The role of floc density in solid-liquid separation

The Role of Floe Density in Solid-liquid

Separation Professor John Gregory

Department of Civil and Environmental Engineering, University College London, Gower Street, London, WC1 E 6BT, UK

Presented at the Filtech Europa 97 Conference in Diisseldorf, Germany on 16 October 1997

Flocculation is a very important step in many solid-liquid separation processes and the structure of floes can greatly influence the efficiency of separation. Floes are typically fractal objects, for which the density decreases appreciably with increasing floe size. The open structure of large floes can give much lower sedimentation rates than for more compact floes of the same mass, because of increased drag. For similar reasons, cake filtration rates can be affected by floe density. Basic concepts of fractal aggregates are briefly reviewed, and the factors which influence floe density considered. Some important practical consequences are discussed.

F locculation is often of crucial importance in solid-liquid separation. Aggregates of fine particles (floes) are formed in coagulation/flocculation processes, so that separation can

be carried out more efficiently. For instance, filtration processes can be greatly enhanced by a prior flocculation step. This is the case for depth filtration, where fine particles (of the order of 1 pm) are not readily captured by typical filter grains, and also in various dewatering operations, where filter cakes of very low permeability can be formed if the particles are very small. In both cases increasing particle size by flocculation can greatly improve the filtration performance. Sedimentation rates can also be greatly enhanced by flocculation. However, flocculation not only increases the effective particle size, but can also produce aggregates of rather low density. This too has significant implications for solid- liquid separation.

The growth of particle aggregates or floes, under many conditions, leads to rather open fractal structures, for which the effective density decreases as the size increases. This has extremely important practical consequences as well as being of considerable fundamental interest. The basic concepts of aggregate growth and form will be reviewed, together with some discussion of practical implications.

Figure 1: Two dimensional model of self-similar aggregate structure.

FRACTAL NATURE OF FLOCS

When solid particles aggregate, no coalescence can occur and the resulting clusters may adopt many different forms. In the sim- plest case of equal spheres, there is no doubt about the shape of a doublet, which must be in the form of a dumbbell. However, a third particle can attach in several different ways and with higher aggregates the number of possible structures rapidly increases. In real flocculation processes, floes containing hundreds or thou- sands of primary particles can arise and it is impossible to provide a detailed description of their structure. Some convenient method is needed, which enables aggregate structure to be characterised in general terms, but still conveying useful information. A great deal of progress was made in this area during the 1980s largely as a result of computer simulation of aggregate formation and the study of model aggregates.

MODEL STUDIES: FRACTAL CLUSTERS

Aggregates are now recognised as fractal objects (Meakin, 1988). If, for a large number of aggregates, the mass is plotted against aggregate size (diameter, for example), the plot may be linear, but with a non-integer slope. (For regular, 3-dimensional objects the slope of such plots is 3). For aggregates, the slope of the line, d,, is called the fractal dimension, and can be considerably less than 3.There are several other ways of defining fractal dimension (e.g. Jiang and Logan, 1996). Strictly, d, should be called a mass fractal dimension, but the general term will be used here. The lower the fractal dimension, the more open (or ‘stringy’) is the aggregate structure.The relationship between aggregate mass, M, and size, L, is just:

M a Ldfi- (1)

The ‘size’ L can be defined in various ways and in fundamental studies it is often taken as the radius of gyration of the aggregate. However, the precise definition of L does not affect the form of eq (1) and it may be convenient to use the largest diameter of an irregular aggregate as the measure of its size. If the relationship in eq (1) applies over a wide range of aggregate sizes, then it implies that the aggregates have a self-similar structure, which is independent of the scale of observation (or the degree of magnifi- cation).This concept is illustrated schematically in Figure 1, where the fundamental unit is assumed to be a triplet of equal spheres and the structure shown has four levels of aggregation. This simple 2-dimensional picture is not intended to represent real aggregates, but only to convey the idea of self-similarity. It is reminis- cent of earlier ideas (e.g. Michaels and Bolger, 1962) on the

.::::. .::::. .::::. ::::: l-l -. = z g ; t% x ‘; 8 3 ; e G % . 2 0 3

(4 (b)

log (size)

Figure 2: Schematic diagram of a) particle cluster and b) cluster-cluster aggregation, showing the corresponding log-log plots of aggregate mass vs. size. Fractal dimensions are the slopes of these lines.

