the amount of polymer added is well above optimum and only a small fraction needs to adsorb in order to give the most rapid floc- culation rate. For instance, if, at, “optimum” dosage of flocculant, 90% of the added polymer must adsorb to give the most rapid rate, a five-fold increase in the polymer dosage implies that only 18% of the added polymer needs to be adsorbed to give the same flocculation rate. According to Eqn (2) this would give an ll-fold reduction in the adsorption time. At longer times, excess poly- mer adsorbs and may cause restabilisation of the particles and a declining floc- culation rate. Even at the optimum dosage, the monitor response eventually levels off, as the floes grow to a limiting size, determined by the shear condi- tions in the stirred vessel. Some examples of experimental results with fairly dilute suspensions will be given in the next section.

In more concentrated suspensions, adsorption rates become too rapid for any lag time to be apparent in a set-up like that in Fig. 3a. However, another effect may be found when the amount of added polymer is below that required to give the most rapid flocculation rate. At sub-optimal polymer concentra- tions, a brief period of rapid flocculation can be observed, followed by a steep decline in the monitor response, almost back to the value for the original, un- flocculated suspension [ 251. The peak in the monitor response can be very sharp, lasting only a few seconds, and most monitoring techniques are not rapid enough to detect such effects. If more polymer is added after the response has fallen, another peak can occur, higher than the first, followed by another decline to a level rather higher than the previous value. This procedure can be repeated many times until, eventually, the response rises to a limiting value and there is little or no subsequent decline. The reason for this behaviour has not been firmly established, but it may be associated with the extreme range

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Fig. 4. Schematic arrangement for continuous flocculation monitoring.

of shear rates in stirred vessels, mentioned previously. Flocculation may occur in regions of fairly low shear, but the amount of polymer added may not be sufficient to produce floes able to withstand the very high shear rates close to the stirrer blades. So, the brief initial rise in the monitor response would be caused by floes withdrawn from the vessel before they had experienced the highest shear rate. After a few seconds, all of the remaining suspension would have passed through regions of very high shear and the initially-formed floes would be mostly disrupted. Another possibility is that the added polymer may not be mixed sufficiently rapidly and, near the point of addition, particles may acquire sufficient to form floes. With further stirring, redistribution of poly- mer among the particles could then occur, leading to a disruption of the floes formed initially. On balance, the first of these explanations seems the more likely.

While the simple arrangement in Fig. 3a provides a useful means of following a flocculation process in some detail, it is a batch method and not well suited to the routine evaluation of different polymers over a range of conditions. Some form of continuous test would be more convenient and one possibility is shown schematically in Fig. 4. This uses laminar tube flow as a means of promoting particle collisions and hence flocculation. The extent of flocculation for a fully- destabilised suspension in tube flow can be calculated fairly simply [ 261 and depends only on the tube dimensions. By mixing suspension and polymer and flowing the dosed suspension along a suitable length of tube (such that de- tectable aggregates can form), to a flow-through monitor, it should be possible to investigate different polymers over wide concentration ranges in a very con- venient manner.

In practice, a continuous flow-through test method, like that in Fig. 4, can give misleading results with some polymeric flocculants. In effect, by measur- ing at a certain distance downstream from the dosing point, just one point from curves like those in Fig. 3b is chosen and, depending on the point selected, the monitor response may not truly reflect the effectiveness of the polymer at the given dosage. The main problem is relatively slow polymer adsorption, which, as we have seen, is likely to be found in sheared suspensions. A length of tubing chosen to give measurable aggregation of a fully-destabilised suspension may

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TABLE 1

Properties of the polymers used

Polymer % Cationic Intrinsic viscosity (cm3 g-‘)

Molecular weight Diameter (nm)

A 30 2.0 4.5 x 105 60 B 30 6.5 2.7x lo6 110 C 50 7.0 3.0 x 106 260

provide insufficient opportunity for adequate polymer adsorption, so that very little change in the monitor response would be observed. Clearly, for rapidly- adsorbing polymers, this would be less of a problem. Some examples will be given in the next section.

EXPERIMENTAL

In this section, some selected examples of results using the test procedures previously described will be given. These are taken from systematic studies which will be fully reported elsewhere.

