Mechanisms of agglomerate growth in green pelletization

97

Powder Technology 7 (1973) 97-105 BElsevier

Sequoia

SA.,

Lausanne

- Printed

in The Netherlands

Mechanisms of Agglomerate Growth in Green Pelietization K. V. S. SASTRY

and D. W.

FUERSTENAU

Departtent of Malerialr Science and Engineering. Unimrsit_v of California, Berkele_v_ Calif. 94720 (U.S.A.) (Received

May 24, 1972)

Summary

T-HYSICAL

TJte mechanisms responsible for the formation a& growth of agglomerates in balling or granulation can be describedas nucleation, coalescence, abrasion transfer, breakage, and snowballing. TItese mecbanistns have been identijed by means of tracer studies using two calcites wbicb have similar green

pelletizing

behavior but dfferent fluorescent citaracteristics. Precise dejinitions of the growth mechanisms, so as to be usefulfor nlatheI,laticalnlodelilrg of agglomeration processes, are given. Further, bebanior of particulate materials growth mechanisms is discussed.

tke batch balling in terms of the

INTRODUCTION

For an understanding and quantitative representation of ball growth processes and for an evaluation of green ball products, it is necessary to have detailed knowledge of the mechanisms that give rise to agglomerate growth. Recently, Capes and Danckwerts’.3 found, by employing tracer studies, that breakage and layering is an important growth mechanism in the granulation of coarse, closely-sized sands. Based on experimental observations with pulverized iimestone (with a natural size distribution), Kapur and Fuerstenau77’8 proposed that coalescence is mainly responsible for agglomerate growth_ For mathematical modeling agglomeration processes, a complete Iist of the mechanisms and their precise definitions is required, but is not yet available. Providing such a summary is the major purpose of this paper. Specifically, growth mechanisms have been identified by using tracer experiments, and the results of these experiments are summarized in this paper.

CONCEPTS

Forces contributing to the formation of green pellets from particulate solids are of two kinds6: natural (or physical) and applied (or mechanical). The natural forces responsible for the formation of agglomerates can result from a number of sources: (a) the attraction between solid particles due to van der Waals’ forces, magnetic forces, or electrostatic charges, (b) the interlocking effects between particles, depending on the shape of particles, (c) the adhesional and cohesional forces in bridging bonds, which are not freely moveable, and. very importantly, (d) the interfacial and capillary forces due to the presence of a liquid phase. The strength of green agglomerates results from the physical forces that hold the particles together; and the magnitudes of these physical forces are dependent on the particle size, surface charge: crystal structure, the proximity of the particles, the amount of additive+ and other physical-chemical properties of the system. In a recent contribution, Rumpf’ l has given a detailed account of these forces and developed expressions for estimating their magnitude. His calculations indicate that the major contribution of the physical forces, in the presence of a liquid which completely wets the solid particle surface, is from the capillary attraction between the particles due to the air-liquid interfacial tension. These capillary forces are dependent on the relative distribution of the liquid and air phases in the porous agglomerate4-6.g-1’. When the ratio of the liquid to the void volume of the agglomerate is quite low, the liquid is held in discrete lens-like rings at the point of contact between particles; and the air phase forms a continuous phase (Fig_ la). The entrapped liquid is said to be in a pendular state. The strength of this pendular bond arises from the ne-

K. V. S. SASTRY. D. W. FUERSTENAU

98 gative capillary pressure and the surface tension of the liquid. By increasing the liquid content or by reducing the pore volume of the agglomerate, the liquid rings tend to coalesce and form a continuous network, resulting in the airphase becoming trapped. The agglomerate now is said to be in a funicular state (Fig. lb). Finally, the agglomerate is said to be in a capillary state when the void volume of the pellet is completely tilled by the liquid (Fig. 1~). FAIR o$

LIOUID

m

SOLID

In kinetic analyGs of the process of granulating particulate materisls, it is a common practice to refer to growth mer hanisms’*3*‘*8-‘o-1 z-r4 as responsible for agglomerate formation rather than to describe the procers in terms of the natural and mechanical forces. Such a viewpoint is advantageous and can be justified because of the incomplete quantitative understanding of the microscopic occurrence of the governing forces in pellet growth. Thus it may be considered that the so-called growth mechanisms are the phenomenological or macroscopic representation of the prevailing physical and mechanical forces.

