inert drying gas. still apply
zoo[
‘I’hedrying mechanism discussed here would
Acknowledgment
‘I’he authors thank E. S. DellaMonica for his chemical analyses and the late J. €5. Claffey for assistance in the design of the equipment
R E L A T I V E HUM1D l T Y
e
Q
24\%
A
3 5
40-
0
-
Nomenclature
w‘
5 20-
D
= effective diffusion coefficient. = slab thickness, cm.
L
I-
Ll’
?!!
moisture content a t any time, Ib. water,’lb. dry solids dry solids = initial moisture content: Ib. water Ib. dry solids = drying time: sec. =
0 f 10-
TI,
t-
8 -
0
6 :
literature Cited
2
e
2
sq. cm./sec.
= equilibrium moisture content, Ib. water:lb.
(49 Aceto, N. C . . Sinnamon. H. I.. Schoppet. E. F., Eskew, R. K . , J . UQ27y & I . 45, 501 (1962). (2) ~, Craig. J. C.. Jr., U. S. Department of Agriculture. Philadelphya 18; Pa.. private c o m m k c a t i o n . (3) Craig, J. C . , Jr.. Aceto, N. C., DellaMonica, E. S., J . Dairy
4-
c
220
40
60
80
100
120
DRYING TIME, MINUTES
Scz. 44. 1827 11961). (4) Eskkiv, K.K.% .\&to, N. C.. Sinnamon, H . I., Schoppet. E. F., Ibtd., 41, 753 (1958) (5) Manrahan, F. P.. Tamsma, .A,? Fox. K. K., Pallansch, M. J . . Ibid.,45, 27 ‘(1962)’. (6) Jason, A . C.. in “Fundamental .4spects of the Drhydration of Foodstuffs,” p. 103, Society of Chemical Industry, London, England. 1958. (7) Marshall, \V.K., Jr.. Friedman. S. J., in “Chemical Engineers’ Handbook.“ J. H . Perrv. ed.. 3rd ed.. u. 809. McGraw-Hill. Kew York. 1950. (8) Morgan. A. I., Jr., Ginnette. L. F., Iianclall, J. M., Graham, R.P., Food En,?. 31, 86 (September 1959). (9) Sinnamon, H . I., Aceto, S . C., Cskew, I ported for such beds (7): indicating the presence of structure attributable to cohesive forces. Interparticle forces also account for the finding that reduction i n volume of such beds by direct compression is possible. but only with relatively Present address, ‘l’he M.W. Kzllogg Co., Jersey City, N. .J
large forces whose magnitude must be increased rapidly as bed density increases. On the other hand, coarse particles (larger than 0.1 m m . in diameter) show no indication of interparticle attraction in that they always pack closely 1.15 to 40Yc void volume) in beds. How freely under their own kveight. and are quite incompressible. ‘l’he characteristics just mentioned make beds of w r y small particles dificult to handle cominercially. In consequence. fine powders are often agglomerated into relatively large, dense pellets which show the normal packing and flow behavior of particles of large size. The term “ p ~ l l e t ” or “agglomerate” as used here means an assemblage of pariicles held together by interparticle forces and pmx&ng ineasVOL.
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urable physical properties such as dimension and crushing strength. Billings et al. ( 7 ) discovered that beds of fine particles of many different materials can be transformed into large. free-flowing spheroidal pellets by systematic agitation in a mechanical mixer without the application of heat. pressure, or bonding agent. Industrially, such systematic agitation is generally provided by tumbling a mixture of powder and recycled pellets in a sloivly rotating drum. This article reports a n experimental study of ZnO pelletization carried out in a rotating cylinder and proposes an explanation for the findings.
Table I.