Materials

The polymeric flocculants used were kindly supplied by Allied Colloids Ltd and were all copolymers of a&amide and dimethylamino-ethylacrylate (DMAEA), the latter fully quaternised to give strong cationic groups. The intrinsic viscosity and proportion of DMAEA (and hence the % cationic char- acter) were given by the manufacturer. The molecular weights were calculated from the Mark-Houwink equation, using the constants lz= 3.7 x low2 cm3 g-l and a! = 0.66. The dimensions of the polymers in 0.2 M NaCl were determined by photon correlation spectroscopy (i.e. from the diffusion coefficients). The properties of the polymers used, designated A-C, are given in Table 1. These were prepared as 1 g 1-l solutions and diluted as required.

The suspensions used were as follows: Kaolin: SPS grade kaolin (English China Clays) dispersed in water at pH 7

and fractionated by sedimentation to give particles predominantly below 2 pm in size.

Silica: Sikron F 600 (Quarzwerke GmbH, Cologne, F.R.G. ) dispersed in water and fractionated by sedimentation to give particles mainly in the size range l-3 pm.

Yeast cells: compressed baker’s yeast (DCL) dispersed in water and used immediately.

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All reagents used were of Analar grade. The water was from an Elga ‘Spec- trum’ reverse osmosis/activated-carbon/ion-exchange unit.

Methods

Test procedures like those shown in Figs 3a and 4 were used. In the case of the batch tests, suspensions were stirred in a beaker, using either a paddle stirrer or a magnetic stirrer. For continuous tests the suspension and polymer solution were pumped at equal rates and mixed in a three-way tap before flow- ing through a 2-m length of coiled l-mm diameter tubing. The polymer dosing rate was changed by changing the concentration in the feed solution.

In both cases the monitor used was a PDA 2000 (Rank Bros Ltd, Bottisham, Cambridge, U.K.), which enables a suspension flowing through transparent tubing to be monitored directly in the tube, without the need for a separate flow cell. The outputs from the PDA 2000 represent the mean (dc) value of the transmitted light intensity, the rms value of the fluctuating (ac) compo- nent and the ratio of these quantities (R=rms/dc). In the results presented here only the ratio output will be considered. In all cases a l-mm tube was used.

RESULTS

Batch tests: effect of stirring rate

The system chosen here is a 100 mg 1-l kaolin suspension, flocculated with polymer B at a concentration of 0.5% (expressed as w-t% of the kaolin). The polymer was added as a 0.1% solution to 200 ml of suspension, stirred at var- ious rates with a two-blade paddle stirrer. At the maximum stirring rate (200 rpm) the mean shear rate is estimated to be about 250 s-l. Suspension was sampled at a flow rate of about 3 ml min-’ through the monitor and the ratio response was recorded continuously on a chart recorder. Generally, tests lasted for less than 10 min and so no recirculation was necessary. The results are shown in Fig. 5.

As the stirring rate is increased the flocculation rate becomes greater (as judged by the slopes of the linear parts of the curves) and the time to achieve the maximum rate is reduced. Both of these effects are consistent with the concepts outlined previously - the increased flocculation rate is simply a result of the higher rate of shear-induced particle-particle collisions and the reduced lag time indicates that the required amount of polymer is adsorbed more rap- idly at higher shear rates. The size of the polymer molecule and the shear rates used are such that orthokinetic transport would be more important than dif- fusion in the adsorption process.

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Fig. 5. Ratio response after adding polymer B (0.5% w/w) using the arrangement of Fig. la at different stirring rates.

to a 100 mg 1-l kaolin suspension,

Batch tests: effect of polymer type

In this case the suspension is of silica particles at 65 mg I-’ concentration, stirred at 200 rpm in the same set-up as that used for the kaolin suspension. Polymers A, B and C were used at about their optimum concentrations. In the case of A and B the optimum was about 0.16% by weight of the silica and for C about 0.08%, because of the higher charge density. All of the results shown are for salt-free suspensions, where cationic polyelectrolytes have a rather nar- row range over which flocculation occurs [ 151. Data have been obtained at various salt concentrations but the interpretation of results is complicated by the broader range of effective polymer dosage. In salt-free water, the polyelec- trolyte chains are expected to be in a rather extended configuration and to have dimensions larger than those quoted in Table 1 (which were obtained in 0.2 M NaCl) . The ratio, R, is plotted as a function of time after adding polymer in Fig. 6.