MECHANISMS

OF GREEN

PELLET GROWTH

Fig. 1. Structure of a porous a_pglomeratewith referenceto the relative distribution of air-water-solid phases. (a) pendular (liquid trapped), (b) funicular (air trapped). (c) capillary (air expelled-liquid saturated).

Information for understanding of the growth mechanisms and their range of occurrence can be provided by means of tracer studies’. Capes and Danckwerts’ have shown, by means of tracer investigations, that breakage of smaller granules and layering of the resulting fragments on the surviving pellets is an important phenomenon in the granulation of particulate materials. However, their studies were limited to materials that were coarser and more closely sized than those encountered in common industrial practice. For investigating agglomerate growth mechanisms, a qualitative tracer investigation on cornminuted materials with a natural size distribution was undertaken in this study. Calcites from two regions (Texas and New Jersey) having different fluorescent characteristics were used in the tracer studies because it was not possible to uniformly dye the surface of the fine particles” in a polydispersed-size material (more-

Mechanical forces are required to bring the individual wetted particles, clusters or agglomerate species within the pelletizing charge into contact with one another so that the nat.ural forces can bring about their growth6. This mechanical action of moving the material is imparted by means of rolling, tumbling, agitating, kneading, extruding or compressing in a suitable apparatus. Agglomeration of damp powders makes use of tumbling or agitating the material in balling drums, discs or cones. The tumbling properties of the agglomerate charge are dependent on the physical properties of the powder, size distribution of the growing species, and size, geometry and speed of rotation of the balling device.

Fig. 2. Batch balling kinetics ofground calcites from New Jersey and Texas.

(b)

(cl

MECHANISMS

OF AGGLOMERATE

GROWTH

over, introducing a dye is likely to affect the wettability of particulates and hence change the pellet growth behavior). The calcites were prepared by grinding 4x 28 mesh feed in a laboratory ball mill. The ground calcites had nearly the same size distribution, e.g. the New Jersey calcite had 61 y0 and the Texas calcite 65 y0 by weight of material passing 400 mesh. The surface areas (as determined by a Petmaran air permeability apparatus) of the ground New Jersey and Texas calcite samples were 8300 and 8150 cm’/cm3, respectively. Preliminary studies on the batch balling kinetics of the Texas and New Jersey calcites with two different amounts of added water indicated similar growth trends. as shown in Fig. 2. Tracer studies The tracer studies essentially entail mixing of the two identifiable agglomerates (New Jersey and Texas) that had been growing separately under identical conditions and then pelletizing the mixture for the desired period before examination of their structure. Complete details of the tracer experimental procedure can be found elsewhere’*rs, but briefly a batch balling drum of 9-in. diameter and 6-in. length was used in these experiments. A drum rotational speed of 41 r-p-m. and a feed load of 500 g were chosen as the standard operating conditions. First the Texas and New Jersey calcites were agglomerated separately for N revolutions using W o/o water, and then these granules were mixed in different proportions and agglomerated for an additional 600 revolutions. The resulting agglomerates were sectioned into two halves through a random plane and photographed under ultraviolet light. The photographs of the sectioned green pellets from four typical tracer experiments are presented in Fig. 3, with the respective experimental conditions being included in the figure. The Texas and New Jersey calcites appear as black and white, respectively, photographed under ultraviolet illumination However, when a pellet consisted of a predominant portion of New Jersey calcite (white) with traces of a Texas calcite (black) layer. the contrast in a photograph is somewhat poor and direct observations under ultraviolet light are needed to identify such agglomerates_ Figures 3(a) shows the structure of the sectioned green pellets that were produced by agglomerating a mixture consisting of half New Jersey and half Texas calcite granules (N=200, W=15.8) for 600 revolutions. These sectioned pellets consist of black