Starting Mixtures of Kadox 72 Zinc Oxide Agglomerates Used in Prolonged Tumbling Runs
.Wixture
Description
A
Powder as received in manufacturer's shipping hag after sifting through a 30 mesh U.S.S. screen Powder as recei\-ed in manufacturer's shipping hag and sifted through a 200 mesh U.S.S. screen (bulk density, pb = 0.54 gramicc.) -12 to +16 mesh agglomerates (hulk density, pb = 0.56 gram/cc.) obtained from manufacturer's shipping bag 50 parts by weight of agglomerates -200 mesh in size from Mixture B, and 50 parts by weight of agglomerates -40 to +50 mesh in size (hulk density of pi, = 0.58 gram/cc.) obtained from manufacturer's shipping hag
B C D
Experimental
This investigation was limited to the following three grades of Z n O : B.E. 7'. Trade S a m e
.Wanufacturer
Kadox 72 St. Joe G.L. 42 XX 504
New Jersey Zinc Co. St. Joseph Lead Co. New Jersey Zinc Co.
Surface, Sq. .2leters/ Gram
8.2 4.1
0.82
Equiualent Paiticle Diameter, P
0.13 0.26 1.3
.As received, each material was found to exist as agglomerates which. in the case of Kadox 72 and St. Joe G.L. 42, ranged in size from -325 mesh to pellets about 2 inches in diameter. Agglomerates of these t\vo materials, Lvhile Tveak: were strong enough to be handled. hand-screened. and sized. Agglomerates of XX 504. on the other hand: Lvere too fragile to be sized, but broke u p and recombined Lvhile screening. .4s received, the bulk density of both Kadox 72 and St. Joe G.L. 42 was betbveen 0.5 and 0.6 gram per cc., ivhile that of X X 504 was 1.7 grams per cc. T h e true density of Z n O is 5.7 grams per cc. Pelletization behavior was studied by tumbling 100 grams of these materials for varying times in glass bottles of 1000-cc. capacity and anal>-zing the product. At the outset! mixtures of agglomerates of selected diameters were charged to the bottles. and dried by heating to 110' C. a t pressures of less than 0.1 m m . of Hg. Dry air a t room temperature and pressure \vas next admitted to the bottles. which were then sealed, placed on their sides on rollers. and rotated for from 5 minutes to 120 hours a t 110 r.p.m. I n some cases? a scraper bar held magnetically against the inside top wall of the bottle was inserted to prevent excessive wall cake formation. At the end of a run. the charge \vas analyzed for change in agglomerate size and size distribution and for changes in agglomerate properties. Crushing strength was measured by compressing the agglomerate between two parallel microscope slides, one of Lvhich \vas fixed in position. Lvhile the other \vas attached to one a r m of a laboratory balance. This technique has been described (8).
revolutions to a steady-state product comprising uniform agglomerates Lvhich \yere perhaps a trifle larger and denser than the steady-state Kadox product. TVhile the size and density of agglomerates in the steadystate product were unaffected by the size and size distribution of the agglomerates in the initial charge, the paths whereby this steady-state product was attained differed greatly. T h u s , when starting with Kadox fines, namely mixture B of Table I, growth and densification during the first 40,000 revolutions occurred slowly: as is evident from Figure 1 . Moreover. most of the agglomerates in the bed were a t each moment of a single diameter, and this diameter increased with time. The steady-state product, in which most of the agglomerates present were 30 to 40 mesh, was then attained between 40.000 and 635,000 revolutions. Alternatively, when starting with a system containing both fines and coarse agglomerates, as in mixture .L\ of Table I. larger agglomerates grew a t the expense of the smaller. The agglomerates present \vere not always of the same size. Change in agglomerate size distribution with time and the approach to steady-state conditions are illustrated in Figure 2. The bulk density of all sizes was found to increase during this process. Finally, mixture C of Table I. containing only coarse agglomerates of -12 to f l 6 mesh, was reduced to the MESH OPENING
- mm.
