A

The floe strength expressed in this way is a force per unit area (or pressure) and values from a few Nm'2 up to around 1000 Nm~2 have been reported, depending on the system. This means that, for typical floes of around 100 pm in size, the actual force required for breakage would lie somewhere in a range from nN - pN.

The number of particle-particle bonds per unit area must depend on the density of the floe and hence on the fractal dimension. For open, low density structures (low df), there will be few bonds per unit area and so the floes should be relatively weak. More dense floes should have higher strength. It may be that denser floes are more prone to surface erosion, rather than splitting (see Fig. 9), although there is little experimental evidence on this point. Furthermore, as aggregates grow, they become less dense, and the strength, as defined by Eq. (22) should decrease. This would be another factor determining the maximum floe size.

Another influence is the size of the primary particles. Generally, the smaller the primary particles, the stronger the floe [16]. This can be explained by the larger number of particles within an aggregate of a given size and hence the larger number of particle-particle contacts per unit area.

The strength of bonds between particles is extremely important in determining floe strength. When particles are coagulated by simple salts only van der Waals attractive forces are operative, giving rather weak aggregates. Hydrolysing metal salts and, especially, polymeric flocculants can give considerably stronger floes. High molecular weight polymers acting by the 'bridging' mechanism can give very strong (and hence large) floes.

In summary, floe strength is greater for:

• smaller primary particles

• stronger inter-particle attraction

5.3. Reversibility of floe breakage

Although it has long been recognised that floes may be quite fragile objects, which may be broken at increased shear rates, it is often assumed that this breakage is reversible, so that broken floes can re-form when the shear rate is reduced. However, for floes typical of those produced in water treatment plants, breakage may not be easily reversed. This effect has been known for some time (e.g. Francois [18]), and has more recently been the subject of systematic studies [8,19, 20].

Fig. 10 shows the results [20] of modified jar test experiments with continuous monitoring of Flocculation Index, in the same way as in Figs. 4 and 5. Kaolin clay suspensions (50 mg L"1) were flocculated with aluminium sulphate ('alum') and 2 commercial polyaluminium chloride products (PACla and PAClb). All were added at an equivalent dosage of 3.4 mg L"1 as Al. After a short rapid mix period (10s at 400rpm), floes were formed by stirring at 50 rpm for 10 minutes. The stirring speed was then increased to 400 rpm (an increase of effective shear rate by a factor of more than 20). The stirring speed was maintained at 400 rpm for 10 seconds and then restored to 50 rpm.

It is clear from Fig. 10 that the three coagulants give different plateau values of FI, indicating significant differences in floe strength, in the order PAClb > PACla > Alum. On increasing the stirring speed, the FI shows a sudden and very rapid decrease in all cases, showing extensive floe rupture, rather than surface erosion. When the stirring speed is restored to 50 rpm some increase in FI occurs, but only to a limited extent. This shows that for all these coagulants, floe breakage is only partially reversible. Although the three coagulants show quantitative differences in floe growth, breakage and re-growth, the relative degrees of breakage and re-growth are reasonably similar. This indicates that the mechanisms of flocculation are broadly similar.

The time for which the high shear rate is applied (the floe breakage time) has a significant effect, as shown in Fig. 11. Here the breakage time is varied from 10 s to 5 min, but other conditions are the same as for Fig. 10. The coagulant is alum (3.4 mg L"1 Al), but very similar results are found for the PAC1 samples. It is clear that increased breakage times do not give smaller floes - breakage seems to be practically complete after 10s. However, extended breakage times give less re-growth after the stirring speed is reduced. This is especially apparent for the 300s case.