99 and white patches which correspond to portions of Texas and New Jersey calcites, respectively. Thi: structure suggests that the agglomerates were growing by a clumping or coalescence. Pellet growth by this mechanism of coalescence was found to be the important mechanism in the earlier stages of the batch balling experiments run with different amounts of water. In a second test, equal proportions of New Jersey and Texas calcite granules (N= 120. W= 14.5) were mixed and agglomerated for 600 revolutions. Figure 3(b) presents the photographs of the resulting agglomerates, in which four types of granule structure can be observed: (I ) Clear evidence of growth by coalescence_ (2) Pellets with predominantly New Jersey calcite and small portions of Texas calcite. or r:ice rersa. (3) Texas calcite pellets with a layer of New Jersey calcite, (4) New Jersey calcite pellets with small amounts of Texas calcite layer. At first it was thought that type 2 pellets were produced by coalescence of two granules and type 3 by breakage and layering’ ; the type 4 agglomerates could not be explained. Then a close observation of several tracerexperimentswasmadewhichindicated that the breakage of an zgglomerate always results in two or three fragments with finite size and never produced a collection of fines. The broken fragments later disappear in a similar manner by which two individual pellets coalesce and give rise to type 2 pellets. Since the breakage event of a granule does not yield a collection of fines, the layering of type 3 pellets cannot be the result of breakage_ It appears that during the tumbling of the agglomerating charge the pellets must have transferred material by abrasion. Thus, the Texas calcite pellets picked up a layer of New Jersey calcite by abrasion to form the type 3 pellets. As indicated earlier. a layer of Texas calcite on New Jersey pellets is hard to observe in a photograph. However, a close observation of New Jersey pellets (which were found to be of type 4 by direct observation under ultraviolet light) in Fig. 3(b) indicates the presence of a Texas calcite layer. Thus, it is noted that as a result of abrasion transfer mechanism pellets mutually transfer material among one another and result in both type 3 and type 4 pellets. In another set of tracer experiments, the disap pearance trends of smaller pellets at late stages of batch pelletization were investigated. The New Jersey and Texas granules were initially produced

100

K. V. S. SASTRY.

D. W. FUERSTENAU

Fig 3. Photographs (1 x ) of the sectioned green pellets from tracer studies using New Jersey (white) and Texas (black) calcites. The individual calcites were lirst agglomerated (water content W) up to IV revolutions, then mixed in different proportions as indicated and pelletized for an additional 600 revolutions. (a) W= l5.80/O by wt., N=?OO rev, I/2 Texas and I/2 N-L (b) W= 14.5% by wt., N= IZOOrev, l/2 Texas and l/Z N.J. (c) U’= 15.8% by wt., N= 1200 rev. -5.6 mm N.J. and i-5.6 mm Texas. (d) W= 15.8% by wt., N = lZO0 rev, -5.6 mm Texas and +5.6 mm N.J.

by agglomerating the individual calcites (W= 15.8 %) for 1200 revolutions. In the first test, all the New Jersey pellets smaller than 5.6 mm and all the Texas pellets larger than 5.6 mm were agglomerated together for another 600 revolutions, while in the second test larger New Jersey and smaller Texas granules were pelletized. Photographs of the resulting granules are shown in Figs. 3(c) and (d),

where the agglomerates are observed to be of types 2,3 and 4. From these photographs it may be further concluded that abrasion transfer was the mechanism which caused the layer type of agglomerate structure. The presence of the type 2 granules indicates that breakage of pellets results in a limited number of fragments of finite size. If, in fact, the breakage and layering mechanism proposed

MECHANISMS

OF

AGGLOMERATE

101

GROWTH

formally. Such a formal representation is usefu! conceptually and necessary for any mathematical modeling of agglomeration processesls. First, it is noted that in industrial balling systems. the balling devices are continuously operated by making a constant supply of new feed available to previously formed seed pellets. Thus, for a general description ofgreen pelletization processes, it is convenient to conceptualize that the agglomerating system consists of two classes of species: the wellformed species and the added moist feed. The “wellformed species” are defined to be those with finite size and those which undergo changes in their number and size by the occurrence of any of the growth mechanisms (to be discussed below). The mathematical representation of green pellet growth kinetics and size distributions 7s concerned with the well-formed species. The “added moist feed” is considered to consist of species of infinitesimal size and they simply contribute to the formation and/or growth of well-formed species. It is noted that these concepts of the well-formed species and added moist feed are in analogy to the growing crystals and molecular species in solution, respectively, in the unit operation of crystallization_ In the following paragraphs, each of the agglomerate growth mechanisms will be defined formally.

by Capes and Danckwerts2*3 is present, the New Jersey pellets in Fig. 3(d) should show a predominant calcite layer. These experimental results qualitatively indicate the mechanisms that are occurring during the pellet growth process. More extensive tracer studies on comminuted materials are needed in order that a better and complete understanding of the growth mechanisms can be obtained. However, based on the present studies on ground calcites, the following conclusions can be made: (1) the growth of green pellets in the initial stages of a batch balling experiment proceeds by the mechanism of coalescence, (3) abrasion transfer of material within the agglomerating charge is a very important growth mechanism, and (3) there is evidence of limited breakage of granules in the later stages of a batch ba!ling experiment. However, each peIIet on breakage produces a linite number of fragments with finite size. The broken fragments are too large to lead to layering of the surviving pellets.