Results
Agglomerate Formation. For both Kadox 72 and St. Joe G.L. 42. tumbling a mixture of fines (agglomerates finer than 200 mesh) and larger agglomerates always resulted in the groivth of the latter a t the expense of the fines. until these disappeared. This relatively brief firrt stage was followed by a protracted second stage during which the size distribution of the surviving agglomerates narrowed while agglomerate density increased. Prolonged tumbling transformed all systems into beds of spherical agglomerates of very nearly uniform diameter, density. and crushing strength. .4gglomerate properties Lvere then not significantly changed by further tumbling. Thuq, the four mixtures of Kadox 72 shown in Table I. initially differing greatly in agglomerate sizes and size distribution. Lvere all converted after about 500,000 revolutions into a '.steady-state" product comprising agglomerates of -20 to f50 mesh size and having a bulk density of about 1.5 grams per cc. Similar initial mixtures of the St. Joe material were transformed after an equal number of 198
I&EC
PROCESS DESIGN A N D
DEVELOPMENT
t
1
401
I
I
I
@ Altar @ After
0.40 a 105 Raws
@ Aftar
€ 3 4 I105 R I M
1.19
i
IO5 Rev*
3 u
'200
SO
50 40 30 20 100 70 US STANDARD SCREEN SIZE
16
12
Figure 1. Agglomerate size distribution vs. rolling time for system containing only fines M a t e r i a l was mixture B (Table I), rolled in d r y air in 1000-cc. bottle equipped with scraper a t 110 r.p.m.
final condition by agglomerate breakage. as shown in Figure 3. Inspection o f t h e final mixtures in Figures 1, 2, and 3 attained after .500.000revolutions shows these to be quite similar in agglomeratr size and size distribution. 'I'he behavior of M X 504 differed from that of Kadox and S t . Joe G.1,. 42 in that tumbling altered neither its hulk density nor the apparent size distribution of the agglomerates present. It was necessary to judge size distribution visually; size analysis by screening failed because agglomerates broke down on the screen b u ~immediately reformed on passing through the screen. 'Ihus. this material appeared always to exist in a steady-statr condition. Crushing Strength. \Vhen subjected to compressive force short of that causing failure by crushing. agglomerates were round to be irreversiblv deformed. Thus, when pressed between flat surfaces, agglomerates developed slightly flattened ends. T h e amount of' such deformation was small and declined as the particle density increased. \Vhen a n agglomerate was subjected to a compressive force great enough to cause failure, it broke into a number of smaller fragments, each of which contained a large number of particles. T h e crushing strength of agglomerates made from a given material was found to be the same at equal agglomerate diameter D and packing fraction @ regardless of rolling time and agglomerate history. Crushing strength is here defined as P / D 2 : namely the total compressive force on the pellet divided by the square of the diameter. Agglomerates made from Kadox 72 had a higher crushing strength than agglomerates made from St. Joe G.L. 42, while agglomerates of XX 504 were too fragile to be tested by the experimental methods used here. 4 s shown in Figure 4. crushing strength for any given diameter increased with the packing fraction and varied directly with the agglomerate diameter squared. T h e equation for the lines drawn on Figure 4 through the experimental points is as follows :
log(P,,'D2) = 5.33 q
-M
where M i s 0 . 7 3 5 f o r K a d o x a n d 1.105forSt. Joe.