All of the polymers show an initial lag period, followed by a nearly linear rise in R with time. A simple measure of the lag time can be obtained by extrapo- lating the linear part back to the initial value. This procedure gives times of 5.2, 3.2 and 2.1 min for polymers A, B, and C, respectively, which are in the correct order on the basis of molecular size, if orthokinetic adsorption predom- inates. The largest polymer ( C ) should have the highest adsorption rate con- stant and the shortest adsorption time, as observed. If diffusion were the important transport mechanism, the lag times would be in the reverse order. The slopes of the lines indicate that the flocculation rates increase with mo-

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I I 5 IO

Time hin)

Fig. 6. Ratio response after adding polymers A (0.16% w/w), B (0.16%) and C (0.08% ) to a 65 mg 1-l silica suspension, using the arrangement in Fig. la at a stirring rate of 200 rpm.

lecular size, since they are in the order C > B > A, although this would need to be confirmed by an independent technique.

Batch versus continuous tests

In this case yeast suspensions were used at a concentration of 1 g 1-l (ex- pressed as dry cell mass), using polymers B and C. In the batch tests the sus- pensions were stirred with a magnetic stirrer and sampled through the monitor at a rate of about 5 ml min-I. For various dosages of cationic polymers the ratio response was monitored and gave traces similar to those described pre- viously. In order to compare the effects of different polymers at different dos- ages and for comparison with the continuous tests, we shall quote only the response obtained two minutes after adding the polymer. At around optimum dosage, this time is sufficient to reach a limiting value of the ratio output. For

247

I-

3-

>-

I -

I

I

i

x’ x’

/

3 - _x- --_

-- , ‘X-- - - - - _x-

Fig. 7. Comparison of ratio response for polymer B at various dosages with a 1 g 1-l yeast suspen- sion, using batch ( 0 ) and continuous ( X ) testing.

the continuous tests, yeast suspension and polymer solution were mixed and flowed through 1 m of coiled l-mm tubing to the monitor at a total flow rate of about 10 ml min-‘.

The results of such tests, for polymers B and C, are shown in Figs 7 and 8, for which the monitor settings were identical in all cases, so that the ratio responses are directly comparable. Considering first the batch tests, it is clear that C is effective in rather lower amounts than B, only about half the dosage being required to give the maximum response. This must be a consequence of the higher charge density of C and indicates again the importance of charge effects. However, the maxima are at about the same level, implying similar degrees of flocculation at the optimum dosages. The results of the continuous tests are quite different for the two polymers. With C, the maximum response is found with a dosage slightly higher than in the batch tests, but the maximum

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4 I I

10 20 :o Polymer Dose (mg/g)

Fig. 8. As Fig. 7, but with polymer C.

value is not greatly different in the two cases. By contrast, polymer B shows very much lower responses at all dosages and no clear optimum.

The interpretation of these results becomes easier if the residence time in the tube between the dosing point and the monitor is considered. With a flow rate of 10 ml mine1 and a tube volume of only about 0.8 ml, the average resi- dence time is less than 5 s. Although this is a rather short time, simple calcu- lations [ 261 indicate that there should be sufficient particle collisions, induced by tube flow, to give a degree of aggregation comparable to that occurring after l-2 min in a stirred beaker however, this aggregation will only occur if the yeast cells are adequately destabilised in a very short time and this may not be the case with some polymers. The implication of the results in Fig. 7 is that polymer B adsorbs relatively slowly under tube flow conditions and that .ad- sorption is not complete when the dosed suspension reaches the monitor. The fact that polymer C does not show such a discrepancy between batch and con-

249

tinuous tests is consistent with the more rapid adsorption of this polymer in sheared suspensions (Fig. 6).

CONCLUSIONS

It has been shown that dynamic effects have to be considered carefully in assessing the action of polymeric flocculants in sheared suspensions. Under realistic conditions, the rate of polymer adsorption can be relatively slow, com- pared to the particle collision rate and this can have important implications in the interpretation of results from rapid flocculation tests. For a detailed inves- tigation of the flocculation of a suspension, after adding a chosen polymer at a particular concentration, the response from a suitable detector needs to be monitored from the moment of addition of flocculant until no further change occurs. An arrangement like that in Fig. 3a would be suitable for such a purpose and could give valuable information on, for instance, rates of polymer adsorp- tion and strength of floes (from the effect of increased stirring rate on the response). If a more rapid test procedure, for continuous or on-line monitor- ing, is required, then tube flow and optical monitoring is an attractive combi- nation. However, the results from such a test could be misleading under some conditions, because of slow polymer adsorption.