FORMAL REPRESENTATION MECHANISMS

OF

GROWTH

The qualitative results of the tracer studies presented thus far and the general observations of pelIet growth processes make it possible to hypothesize and define the basic growth mechanisms

Nucleatiolt Any formation

o+jy: i

()+@a -

Pi + Pj -

(a)

(b)

Pi-j

+(g

h.9

Pi+

Pj 4

z:

:

211

0

-0

Pi+Pj~Pi~jP(

B

of new pellets in an agglomeration

+a0 0

00

Pi+*+lj-k)Pl

igBi

td)

TtsX%

L:::

Fig 4. Formal representation of growth mechanisms. The symbol f’; is used to represent a green pellet of n~ass q( = ih) and Pot refers to the freshly-added nuclei of mass h. (a) coalescence, (b) breakage, (c) abrasion transfer, (d) snowballing and nucleation.

102

K.

system from an extra supply of moist feed (Le. generation of well-formed species; Fig. 4d) is termed nucleation. The nucleation of new species results from capillary attraction between a collection of individual msrst feed particles. In a batch system, the formation of nuclei pellets has been found to occur within the first few drum revolutions’. The occurrence of nucleation thus brings changes in both mass and number of well-formed species in the system. Coalescence This mechanism is pictorially represented -%IFig. 4(a)_ It refers to the production of large-size species by means of the clumping of two or more colliding granules. For the sake of mathematical simplicity, binary coalescence is considered to be the elementary event. Thus, coalescence of two colliding agglomerate species, say pellets of masses mi and mj, leads to the formation of one larger size pellet, with mass (rn,+n~~=n~,+~). This representation of the coalescence mechanism associates with it certain typical properties, i.e. coalescence events cause discrete changes in agglomerate masses and contribute to an overall decrease in the number of pellets, but do not change the total mass of the system. Breakage The breakage of the pellets leads to the formation of a collection of daughter fragments, either all of the same size or of different sizes. These broken fragments are considered to belong to the class of well-formed species. Figure 4(b) is a schematic representation of this mechanism and for convenience it is shown that all the broken pellets are of unit size. These daughter fragments then redistribute on the survivingpellets,thuscausingtheso-calledlayering’. TABLE

V. S.

SASTRY,

D. W.

FUERSTENAU

In the mathematical representation of this growth mode, the redistribution of the broken fragments is considered to belong to the general class of coalescence events. Clearly, breakage causes discrete changes in agglomerate masses, generates more wellformed species, and does not change the total mass. Abrasion transfer Due to interaction and abrasion of the agglomerate species in the pelletizing charge, a certain mass of material is transferred from one species to the other. This is termed “abrasion transfer’ (Fig. 4c)_ Mathematically, it is expected, on each encounter between the species, an infinitesimal mass of material is transferred from one to the other with no preference of exchange in either direction. The abrasion transfer growth mode does not change either the total number or total mass of the pellets in the system and causes only continuous changes in sizes. Snowballing (layerilzg) Whenever new moist feed is supplied to a system of pellets, the pellets act as seeds and tend to collect the newly added moist tines’-‘4. This mechanism will be termed “snowballing” (Fig. 4d), and sometimes it is referred to as “layering.” It is idealized that all the added moist feed nuclei are of unit mass (h) and are not considered to belong to the population of agglomerates undergoing size changes. Furthermore, the pellets change their mass by snowballing in steps, each step occurring in an infmitesima1 interval of time and an increase of unit mass by collecting one new feed nucleus. Thus, it is clear that snowballing causes continuous changes in pellet size (mathematically, as feed nucleus mass h-to), resulting in an increase in the total mass of the sys-

1

Formal representation of the pellet growth mechanisms

Agglomerate

size changes

Mechanism of pellei growrh

TOId numbefl

TOllI mass

Discretely

Con;inuoudy

Nucleation Binary coalescer.ce Breakage Abrasion transfer Snowballing

Yes(+I) Yes(-I) Yes (n-

Yes No No No Yes

Yes Ye.5 Yes No NO

NO NO No Yes Yes

NO NO

1)

* The numbers in parentheses indicate net change in the population due to occurrence of one mechanism event, and n refers to the nunsher of ftagments formed due to breakage of one pellet.