‘hierarchical’ nature of aggregation, in which small aggregates combine to form larger ‘floes’. Such models were normally restrict- ed to just a few discrete levels of aggregation, rather like the simple picture in Figure 1. The essence of self-similar aggregates is that there is a continuum of levels from large-scale structures down to individual primary particles.

Computer modelling of aggregation has given very useful insight into the process. Early studies were based only on the ran- dom addition of single particles to growing clusters (Void, 1963). Later simulations (Meakin, 1988) of diffusion-controlled aggregation, with single particle addition gave fairly dense structures, with d, about 2.5. Diffusion-limited aggregation (DLA) implies that there is no repulsion between colliding particles and that each collision leads to attachment.

In many cases, single-particle addition is not a realistic model, since, throughout most of an aggregation process, growth occurs as a result of cluster-cluster encounters. In this case, simulations and experimental studies on a range of model colloids (Lin et al, 1989) show much more open structures with a fractal dimension of around 1.8.

Intuitively, there is a simple reason for the difference in structure of aggregates produced by particle-cluster and cluster-cluster aggregation, illustrated in Figure 2 In the former case, a particle is able to penetrate some way into a cluster before encountering another particle and sticking. In an encounter of two clusters the first contact is likely to occur before the clusters have inter-pene- trated to a significant extent, which leads to a much more open structure.

When there is inter-particle repulsion, so that the collision efficiency is reduced, aggregation is then said to be ‘reaction-limited’ and very different aggregate structures can be obtained under these conditions. It is found (Lin et al, 1989) that reaction limited aggregates are more compact than those produced by DLA, with a fractal dimension d r = 2.1, for the cluster-cluster case. Again, it is not difficult to find an explanation for this effect. When the collision efficiency is low, particles (or clusters) need to collide many times before sticking occurs. This gives more opportunity to explore other configurations and to achieve some degree of inter- penetration.

Less attention has been paid to aggregates produced by mechanisms other than diffusion. There is evidence that ‘ballistic’ aggregation (where encounters occur as a result of linear trajecto- ries) gives rather more compact structures, especially in the particle-cluster case, where d, can approach a value of 3. In the cluster-cluster case simulations of ballistic aggregation give d, c 1.9 (Tence et al, 1986). It is not clear how ballistic aggregation relates to shear-induced collisions and orthokinetic flocculation.Torres et a/ (1991 b), have simulated aggregation in viscous flows and found that aggregates produced by cluster-cluster encounters in shear and extensional flow are very like those formed by DLA, with

d r ^- 1.8. For particle-cluster aggregation, much more compact structures result with d, values up to about 2.9, although there is some dependence on the nature of the flow.

Experimental studies on practical systems have shown good agreement with computer simulations and model studies. For instance, measurements of fractal dimensions of aggregates formed from colloidal nickel hydroxy carbonate have been report- ed by Hoekstra et a/ (1992), for both perikinetic and orthokinetic aggregation and for high and low colloid stability. Although their systems were far from ideal, the results were broadly in line with previous model studies and simulations. For rapid, diffusion controlled aggregation, a fractal dimension of 1.7 - 1.8 was found. At low salt concentration, where aggregation was reaction limited, d, was in the region of 2.0 - 2.1. For orthokinetic aggregation (in Couette flow) at high salt concentration, d, was found to be shear- dependent, increasing from 1.7 at zero shear to about 2.2 at a shear rate of 200 s-l. For orthokinetic collisions under reaction- limited (low-salt) conditions, fractal dimensions up to 2.7 at 200 s1 were found. Salt-induced aggregation of latex spheres in Couette flow (Jiang and Logan, 1996) gave rather low fractal dimensions (about 1.5 - 1.8), but in a paddle mixer somewhat higher values were found.