ACKNOWLEDGEMENTS

Some of the experiments reported here were carried out by A.F. Toussaint, as part of a project funded by Wiggins Teape Research and Development Ltd, and by S.-Y. Lee under a SERC CASE Studentship with BP Research plc.

REFERENCES

6 7 8 9

10 11 12 13 14

R.J. Akers, Flocculation, I. Chem. E. London, 1975. G.J. Fleer and J. Lyklema, J. Colloid Interface Sci., 55 (1976) 228. F. Csempesz and S. Rohrsetzer, Colloids Surfaces, 31 (1988) 215. R.W. Slater and J.A. Kitchener, Discuss. Faraday Sot., 42 (1966) 267. J. Gregory, Polymer Flocculation in Flowing Dispersions, in Th.F. Tadros (Ed.), The Effect of Polymers on Dispersion Processes, Academic Press, London, 1982, pp. 301-321. A. Amirtarajah and S.L. Trusler, J. Environ. Eng., 112 (1986) 1085. J. Lee and G.G. Fuller, J. Colloid Interface Sci., 103 (1985) 569. J.L. Cleasby, J. Environ. Eng., 110 (1985) 875. W.H. Grant, L.E. Smith and R.R. Stromberg, Faraday Discuss. Chem. Sot., 59 (1975) 209. L.A. Spielman, J. Colloid Interface Sci., 33 (1970) 562. T.G.M. van de Ven and S.G. Mason, Colloid Polym. Sci., 255 (1977) 468. T.W. Healy and V.K. La Mer, J. Colloid Interface Sci., 19 (1964) 323. R. Hogg, J. Colloid Interface Sci., 102 (1984) 232. W.E. Walles, J. Colloid Interface Sci., 27 (1968) 797.

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15 16 17

18 19

20 21

22 23 24 25 26

J. Gregory, J. Colloid Interface Sci., 42 (1973) 448. A.L. Wigsten and R.A. Stratton, ACS Symp. Ser., 240 (1984) 429-444. P. Sehn and R. Gimbel, Effect of Polymers on Particle Adhesion Mechanisms in Deep Bed Filtration, in J. Gregory (Ed.), Solid-Liquid Separation, Ellis Horwood, Chichester, 1984, pp. 315-341. A.F. Horn and E.W. Merrill, Nature, 312 (1984) 140. W. Ditter, J. Eisenlauer and D. Horn, Laser Optical Method for Dynamic Flocculation Test- ing in Flowing Dispersions, in TbF. Tadros (Ed.), The Effect of Polymers on Dispersion Processes, Academic Press, London, 1982, pp. 323-341. L.A. Glasgow and Y.H. Kim, J. Environ. Eng., 112 (1986) 1158. J. Gregory and D.W. Nelson, A New Optical Method for Flocculation Monitoring, in J. Gre- gory (Ed.), Solid-Liquid Separation, Ellis Horwood, Chichester, 1984, pp. 172-182. J. Eisenlauer and D. Horn, Colioids Surfaces, 14 (1985) 121. J. Gregory, J. Colloid Interface Sci., 105 (1985) 357. J. Gregory and D.W. Nelson, Colloids Surfaces, 18 (1986) 175. T.O. Kayode and J. Gregory, Water Research, in press. J. Gregory, Chem. Eng. Sci., 36 (1981) 1789.

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DISCUSSION

H.N. STEIN (Eindhoven University of Technology, Eindhoven, The Netherlands)

One difficulty in interpreting coagulation data in sheared suspensions is that, unless you take extensive precautions, the shear rate tends to vary over your sample. This is especially true for your batch reactor, where the onset of tur- bulence usually occurs at quite low stirring rates. How did you ensure that the presence of the polymers does not change the flow pattern by suppressing tur- bulence, such as to endanger the comparison between your Figs 7 and 8? Such a suppression of turbulence might be caused by the increase in viscosity due to the presence of the polymer, which is probably not identical for your polymers B and C.