MECHANISMS

OF AGGLOMERATE

GROWTH

tern and does not change the total number of pellets. The concepts developed thus far regarding the pellet-growth mechanisms can be conveniently summarized by Table 1 (and illustrated by Fig. 4) which provide precise definitions for the mechanisms ofpellet formation and growth. It may, furthermore, be added that these live growth mechanisms form a complete set of elementary events that cause changes in number and/or size of the pellets. Any other growth phenomena that may be conceptualized would be a subset of one of these five elemer.tary growth mechanisms. Of course, physical addition or removal of pellets due to input or output at a given location is to be accounted for separately since such changes in population are not inherent to agglomeration phenomena.

BATCH PELLETIZATION MATERIALS

BEHAVIOR

0

P

1

500

NUMBER

000

OF

I

DRVM

1500 2000 REVOLUTIONS. t

2500

I

Fig. 5. The average green pellet diameter as a function of the number ofdrum revolutions. These results indicate the reproducibility of growth kinetics determined in the batch balling experiments.

OF PARTICULATE

In terms of the basic physical phenomena and mechanisms that are responsible for ball growth, we shall now discuss the batch balling behavior of particulate materials with a natural size distribution, that is cornminuted materials. Our example will be the batch balling of taconite concentrates; details of our laboratory batch balling process have been described elsewhere13. Briefly, the process consists of mixing the required amounts of water with a batch of particulate material (bentonite is dry mixed first, when added) and then tumbling the moist charge within the balling drum. After various time intervals, the size distribution of the agglomerates is determined, from which the average pellet diameter and other parameters are calculated. Figure 5 presents the average pellet diameter as a function of the number of drum revolutions during the batch balling oftaconite concentrates with 0.5 % and 10.8 “/, by weight of addition of bentonite and water, respectively. This green bal! growth curve shows a characteristic S-shape indicating varying agglomeration rates. Kapur and Fuerstenau’, experimenting on the green pelletization of limestone, found a similar characteristic behavior and, based on their experimental observations, they proposed that the agglomeration of such limestone powder proceeds through three stages of growth : (a) nuclei, (b) transition, and (c) ball growth regions (as shown in Fig. 5 for taconite). From ball growth curves such as those given in Fig. 5, it is difficult to identify these three regions precisely. However, by presenting

0

1000 NUMBER

OF

DRUM

ZGUO RE”Ol_UTION*.

t

3000

Fig. 6. The differential growth rate curve for taconite concentrate.

agglomerate growth rates on a differential (as in Fig. 6) rather than an overall basis (as in Fig. 5) i.e. by plotting the rate of change of the average diameter as a function of the number of drum revolutions, it is seen that the ball growth occurs in three distinct regions of increasing, maximum and diminishin g growth rates”. Thus the differential growth plot (Fig. 6) provides a basis for identifying the three growth regions proposed by Kapur and Ftierstenau’. Physical reasoning and earlier observations on pellet growth mechanisms lead to the following interpretation of taconite balling characteristics in a batch experiment. During the mixing of water into the finely divided particulate assembly of taconitebentonite mix (or any other polydispersed material), highly porous, loosely held floes of solid particles are formed. These floes are the result of the pendular bonds due to the presence of the water between the irregularly packed network of particles.

104 On tumbling this moist charge in the balling drum, the particles rearrange and pack together within a Z”w drum revolutions’ and form into stable porous spherical nuclei (i.e. result in the generation of wellformed species) because of capillary attraction between particles. These initial nuclei can formally be represented by a three-phase pendular or funicular type of structure. On further tumbling of the charge, the nucIei collide with one another, with some collisions tending to form a capillary neck and resulting in successful coalescence. This accretion process proceeds as the nuclei continue to grow by coalescence, with simultaneous compaction, and squeezing and transfer of water onto the agglomerate surface. With increasing amount of water appearing on the surface along with continuing growth, which can be observed during the course of the experiment, the efficiency of coalescence also increases_ This brings about an increased rate of pellet growth (Fig. 6) During this process of growth and compaction, the pellet structure slowly passes through the pendular and funicular regimes to a capillary regime. At about the time the agglomerates are compacted to their minimum porosity, the excess water appears on the surface of the pellets (which then appear to glisten), resulting in maximum rate of growth. This region is the “transition region”‘. The porosity of the green pellets at this growth stage is approximately equal to the added water content A green pellet in this region is nominally considered to be in the capillary regime where it is held together by Ine surface tension of the water envelope surrounding it, by the negative capillarity and by the surface and frictional forces between interlocked particles of a well-packed assembly. Moreover, the pellets exhibit a marked dilatant behavior which can be observed by squeezing the pellet and causing the moisture on the surface to recede into the interior_ The growth rate of green pellets beyond the transition region diminishes because of the low efiiciency of coalescence and because other modes of growth, like abrasion transfer, are inherently slower. The reduction in the efficiency of coalescence results from such factors as less deformability, less available surface moisture,and increasing separating torque on the agglomerate twin. CONCLUSIONS