The assumption so far that contacts between particles, once formed, are permanent, means that aggregates cannot undergo any subsequent restructuring. In fact, changes in aggregate structure have often been observed, always giving more compact forms (higher dr). For example, Aubert and Cannell (1986) found that coagulation of silica particles, under diffusion-controlled conditions, initially gave aggregates with d, = 1.75, but, after a few hours, these became more compact, with d, R 2.1, which is the value achieved by reaction-limited aggregation.

It is very likely that agitation, as in stirred vessels, is effective in giving some compaction of floes (higher dF), probably by caus- ing some deformation and re-arrangement. Another possibility is that breakage and re-formation of floes in sheared suspensions leads to more compact structures (Clark and Flora, 1991). The nature of the interaction between particles in a floe must be important in this context.This a subject of great practical interest, but it has not received much fundamental attention.

FLOC DENSITY

A very important consequence of the fractal, self-similar nature of aggregates is that their density decreases appreciably as the size increases. Actually, such behaviour had been empirically observed well before the concept of fractal aggregates was introduced. Lagvankar and Gemmell (1968) found that floes produced under water treatment conditions had effective densities that decreased markedly with increasing size. Similar observations had been made in Japan from the 1960s by Tambo and co-workers (see Tambo and Watanabe, 1979).

The effective, buoyant density of an aggregate in a liquid, ps is simply:

(2)

where ps, pL and pF are the densities of the solid particles, the liquid and the aggregate (floe), respectively, and OS is the volume fraction of solid in the floe.

Since most measurements of floe density involve some form of sedimentation procedure, the buoyant density, ps is the relevant property. When pE is plotted against the floe size, a, in log-log form, a linear decrease is often found, implying a relationship of the form:

p,, = Bd (3)

where 6 and y are constants. The log-log plots from floe density measurements are often

like that shown schematically in Figure 3.There is typically a high degree of scatter about the best fit line, which means very substantial variation in the density of floes of a given size. Nevertheless, there is usually a good linear correlation and the slope of the line can be quoted with some confidence.

. ,Becau’se of the proportionality between pE and $s, it follows that the exponent y is related to the fractal dimension:

dF = 3-r (4)

Measurements of aggregate densities for many suspensions of practical interest, including mineral particles, sewage sludges and aluminium hydroxide floes give y values in the range 1 - 1.4, corresponding to fractal dimensions of 2 - 1.6, which are in line with those obtained by simulation and in model systems. This lends considerable support to the idea of ‘universality’ in particle aggregation (Lin et a/, 1989).

The values of y quoted above imply a very substantial decrease in density with increasing floe size. With y = 1.2 (dr = 1.8), a 1 O-fold increase in size gives a 1 g-fold reduction in the effective floe density. For the same value of y, a lOOO-fold aggregate would have a size about 45 times larger than that of the primary particles and a solid content of only about 1%. In concentrated suspensions, the initial solids concentration may be a few volume percent, which sets a limit to the floe density. Zrinyi eta/ (1988) found a very large increase in settled floe volume, for the same mass of particles, as the solids concentration in flocculating suspensions was reduced, showing a marked reduction in floe density with decreasing solids concentration. Fractal growth concepts may not be so applicable in highly concentrated suspensions.

In practice, large, dense floes may be preferable, since they have high sedimentation rates and are more easily dewatered. In batch processes, where the predominant floe growth mechanism is cluster-cluster aggregation, the density of large floes will normally be quite low, because of the low fractal dimension. More compact structures can be obtained by the particle-cluster growth mechanism or by applying shear to give some restructuring. It is very significant that substantial improvements in filterability of floes can be achieved by recirculation of flocculated solids (Knocke and Kelley, 1987). In this way newly-introduced, unfloccu- lated particles are brought into contact with pre-formed floes and aggregation of the particle-cluster type would be expected.. The higher density of floes formed in upflow clarifiers, where incoming particles flow through a layer of pre-formed floe, can probably be explained by essentially the same reasoning.