J. GREGORY (University College London, London, United Kingdom) It is unlikely that with the very low polymer concentrations used in our work,

that effects on turbulence would be important. The striking differences be- tween Figs 7 and 8 apply to the case of tube flow, which was always laminar.

S. HARLEY (University of Bristol, Bristol, United Kingdom) (1) Would you expect, and have you observed, differences in floe morphol-

ogy between charge-destabilised systems and polymer-destabilised systems? (2) Does the system represented by Fig. 3 (b ) (curve 3) have any added

electrolyte? In the case where there is only a small primary maximum is it possible that polymer bridging acts to bring the particles close together and thence into a primary minimum, thus enhancing the aggregation rate?

J. GREGORY (University College London, London, United Kingdom) (1) No systematic studies on floe morphology have been conducted. Many

qualitative observations indicate that for given shear conditions, polymeric flocculants produce larger floes than simple salts, because of the stronger bind- ing. Larger floes are more open in structure than smaller ones. (2) In our experiments, the electrolyte concentration was 10m3 M NaCl. It

is likely that, in bridging flocculation, particles are not in true (“primary min- imum”) contact. Polymer bridges can often span the distance over which elec- trical repulsion operates. Rate enhancement is much more likely to be due to an increased collision radius, as a result of the adsorbed polymer.

L. WAGBERG (STFI, Stockholm, Sweden) Since most of Dr Gregory’s experiments are performed in turbulent suspen-

sions the discussion on the time scale of different processes should include turbulent effects. This has been done by, for example, Argaman and Kauf-

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mann, Glasgow, and Saffman and Turner. Argaman and Kaufman derived tur- bulent diffusion coefficients from spectral analysis of velocity fluctuations which were of the order of 1000 times the ordinary diffusion coefficients. Saff- man and Turner also derived equations for the collision frequency between particles, smaller than the microscale of turbulence, in turbulent flow. These equations could be used as a comparison. They would probably show very fast adsorption and flocculation processes, dependent on a number of factors such as particle concentration, shear field, polymer, etc.

J. GREGORY (University College London, London, United Kingdom) All calculations were based on the assumption of uniform laminar shear and

no attempt was made to compare the predictions with the results obtained in stirred vessels. However, in such systems, the rates of polymer adsorption and flocculation would probably be of the same relative order as that calculated for laminar shear. Absolute rates could depend greatly on the particle (and poly- mer) concentration.

E. PELSSERS (Agricultural University, Wageningen, The Netherlands) (a) Smoluchowski predicts a gradual decrease of primary particles as func-

tion of initial particle concentration. In the case that the adsorption and con- formation change of the polymers is much slower than the particle collision frequency, flocculation can be prohibited. This is the case at low initial particle concentration and this is non-Smoluchowski behaviour.

( b ) For p01y ( ethylene oxide ) [ Mviscosity = 8. 106] adsorption on polystyrene latex we find non-Smoluchowski aggregation.

J. GREGORY (University College London, London, United Kingdom) The Smoluchowski expressions are for collision frequencies and need to be

modified by a collision efficiency factor (cu) to give aggregation rates. During polymer adsorption, a! may vary considerably, giving different aggregation rates, although the collision frequency may be correctly given by the Smoluchowski result. Non-Smoluchowski aggregation arises when the polymer adsorption is SIOW and the amount of polymer added is only just sufficient to cause floccu- lation. There is then a long period before flocculation begins. The same applies when the polymer is added in excess, so that for a certain period the particles are destablised, but subsequently acquire sufficient polymer to cause re-sta- bilisation. Alternatively, the initial period of flocculation may correspond to an extruded configuration of the adsorbed polymer. With a “flatter” configu- ration, bridging may no longer be possible.

A. HOWE (Institute of Food Research, Norwich, United Kingdom) Concerning polymers in flow fields, if the flow is sufficiently high to align/

stretch the polymer in the direction of the flow, will the particles also be aligned?

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If this is the case then is the cross-sectional area of the polymers, as seen by the particles, reduced (rather than increased as you suggested).

J. GREGORY (University College London, London, United Kingdom) In a shear field, particle aggregates and polymer chains tend to rotate, rather

than adopt a given alignment. This should give an enhanced chance of capture.