Time (s)

Fig. 10. Floe growth, breakage and re-growth with three coagulants, all at 3.4 mg L"1 as Al. Arrow shows increase of stirring speed (floe breakage)

Fig. 10. Floe growth, breakage and re-growth with three coagulants, all at 3.4 mg L"1 as Al. Arrow shows increase of stirring speed (floe breakage)

Fig. 11. Flocculation, breakage and re-growth with alum (3.4 mg L"1 Al) for different breakage times. The figures on the curves are the times (s) that the stirring speed was held at 400 rpm

Fig. 11. Flocculation, breakage and re-growth with alum (3.4 mg L"1 Al) for different breakage times. The figures on the curves are the times (s) that the stirring speed was held at 400 rpm

Another important effect is that of rapid mix time [8], We have already seen in Fig. 5 that rapid mix time has a very significant effect on floe growth. However, the breakage and re-growth of these floes follows roughly the same pattern, irrespective of rapid mix time. The results in Fig. 12 are from the same experiment as Fig. 5, using PAClb at 3.4 mg L"1 Al, but in this case floe breakage (10s at 400 rpm) and re-growth (at 50 rpm) are also shown. In all cases floes break to about the same FI value and there are only minor differences in FI after re-growth. This means that, although floes formed after longer periods of rapid mixing are smaller, they break to a lesser extent and show more complete re-growth.

Fig. 12. Showing the effect of rapid mix time (400 rpm at times shown on curves) on floe growth, breakage and re-growth

Fig. 12. Showing the effect of rapid mix time (400 rpm at times shown on curves) on floe growth, breakage and re-growth

The irreversible floe breakage found for hydrolysing coagulants is not observed for some other additives. For instance, the cationic polyelectrolyte polyDADMAC shows almost complete re-growth of floes after breakage [19]. Fig. 13 shows the results of tests under the same conditions as for Fig. 10, for PAClb and polyDADMAC, except that in the latter case the period of floe growth at 50 rpm was extended to 30 minutes, because of the longer time

Fig. 13. Formation, breakage and re-growth of floes with PAClb and polyDADMAC

Fig. 13. Formation, breakage and re-growth of floes with PAClb and polyDADMAC

Several important points emerge from Fig. 13. The FI value achieved by polyDADMAC is considerably higher than with PAC1, indicating that the former gives larger and stronger floes. The slower onset of flocculation with polyDADMAC is explained by the relatively slow adsorption of this flocculant. Also it can be seen that the rate of flocculation is lower with polyDADMAC, even though the floes eventually grow larger. The explanation is essentially the same as that given earlier in relation to Fig. 4. The cationic polyelectrolyte destabilizes the particles by charge neutralization, but no new particles are produced, so the collision rate remains quite low compared to the 'sweep floe' case. In both cases, there is a sudden and very rapid decrease in FI when the stirring speed is increased, as before. However, the re-growth behaviour is quite different for the two additives. With the polyelectrolyte, re-growth of floes occurs to give nearly the same FI value as before breakage, indicating almost complete reversibility of floe breakage. By contrast, with PAC1, as shown previously, the broken floes re-grow only to a limited extent.

Reversible floe breakage would be expected when the interaction between particles is of an essentially physical nature, such as van der Waals or electrical attraction. The cationic polyelectrolyte in this case is of high charge and fairly low molecular weight, and is believed to act by an 'electrostatic patch' mechanism, giving electrostatic attraction between positive and negative 'patches' on the surfaces of neighbouring particles. There is no obvious reason why such bonds should not re-form after breakage. Particles coagulated by simple salts are held by van der Waals attraction and complete reversibility of floe breakage is found.

The irreversible floe breakage has been found for a wide range of coagulants based on aluminium and iron (III) [19], including pre-hydrolysed forms such as PAC1. It is very likely that, under most practical conditions, the effect of these additives depends on the precipitation of an amorphous metal hydroxide, which binds impurity particles together ('sweep flocculation'). Although the details are not clear, it is possible that the breakage of 'sweep floes' involves breaking chemical bonds within the hydroxide precipitate, and that this is responsible for the fact that broken floes do not completely re-form.

Since floe breakage is quite likely to occur under water treatment conditions, the irreversibility is likely to have important practical consequences. However, this aspect has received rather little attention so far.

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