(11
Tests were made of the crushing strength of St. Joe agglomerates submerged in various liquids. 'The mesh size of these agglomerates was - 16 to $20, Lvhile their packing fraction q was 0.54. Submerged strength \vas found al\vays to be smaller than in air, and it decreased as the liquid polarity increased. Thus: the submerged strength in cyclohexane and dioxane was about ?5yoof that in air but was 7ero in water. in hvhich the agglomerates fell apart spontaneousl)-. \\:ater adsorption tests sho\\-ed that the specific, adwrption, expressed as grams of w'ater per gram of % n o . \ \ a \ iiideprndent of the size. density, and history of the agglorneratrs present but \vas uniquely determined by the size (and aurfacr) of the component parricles. 'l'his indicates that the fractional particle area which is blocked off by interparticlr contact is very small: even in the densest agglomerates formed. Discussion
Attractive Forces between Particles. T h e formation of agglomerates indicates the existence of attractive forces between particles. These forces d o not appear to be electrostatic in nature. Thus, Itahara ( 3 ) created conditions favoring leakage loss of any electrostatic charge present by bombardment of Kadox agglomerates with 3 m.e.v. electrons for 204 seconds a t a flux of l o b electrons per square cenrimeter. It was found that these agglomerates did not disintegrate. and indeed did not shobv any diminution in crushing strength. Again, agglomerate formation cannot be attributed to sintering, capillarity, or mechanical interlocking, since a diminished crushing strength was measured when agglomerates were submerged in liquids, and this varied with the nature of the liquid used. T h e finding that agglomerates of a given grade of ZnO. which is a highly polar material, were strongest in nonpolar liquids and weakest in polar liquids, suggests the presence of long-range secondary forces of the van der b'aals type, Further evidence for this hypothesis is the finding that the forces acting appear nonspecific. T h a t is, the two fine Z n O powders studied here adhered readily to the surface of small spheres of materials as diverse as glass: metals, and plastics and built u p coatings on the outside of these spheres during tumbling. Sim-
MESH OPENING- mm.
-
@
A f t e r 3.3 x 103
@
A f t e r 9.9 I 103 Revs
@
A f r e r 6.3 I: IO5 R e v s
RWS
U
tW
60
a
+
' w
.i I
40
z
4
3 ~
US
STANDARD SCREEN SIZE
Figure 2. Agglomerate size distribution vs. rolling time for system containing both fines and coarse a g g lomerates M a t e r i a l was mixture A (Table I), rolled in dry air in a 1 0 0 0 - c c . bottle a t 1 IO r.p.m. Densities of largest fraction, in order of increosing rolling times, a r e 0 . 5 , 0.8,1 . 1 , and 1.3 grarns/cc.
US
30 20 16 STANDARD SCREEN SIZE
h
8
Figure 3. Agglomerate size distribuiion vs. rolling time for system containing only coarse agglomerates M e t e r i a l was mixture C (Table I), rolled in dry air in 1 0 0 0 - c c . Densities of largest fraction, in order of inbottle a t 110 r.p.m. creasing rolling times, a r e 0 . 5 2 , 1 .O, 1 . l , and 1.4 grams/cc.
VOL.
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199
ilarly, all particulate materials studied by previous workers in this field, if fine enough. were found to pelletize. This behavior can again be attributed to van der Waals forces. Assuming the action of such forces, Lifschitz (5) developed the following expression for Fa,. the attractive force between two spherical particles, each of diameter d:
Bd Fap = - 36a3
The quantity u is the distance of closest approach between the surfaces of two neighboring particles, while B is the force constant whose magnitude depends on the composition of the particle and the surrounding medium. In air or vacuum, erg-cm. have been determined for values of B of about glass and similar polar substances (4). The attractive force between two agglomerates can be expected to involve a relation like Equation 2, with modification of the constants, since the agglomerates contain voids and have a rough surface. Because of this roughness, contacts between neighboring agglomerates occur a t a number of points, instead of a t a single point as with spheres. For agglomerates of a given powder system, Equation 2 would be modified as follows :
Fa, = - A D
(3)
