irrespective of the surface area and the moisture content. The ratio of the largest to smallest size nucleus in the size distribution was found to be approximately constant. The size distribution, thus? can be completely characterized by a single parameter-e.g., D,,,. Using the concept of a hypothetical average-sized nucleus, which accounts for the fact that coalescence occurs in a completely random fashion, relations between the number of successful coalescences to the number of average nuclei combining over a time period were utilized to generate a growth rate equation :
This equation is in good agreement with experimental results for powders of surface area typically encountered in commercial practice. Experiment also indicated the strong influence of moisture content on the rate constant. k .
D
=
D,,,
= diameter of smallest nucleus in a size distribution,
D,,,
= size modulus and diameter
diameter of nuclei, mm. mm.
of largest theoretical nucleus in a size distribution, mm. D,,,, = size modulus when .V = 0, mm. Dmaxi= size modulus when .V = z A S . mm. 1 = ratio of .V"A:V, dimensionless = rate constant for nucjei grolvth. dimensionless = a constant relating 1- with D,,,: dimensionless = distribution modulus of size distribution, mm. = number of balling drum revolutions, dimensionless = small number of drum revolutions over which C,,,, number of average nuclei combine, dimensionless = integrated volume of a size distribution over j = 1 to 0, equal to volume of average nuclei. cu. mm. = volume of average nuclei when .V = 0. cu. mm. = volume of average nuclei when S = i A V , cu. mm. = water content in agglomerates, by volume. per 100 parts of limestone, by volume) dimensionless = cumulative fraction by number of nuclei finer than size D , dimensionless = a constant equal to CmBl/iCmln, dimensionless
Acknowledgment
T h e authors thank T. C. Kuykendall for assisting in the experimental part of this work and T. W. Healy and T. S. Mika for helpful discussions during the course of this work. Nomenclature
A b
= a constant relating k and LV, dimensionless = a constant relating k and It', dimensionless = volume shrinkage factor due to reduction in porosity
C
= number of average nuclei combining to form a larger
C,,,
=
C,,
=
B
of agglomerates, dimensionless agglomerate, dimensionless minimum number of average nuclei combining in a given small number of drum revolutions, dimensionless maximum number of nuclei combining in a given small number of drum revolutions, dimensionless
literature Cited
(1) Bennett, L., Lopez, R. D., Chem. Eng. Prqgr. Symp. Ser. hh. 4.3, 59, 40 (1963). (2) Conway-Jones. J. M., Ph. D. thesis, Imperial College of Science and Technology, London, 1957. (3) Crabtree. D. D.: Kinesevich, R. S.. Mular. A. L., Meloy, T. P., Fuerstenau. D. W., Trans. A I M E 229, 201, 207 (1964). (4) Devaney, F. D.. Pickands Mather and Co., Duluth 2, Minn., private communication, 1964. (5) Kapur, P. C.. Fuerstenau, D. W., Trans. A I M E 229, 348 (1964). (6) Meissner. H. P., Michaels, A . S., Kaiser, R., IND.Esc. CHEM. 3, 3 (1964). PROCESS DESIGN DEVELOP. (7) Newitt, D. M.! Conway-Jones, J. M., Trans. Inst. Chem. Engrs. 36, 422 (1958). RECEIVED for review October 5, 1964 ACCEPTED November 3. 1965 Research sponsored by the American Iron and Steel Institute.
RATE OF PELLETIZATION OF ZINC OXIDE POWDERS H . P. M E I S S N E R , A. S. M I C H A E L S , A N D ROBERT KAISER' Chemical Eqineering Department. Massachusetts Institute of Technology, Cambridge 39, Mass.