SEDIMENTATION RATES

Sedimentation rates of floes formed under a variety of conditions have been measured by direct observation of individual floes, often using movie or video recording. Such techniques enable both size and settling rate to be determined and hence, with appropriate assumptions, the density can be derived. This approach was pioneered by Tambo and Watanabe (1979) and their data clearly showed the size-density relationship for floes, as in eq (3) and Figure 3, for a wide range of practical systems

--

0

0

. l a

\

Slope=-y l

log (size)

Figure 3: Form of size-density relation for flow

including kaolin-alum floes and activated sludge. Developments of the basic technique have been made by other workers including Farrow and Warren (1993) whose method avoids the problem of sampling floes and transferring them to a sedimentation column.

Because aggregates are not usually spherical, expressions for drag coefficient of spheres need to be modified by an empirical factor. The sphericity of floes is assumed to be around 0.8 and, for low values of the Reynolds number, Re, the drag coefficient is given approx- imately by Co = 45/Re (Tambo and Watanabe, 1979) almost twice the corresponding value for spheres (Stokes law). In most cases floes settle sufficiently slowly for Stokes-type expressions to apply.

Another uncertainty arises from the porosity of aggregates and the possibility of flow through the floe structure. The porosity of aggregates results in a decreased drag compared to that for an impermeable sphere of the same size and density (e.g. Chellam and Wiesner, 1993) and the effect becomes very significant for high porosities (fractal dimension less than about 2). This means that floes would settle faster than solid objects of the same size and density.

There is still some uncertainty over permeability effects and, in practice, they are often assumed to be negligible (e.g. Klimpel et a/, 1986). However, assuming that the Brinkman model is appropriate for calculating the permeability of fractal aggregates (see Chellam and Wiesner, 1993) then quite dramatic effects on sedimentation rates can be expected for fractal dimensions of 2 or lessThis is illustrated in Figure 4, where the settling velocity of a 2000-fold aggregate of spherical primary particles (1 pm radius, and with a density of 2.5 g/cm3) is plotted against the fractal dimension of the aggregate.The packing factor for particles in the aggregate is assumed to be 0.7 and the drag coefficient is taken as 45/Re. Results are shown for both permeable and impermeable aggregates. For rather dense aggregates, where the fractal dimension is close to 3, the results are very close and show a reduction in settling rate with decreasing d,. (This is because aggregates with lower d, have the same mass and are subject to the same gravitational force, but the drag is greater because of the larger size.) When d, approaches 2 the permeability of the aggregates gives an appreciably greater settling rate and for even lower densities, the settling rate begins to increase with decreasing d,. In this region, the aggregates are highly porous (solid volume fraction less than 10-3) and the flow through the pores more than compen- sates for the increased size.The theoretical basis for these results is not firmly established and there are several alternative models (see e.g. Lee et al, 1996). Nevertheless it seems probable that permeability effects are important in practice, especially for large floes of low fractal dimension (and hence low density).

COLLISION RATES OF FRACTAL AGGREGATES

The classical Smoluchowski treatment of aggregation kinetics is based on the assumption that the colliding particles are spheres. Even for spherical primary particles, aggregation quickly leads to irregular shapes, and their collision rates cannot be calculated exactly. Only in the case of coalescing liquid droplets could the assumption of spherical particles be justified. Generally, the collision rate between particles of type i and j, per unit time and in unit volume, is given by the second order expression:

where k,j is a rate coefficient and Ni and N, are the number concentrations of i and j particles.

For perikinetic (diffusion-controlled) aggregation, the growth of aggregates gives an increasing collision radius and a reduced diffusion coefficient and these effects tend to cancel out, giving a collision rate coefficient which is not greatly dependent on aggregate size. For fractal aggregates, the hydrodynamic radius (which deter- mines the drag and hence the diffusion coefficient) is likely to be somewhat less than the outer ‘capture radius’, corresponding to the physical extent of the aggregate. For high degrees of aggregation, the ratio of these two radii has been calculated to be about 0.6 (Torres et al, 1991 a).This means that Brownian collisions will occur rather more rapidly than predicted from Smoluchowski theory.

For diffusion-controlled aggregation, it can be shown that the

hydrodynamic radius of aggregates, R,, increases with time according to:

R, a t”dF (‘3)

This provides an experimental method of determining fractal dimensions in some cases. However, for aggregates greater than a few pm in size, perikinetic aggregation is negligible and collisions induced by shear become far more important.