where Fau is the attractive force between two agglomerates of equal size, D is the agglomerate diameter, and A is a constant. Equation 3 is in agreement with the observation that individual fine particles never appear to exist separately in a powder bed but are always associated with others in the form of a n agglomerate having measurable mechanical properties like crushing strength. The internal structure of a n agglomerate is pictured as a rigid open network of particle chains intersecting a t random in space. As the fraction of void space in the agglomerates decreases, because of the compression produced by successive collisions, the average number of contacts per particle with neighbors, and hence the agglomerate strength, Fhould increase. This is confirmed by the experimental findings presented in Figure 4, showing that the crushing strength of agglomerates of a given mesh size increase with 0:the volume fraction of solids. Notice that the strength of Kadox agglomerates was about twice that of the St. Joe agglomerates, presumably reflecting differences in d, the particle diameter. Figure 4 shows further that the quantity P,'D2 is a function of 9. Similar findings have been reported for moist pellets of iron oxide ( 9 ) and for moist sand pellets ( 6 ) . The Z Number. Hamaker ( 2 ) pointed out that inertial forces develop when one member of a two-particle combination is set in motion, and these forces tend to offset interparticle attraction and to destroy the bond. Thus, if one particie in a two-particle union is acted on by a force such as might result from a collision, the particle will undergo an acceleration which it will try to pass on to its partner. T h e inertial force with which the partner resists this acceleration will be the product of its mass and the acceleration. T h e mass of the particle of diameter. d, and density, p. is rpd3,'6. while the average acceleration, a . may be assumed constant for a given powder sys: tem. The average inertial force. namely Fip. can therefore be expressed :
F,,
200
=
arpd3 ~
6
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
By similar reasoning, the inertial force developed on a n agglomerate showing a packing fraction void of @ and diameter D , made of particles whose density is p. is as follows:
T h e stability of a bond between two particles may be characterized by the ratio of the attractive to the inertial forces acting; this is obtained by dividing Equation 2 by Equation 4. I t is next aqsumed that for a given type of particle. the average value of a , the distance of approach, is a constant. All of the other terms in Equations 2 and 4 except d are likewise constant for a given material; hence these can all be eliminated, leaving as a n index or measure of this bond stability the "Z," number. here defined as:
The larger the Z , number, the greater the bond stability. The Z , number can therefore be taken as an index of the ability of particles to form stable agglomerates and is as follows for each of the three materials tested: Material
2, A'umber
Kadox 7 2 St. Joe XX 504
200,000 50.000 2.000
These Z , numbers are at least roughly consistent with the experimental findings (see Figure 4) that agglomerates of the Kadox material are stronger than those of the St. Joe material at equal values of D and 9 ,while only very weak agglomerates formed with XX 504. A similar index can be developed for the flow and packing behavior of agglomerates. From Equations 3 and 5,
(7) t-a i
Inspection shows that agglomerates having large diameters and large volume fraction of solids will have relatively small Z,,
Agglomerate Size X - 1 6 f 2 0 mesh -3Ot40mesh
A - 4 O - t 50 mesh 0 -50
+ 70 mesh
I
I
I
I
Figure 4. Experimental values of crushing strength vs. volume fraction of solids
numbers. This is in agreement with the finding that beds containing mainly large agglomerates were free-flowing, while beds containing a sizeable fraction of -200 mesh agglomerates were not. Pelletization. I n vietv of the foregoing, pelletization may be defined as the transformation of a n original bed of agglomerates into a new agglomerate system having a n altered size distribution and increased density. T h e size of the individual particles themselves remains unchanged in this operation, as shown by the results of the water absorption experiments. T h e pelletization studies described here were made in rotating cylinders, within which each part of the powder bed present also rotates until the gravitational forces overcome the cohesive a n d fractional forces acting on some element of the bed. As a result, with noncohesive beds, individual particles or agglomerates are dislodged and roll do\vn the tilted bed surface. Similarly with