A tracer method has been used to identify the mechanisms of agglomerate formation and growth

K. V. S. SASTRY,

D. W.

FUERSTENAU

during the batch balling or granulation of particulate materials. Two calcites which were found to have similar pelletizing behavior but ditferent fluorescent properties were used in the tracer studies. For the purpose of defining the growth mechanisms and quantifying their occurrence, the concept of “well-formed species” has been proposed. The well-formed species are defied to be those aggregates of finite size which can undergo changes in their number and size by the occurrence of growth events. The initial formation of well-formed species takes place by nucleation of the “added moist feed” which is considered to consist of species of infmitesimal size. During the batch balling process, the prevailing growth mechanisms are nucleation, coalescence. abrasion transfer. and breakage_ In industrial balling drum operation where a continuous supply of moist feed is charged to the system, an additional growth mechanism is important, namely, agglomerates grow by the snowballing (or layering) of the added moist feed onto this surface. It has been noted that the role of water in the agglomeration process is very important, in that the relative occurrence of the various mechanisms is controlled by the amount of moisture and the relative distribution of moisture in an agglomerate. For example, during the batch balling of taconite concentrates, the initial rate of pellet growth (primarily by coalescence) was observed to increase with agglomeration time. This increase in the growth rates was found to be simply due to the increased moisture on the pellet surface.

ACKNOWLEDGEMENTS

Support of this research by the American Iron and Steel Institute is gratefully acknowledged. REFERENCES C. E_ Capes,A note on size distribution in granulation, balling and wet pelletization, Chem. Eng., 207 (1967) CE78-CESO. C. E. Capes and P. V. Danckwerts. Granule formation bv the agglomeration of damp powders. Part I. The mechanism of granule growth, Trans. Inst. Chem. Engrs., 43 (1965) . . T116T214. C. E. Capes and P. V. Danckwerts. Granule formation by the agglomeration of damp powders. Part II. The distribution of gr&ule sizes, Trans. Inst. Chem. Engrs.,43 (1965)TIsT130. R. A. Fisher, Further note on the capillary forces in an ideal soil, J. Agr. Sci.. (a) I6 (1926) 492; (b) 18 (1928) 406. W. B. Haines, Studies in the physical properties of soils, V, J. Agr. Sci., 20 (1930) 97.

MECHANISMS

OF AGGLOMERATE

6 J. 0. Hardesty, Principles of fertilizer agglomeration, C/tern Eng. Progr. Symp. Ser., 60 (48) (1964) 46-52. 7 P. C. Kapur and D. W. Fuerstenau, Kinetics of green pelletization, Trans. AIME, 229 (1964) 348-355. 8 P. C. Kapur and D. W’. Fuerstenau, Size distributions and kinetic relationships in the nuclei region of wet pclletization, Ind. Eng. Chem., process Design De&lop., 5 (1966) 5-10. 9 A. V. Luikov, Heat and Moss Transfer and Capillary Porous

Bodies, Pergamon Press, Oxford, 1966. 10 D. M. Newitt and J. M. Conway-Jones, A conrribution to the theory and practice of rJranulation, Trans. Inst. Chem. Engrs., 36 (1958) 412442.

105

GROWTH

11 H. Rumpf. The strength of _rranules and ag_elomerates. in W. A. Kneppcr (ed.), Agglomerarion. Interscience. New York, 1962. 12 K. V. S. Sastry and D. W. Fuerstenau, Laboratory studies on the batch balling kinetics of taconite concentrates. IX?h Inrern. hfinrral Processing Congr, Prague. CzechosloGnkia. 1970. 13 K.V.S.SastryandD.W.Fuerstenau,Aiaborato~methodfor

determining -the ballinS behavior of taconite concentrates. Trans. AZME, 250 (1971) 64-70. 14 K. V. S. Sastry, The agglomeration of particulate materials by green pelletization, Ph. D. Thesis, Univ. of California, 1970.