In the orthokinetic case, where collisions are induced by fluid motion, it is the effective capture radius of a fractal aggregate that is of paramount importance and this is greatly dependent on the fractal dimension (e.g. Wiesner, 1992). The collision rate coefficient for orthokinetic collisions in a uniform shear field, with shear rate G can be written:

k = 4Ga(: ., <,h.+ .i iii i +I J )- (7) ‘I

Here, the i and j particles are assumed to be aggregates con- sisting of i and j primary particles and the primary particles are assumed to be uniform spheres of radius a,.The radius of an i-fold aggregate, with fractal dimension d,, is simply a,= a,,i’d’F. When d, = 3, i.e. for coalesced, non-fractal aggregates, eq (7) becomes identical to the Smoluchowski result for orthokinetic collisions:

k,, =+G(a, +a,)’ 63)

For typical fractal dimensions of around 2, eq (7) predicts very much faster growth of aggregates than the Smoluchowski result, eq (8). Not only do fractal aggregates grow more rapidly in terms of their mass (or aggregation number), but the effective size grows even more rapidly, because of the relationship between mass and size, eq (1).

Another important consequence of the fractal nature of aggregates arises from their permeability.This was discussed above in terms of sedimentation rates, but collisions of aggregates can also be influenced by permeability.

For solid, impermeable spheres of unequal size, hydrodynamic interactions can significantly reduce the collision frequency and hence the aggregation rate. Essentially, small particles follow curved fluid streamlines around larger particles and are captured much less readily than would be predicted on the basis of rectilinear motion (assumed in the Smoluchowski treatment). Including this effect in computations of orthokinetic collision rates (Han and Lawler, 1992) leads to the conclusion that the shear rate, G, plays a relatively minor role in flocculation. However, allowing for the permeability of aggregates gives intermediate results, so that the rectilinear assumption may not be so serious.

The strength of floes is of great importance in orthokinetic flocculation. Floes typically grow until they reach a certain limiting size, which depends on the applied shear rate. Larger floes are broken into fragments, which may then undergo further aggregation. The density of floes must play a very important role in determining their strength.The more compact the aggregate structure, the more inter-particle contacts there must be, since a given particle will have more close neighbours. Since the strength of a floe

0.5

k=2000

ap=lpm - - -Impermeable __ Permeable

I s.g = 2.5

3 E 0’ ‘G 3

i! z $

___---- _---

0 1.5 2 2.5 3

Fractal dimension

depends on the number and strength of bonds between particles, more compact structures must imply stronger floes. This is not entirely straightforward, since floe strength is often judged by a limiting diameter, which is related to mass through the fractal dimension. When inter-particle bonds are strong, as when polymeric flocculants are used, large, low density floes can form. With weaker binding, smaller aggregates are formed, which have a higher density, simply because of their lower size. The common statement that polymeric flocculants produce more open, low density floes is simply a reflection of the fact that they give stronger floes which can grow larger under given shear conditions. The lower density is an inevitable consequence of the larger size, if the floes have fractal character.

In a sheared suspension, the breakage and re-formation of floes leads eventually to more compact structures, simply because there is a range of floe densities produced and the higher density floes are more able to withstand the shear conditions. This is probably the main reason for the ‘restructuring’ of aggregates which has been often observed (e.g. Aubert and’cannell, 1986)

PRACTICAL IMPLICATIONS

Although the above discussion has been mostly in terms of rather ideal systems, there is no doubt that the structure of floes plays a very important part in practical separation processes. In many cases, compact, high-density floes are desirable, essentially because, for a given mass, the fluid drag is reduced.This implies higher sedimentation and cake filtration rates. However, when the floe structure becomes very open (low fractal dimension) permeability can become significant and could, in principle, lead to a reduced drag and an increased settling rate (see Figure 4). It is unlikely that open floe structures would give any benefit in cake filtration since such floes would be highly compressible, giving a less permeable filter cake.