cohesive powders, packets of material near the surface shear off a n d slide down the tilted bed surface. I n both cases, the dislodged material collides with other agglomerates and with the vessel wall a t the toe of the bed, where it is reincorporated into the main bed mass as the vessel continues its rotation. Agglomerates which a r e subject to minor compressive forces on collision increase in density. Agglomerates undergoing more violent impacts, particularly with the wall a t the toe of the bed, are abraded a n d crushed. T h e small fragments formed are in turn crushed further since. as is evident from Figure 4, small agglomerates are weaker than large agglomerates of a given packing density. .4 size is finally reached whose “Zag” number is large enough to favor adherence to a larger agglomerate. Thus. the groivth of an agglomerate occurs a t the expense of weaker agglomerates. All agglomerates tend to reach the same steady-state size because inertial forces are proportional to the diameter cubed (Equation 5): while crushing strength is proportional to the diameter squared (Equation 1). Consequently, a critical size must exist above which agglomerates will fail by their own impacts. Simultaneously, smaller agglomerates will be destroyed by collision with larger ones. thus causing these larger ones to grow to limiting size. Because of the occurrence of these simultaneous processes. a steady-state agglomerate size is ultimately attained. T h e different paths taken by the mixtures of Figures 1: 2: and 3 in reaching the steady-state condition appear consistent with these observations. For systems containing only fines. as in Figure 1, the do\%,agglomerate growth rate and early increase in density is attributable to the fact that inertial forces in the majority of collisions were too small to cause crushing but great enough to cause a n increase in density. I n the system of mixed agglomerate sizes, Figure 2, the large agglom-
erates crushed the smaller and grew by picking u p the fragments. This rate of growth diminished as all particles became denser and hence stronger and more resistant to crushing. I n the syscem of Figure 3, consisting originally of large particles, these were obviously above the steady-state size and were broken up in collisions. I t therefore appears that cohesive forces of the van der LVaals type act between particles. These forces cause the particles to stick together and form agglomerates. For finer particles, these agglomerates may be caused to change in size and increase in density by simple mechanical agitation. Thus, a bed of agglomerates of low density can be transformed into a system of agglomerates of relatively high density a n d uniform size by tumlding, as in the pelletization process. Nomenclature
constant in Eq. 3, dynes,’cm.
A
=
a
= distance of closest approach between
B
Z, Z,,
= = = = = = = =
cy
=
D d
F M
P
p
=
C$
=
two particle surfaces, cm. constant in Eq. 2 , erg-cm. agglomerate diameter, m m . particle diameter, cm. ( = lo4 microns) force: dynes constant in Eq. 1, dimensionless compressive force, grams force index for particle bond stability. dimensionless index for agglomerate flow behavior, dimensionless acceleration, cm. sec.2 density. grams cc. packing fraction. or volume fraction of solids, dimensionless
Subscripts ap ug
Zp Zg
= = = =
attractive forces between particles attr,active force between agglomerates inertial force of particle inertial force of agglomerate
literature Cited (1) Billings, E.. Offutt, H. H.. U. S. Patents 2,120,540, 2,120,541 (June 14, 1938): 2,316,043 (April 6, 1943); U. S. Patent Reissue 19,750 (Nov. 12: 1935). (2) Hamaker, H. C., Rec. Trav. Chini. 5 6 , 3 (1937). (3) Itahara, S., M. S. thesis, Chem. Eng. Dept., Massachusetts Institute of Technology, Cambridge, Mass.. 1960. (4) Jongh, J. G. V. de, doctoral dissertation, Utrecht Univ.!
The Netherlands. 1958. (5) Lifschitz, E. M.. Societ Phys. J E T P 2 9 , 94 (1954). (6) Newitt, D. M.: Conway-Jones. 3. hf.. Trans. Insl. Chem. Engrs. (London) 36, 422 (1958). (7) Studebaker. M.. Div. Colloid Chern.. 123rd Meeting. ACS: Los Angeles. Calif.. March 1953. (8) Sweitzer? C. D.. Columbian Carbon Co., Princeton. n’. J . , private cornmiinications. 1964; Chem. Eng. ,Yeu.s 32, 4287 (1954). (9) Tigerschiold, M.. Ilmoni. P. A,. A m . Inst. .Mzning M e t . Engrs. Proc. Blast Furnace, Coke Oven, Rau. ’%faterials 9, 18-53 (1950). RECEIVED for review July 10. 1963 ACCF,PTED December 3, 1963
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