It is possible to produce floes which are highly compact and which do not show the characteristic decrease of density with increasing floe size. These have become known as ‘pellet floes’ (e.g. Higashitani et al, 1987). In practice, they can be formed in fluidized beds, with some degree of agitation and with the aid of a high molecular weight polymer (Tambo and Wang, 1993). Although the mechanism of ‘pelleting flocculation’is still not entirely clear, it is likely that floe growth by single particle addition plays an important part, It was shown earlier (Figure 2) that particle- cluster aggregation tends to lead to higher fractal dimensions and hence denser floes. In a stirred fluidized bed newly introduced, destabilized particles come into contact with growing floes. The polymer gives high floe strength to withstand the shear forces and the agitation is likely to lead to some restructuring and densifica- tion of flocs.The high solids level in the fluidized bed also plays an important part.

There are cases where more open, less dense floes are advantageous.This is especially the case where capture processes in fairly dilute suspensions are involved. Here, the effective size of the floes is important, as discussed previously for the case of orthokinetic flocculation. Similar considerations are relevant in the case of deep bed filtration and in flotation processes.

Despite the practical importance of this topic, there is still rather limited information on a number of aspects, partly because of difficulties in measuring floe density under realistic conditions.

REFERENCES

Aubert, C. and Cannell, D.S. (1986). Restructuring of colloidal silica aggregates. Phys. Rev. Leti., 56, 738-741. Chellam, S. and Wiesner, MR. (1993). Fluid mechanics and fractal aggregates. Wat. Res., 27, 1493-1496. Clark, M.M. and Flora, J.R.V. (1991). Floe restructuring in varied tur- bulent mixing. J. Colloicf Intetiace Sci., 147, 407-420. Farrow and Warren (1993). Farrow, J.B. and Warren, L.J. (1993) Measurement of the size of aggregates in suspension. In Coagulation and Flocculation, Theory and Applications. Dobias, B (Ed)., Marcel Dekker, New York, pp 391-426. Han, M. and Lawler, D.F. (1992).The (relative) insignificance of G in

Ham, M. and Lawler, D.F. (1992).The (relative) insignificance of G in flocculation. J. Am. Water Works Assoc., 84(10), 79-91. Higashitani, K., Shibata, T., Kage, H. and Matsuno, Y. (1987). Formation of pellet floes from kaolin suspension and their properties. J. Chem. Eng. Japan, 20, 152-l 57 Hoekstra, L.L., Vreeker, R. and Agterhof, W.G.M. (1992). Aggregation of nickel hydroxycarbonate studied by light scattering. J. Co/bid Interface Sci., 151, 17-25. Jiang, Q. and Logan, B.E. (1996). Fractal dimensions of aggregates from shear devices. J. Am. Water Works. Assoc., 90, 100-l 13. Klimpel, R.C., Dirican, C. and Hogg, R. (1986). Measurement of agglomerate density in flocculated fine particle suspensions. Particle Science and Technology, 4, 45-59 Knocke, W.R. and Kelley, R.T. (1987). Improving heavy metal sludge dewatering characteristics by recycling preformed sludge solids. J. Water Pollut. Control Fed., 59, 86-91. Lagvankar, A.L. and Gemmell. R.S. (1968). A Size-density Relationship for Floes. J. Am. Water Works. Assoc., 60, 1040-1046. Lee, D.J., Chen, D.W., Liao, Y.C. and Hsieh, C.C. (1996). On the free-settling test for estimating activated sludge floe density. Wat. Res. 30, 541-550. Lin, M.Y., Lindsay, H.M., Weitz, D.A., Ball, R.C., Klein, R. and Meakin, R (1989). Universality in colloid aggregation. Nature, 339, 360-362. Meakin. I? (1988). Fractal aggregates. Adv. Co//ok! Interface Sci., 28,

249-331. Michaels, AS. and Bolger, J.C. (1962).The plastic flow behavior of flocculated colloidal sediments. Ind. Eng. Chem. Fund., 1, 153-l 62. Tambo, N.and Wang, XC. (1993)The mechanism of pellet flocculation by fluidized bed operation. J Water SRT-Aqua, 42, 67-76. Tambo, N. and Watanabe, Y. (1979). Physical aspects of flocculation. I. The floe density function and aluminium floe., Wat. Res., 13, 409-419. Tence, M., Chevalier, JR and Jullien, R. (1986). On the measurement of the fractal dimension of aggregated particles by electron microscopy: experimental method, corrections and comparison with numerical models. J. Physique, 47, 1989-l 998. Torres, F.E., Russel, W.B. and Schowalter, W.R. (1991 a) Floe structure and growth kinetics for rapid shear coagulation of polystyrene colloids. J. Colloid Intetface Sci., 142, 554-574. Torres, F.E., Russel, W.B. and Schowalter, W.R. (1991 b) Simulations of coagulation in viscous flows. J. Colloid interface Sci., 145, 51-73. Vold. M.J. (1963). Computer simulation of floe formation in a colloidal sediment. J. Colloid Sci., 18, 684-695. Wiesner, M.R. (1992). Kinetics of aggregate formation in rapid mix. Wat. Res., 26, 379-387.

Zrinyi, M., Kabai-Faix, M. and Horkay, F. (1988) On the sediment volume of colloidal aggregates. 1. A fractal approach to the problem. Prog. Colloid & Polymer Sci., 77, 165-l 70.

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As a service to readers who understand German, French or Spanish better tha; English, the abstracts for the Refereed Papers in this issue follow in these languages.

The role of floe density in solid-liquid separation, by J. Gregory: Pages 376-371

Die Rolle Von Flockungsdichte Bei Fest-flussigstoff-abscheidung J. von Gregory Flockung ist eine wichtige Stufe bei vielen Flussig-Feststoffabscheicfungsprozessen, und die Flockenstruktur kann die Wirksamkeit der Abscheidung stark beeinflussen. Bei Flocken handelt es sich gewohnlich urn fraktale Objekte, deren Dichte bei zunehmender FlockengroBe stark abnimmt. Die offene Struktur groBer Flocken kann viel geringere Sedimentationsraten ergeben als bei kompakteren Flocken des gleichen Volumens, was auf die erhohte Schleppkraft zuruckzufuhren ist. Aus ahnlichen Grijnden konnen die Kuchenfiltrationsraten von der Flockendichte beeinfluf3t werden (5 sn., 4 abb., 25 ref.).

Le role de la densite des floes en separation solide/liquide par J. Gregory La floculation est une etape tres importante dans beaucoup de procedes de separation solide/liquide et la structure des floes peut grandement influencer I’efficacite de la separation. Les floes sont typiquement des objets fractaux pour lesquels la densite decroit de facon substantielle quand la taille croit. La structure ouverte des grands floes peut causer des vitesses de sedimentation beaucoup plus basses que pour des floes plus compacts de meme masse, a cause du plus grand frottement. Pour des raisons similaires, les vitesses de filtration avec gateau peuvent etre affectees par la densite des floes. Les concepts de base des agregats fractaux sont brievement passes en revue et les facteurs qui influencent la densite des floes sont etudies. On discute quelques consequences pra- tiques importantes (5 pags., 4 figs., 25 ref.).

El papel de densidad de agregdos en separacio solido/ liquid0 por J Gregory Floculation es una medida muy importante en muchos procesos de separation de solidos/liquidos, y la estructura de 10s flocos pueden tener gran influjo sobre la eficiencia de separation. Se definen fla- cos camo objetos fractales; la densidad se reduce con aumento de tamatio del floco. La estructura abierta de flocos grandes puede producier muchos ritmos mas bajos de sedimentation que 10s con flocos mas apretados de la misma masa, a causa de la resistencia aumentada. Por esta razon 10s ritmos de filtration de tortas estan afectados por densidad de 10s agregados. Se examinan 10s con- ceptos basicos de agregados fractales, y 10s factores que influyen densidad de flocos. Se discuten las consecuencias practicas (5 pags., 4 figs., 25 refs.).

Simulation of the long-term behaviour of regeneratable dust filters, by Ch. Stijklmayer and W. Hiiflinger: Pages 373-377

Simulation del funcionamiento a Iargo plaza de filtros regenerables para polvo por Ch. Stdcklmayer y W HSiflinger Filtros regenerables periodicamente, con formation de tortas, han tornado un papel dominante comercial en la purification de aire, a causa de la capacidad excelente de acumular polvo. Sin embargo, debida a falta de modelos de calculo, son necesarias investiga-

ciones intensivas para disefiar optimamente filtros, sobre todo con respect6 a caida de presion residual despues de regeneration, que debe ser la mas pequena y estable posible. Se puede simular con el model6 el aumento de la torta de polvo sobre filtro (needle felt) incluyendo la regeneration del medio filtrante y el calculo de la caida de presion durante filtration y despues de regeneration. Se ha empleado el model6 para estudiar el influjo de 10s dos paramet- ros de tales filtros - la velocidad de filtration y la caida maxima de presion APmax, cuando hay regeneration - sobre la caida residual de presion. Se ha demostrado la rayon por que una alta caida maxima de presion APmax, y una alta velocidad de filtration pueden dar un aumento a largo plaza de la caida residual de presion de un filtro - efecto bien conocido de experimentation y, desde luego, no deseado (5 pags. 10 figs., 1 tab., 6 refs. ).

Simulation Des Langfristigen Verhaltens Regenerierbarer Staubfilter von Ch. Stijcklmayer und W Hljflinger Periodisch regenerierbare kuchenbildende Filter haben sich bei der Luftreinigung wegen ihrer ausgezeichneten Staubsammel- fahigkeiten eine kommerziell dominierende Rolle erworben. Mangels Berechnungsmodellen sind jedoch gewohnlich intensive experimentelle Untersuchungen erforderlich, urn derartige Filter optimal zu konstruieren, insbesondere im Hinblick auf den Restdruckabfall nach Regenerierung, der mdglichst gering und sta- bil sein sollte. Das in der vorliegenden Arbeit beschriebene Simulationsmodell ist in der Lage, die Entstehung eines kompress- iblen Staubfilterkuchens auf einem Nadelfilz einschl. Regenerierung des Filtermediums und Berechnung des Druckabfalls wahrend der Filtration und nach der Regenerierung zu simulieren. Dieses Model1 wurde dazu verwendet, den EinfluB der beiden wichtigsten Betriebsparameter derartiger Filter - die bei der Regenerierung anfallende Filtrationsgeschwindigkeit und den dabei stattfindenden maximalen Druckabfall APmax - auf die Geschwindigkeit und den maximalen Druckabfall zu untersuchen. Es wird dargelegt, wie ein hoher Druckabfall APmax und eine hohe Filtrationsgeschwindigkeit zur langfristigen Erhohung des Restdruckabfalls eines Filters beitragen konnen - eine Auswirkung, die aus Experimenten wohlbekannt ist und selbstverstandlich ver- mieden werden sollte (5 sn., 10 abb., 1 tab., 6 ref.).

Simulation du comportement a long terme de filtres depoussiereurs regenerables par Ch. Stticklmayer et W, Hijflinger Les filtres depoussiereurs a regeneration periodique ont joue un role preponderant sur le marche de la purification de I’air en raison de leur excellente aptitude au depoussierage.Toutefois, a cause du manque de modeles de calcul, des investigations experimentales intenses sont generalement necessaires pour calculer de facon optimale de tels filtres specialement pour assurer une chute de pression residuelle apres regeneration aussi petite et stable que possible. Le modele de simulation decrit dans cet article est capa- ble de simuler la croissance d’un gateau de poussieres compressible sur un feutre aiguillete y compris la regeneration du media fil- trant et le calcul de la perte de pression pendant la filtration et apres la regeneration. Le modele a ete utilise pour examinmer I’influence des deux parametres operatoires les plus importants de ces filtres pour la chute de pression residuelle, a savoir la vitesse de filtration et la chute de pression maximum quand la regeneration est effec- tuee. On montre pourquoi une chute de pression maximum elevee et une haute vitesse de filtration peuvent conduire a une augmen- tation a long terme de la chute de pression residuelle du filtre, un effet qui est bien connu par I’experience et doit par consequence etre evite (5 pags., 10 figs., 1 fab., 6 ref.).

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