mass of powder particles less than 1 A micron : . in. size . can be converted into closely sized, dense, N
UUCOUPACTED
free-flowing pellets by systematic agitation. This transformation, which may be in a drum, by is dry pelletization The Object here is to present quantitative data On the growth rate Of Of a divided zinc oxide pigment. 1
10
Present address, M.\V. Kellogg Co., New Market, N. J. I&EC PROCESS DESIGN AND DEVELOPMENT
State of the Art
Studies by Voyutski et ~ l (7), . Studebaker (5),and especially Billings and Offutt (,) suggest that any dry powder material bvill pelletize without the use of a binder if the prime are small enough, Such pelletization is nucleated, in that the rate of disappearance of loose in an agitated vessel is greatly accelerated by the presence of a sizable volume fraction of "seeds." Any solid objects, nominally greater than 200mesh in size, such as glass spheres, sugar crystals, metal shot,
Solid objects, introduced into a bed of finely divided dry zinc oxide, become coated with powder particles and grow in size when the bed i s tumbled in a rotating drum. While growth occurs on any solid object of suitable size, agglomerates of the powder itself are usually used as seed. Most fine powder systems show such agglomerate growth upon agitation. The growth of larger zinc oxide pellets in beds of zinc oxide powder was found to b e a function of the total revolutions of the drum, independent of the rotational speed. Growth per revolution varies as the peliet density, the square of the pellet diameter, the cube of the volume fraction of ihe pellets present, and inversely as the bulk density of the fines. In larger systems, given the same ratio of b e d volume to drum volume, the increase in total pellet weight per revolution is independent of system size.
vegetable seeds, or recycled agglomerates of the powder itself, may serve as seed. Iluring agitation, these seeds grow at the expense of powder, at a rate influenced by many factors, including seed size and concentration, the nature of the original powder, the geometry of the mixing vessel, and the amount of powder present. Prolonged tumbling ultimately causes all the loose powder to disappear. T o explain these fi:ndings, it has been suggested that forces of the van der Waals type act between particles to form agglomerates and that the apparent properties of the po\vder bed are a function of the type of agglomerates present 1.2). For bigger particles, inertia is large compared to these van der Waals attractive forcea, so that there is little evidence of association. A s the particles become smaller, however, the ratio of attractive forces to inertial forces increases rapidly. I n consequence, finer particles cling to each other a t their points of contact strongly enough to form detectable agglomerates, whose stability increases as the particle size decreases. Thus, pigment grade powders are usually agglomerated. The properties of powder agglomerates depend on the mechanical history of the system under consideration. For example, pigment grade powders, as they come from the manufacturing process, characteristically have a very lo\\ bulk density, are sticky and cohesive, and appear to consist of small open-structured agglcimerates. Systematic mechanical agitation, as in a rotating drum, transforms such a poi\der system into a mass of larger, free-flowing pellets of relatively high density and considerable crushing strength. Increase in agglomerate density occurs because of the compressive blo\vs and shear forces to which the agglomerates are subject during tumbling. \Yhen such blo\vs are too small to cause shattering. the agglomerate is slightly, but irreversibly, compressed. Physically, this compression involves slippage of the particles to ne\v and tighter orientations \\.herein the number of particle contacts per unit volume (and hence the agglomerate strength) is increased. \\'.hen the blo\vs are great enough to crush the agglomerate, the smaller fragments merge with the existing larger agglomerates \\bile the larger act as new seed. This gro\vth and change in size distribution of the agglomerates occur i1ithout any alteration in the size of the ultimate particles. Experimental Procedure
T h e powder systern studied \vas a commercial grade of French process zinc oxide powder Kadox 72, made by the h-e\v Jersey Zinc Co. ' I h i j material has a BE?' surface area of 8.2 s q , meters per gram, \ihich corresponds to a n equivalent spherical particle diameter of 0.13 micron ( 4 ) . Tumbling experiments \vere performed on prepared mixtures of "balls" (sized agglomerates larger than 200-mesh) and fines (a mixture of agglomerates smaller than 100-mesh). Desired mixtures \\.ere obtained by blending fines Lvith agglomerates of the
desired size, obtained from previously tiimbled material or from fresh poxvder stock. Solid Scotchlite glass beads made by the hiinnesota Mining and Manufacturing Co., having a density of 2.5 grains per cc. and a diameter of 0.39 mm.: were used in some runs as seed. Operations involved placing the desired charge in a 500-, 1000-; or 4000-ml. laboratory borosilicate glass reagent bottle having external diameters of 83. 105. and 174 mm.: respectively. T h e charge \\-as next dried under vacuum (at a pressure below 0.1 inm. of mercury) at 110' C. for 24 hours. After cooling, dry air \\-as admitted until atmospheric pressure \vas attained. l h e bottle \vas then sealed and rotated about its horizontal axis at a constani speed xvithin the range of 33 to 110 r.p.m. Most of the tests \vere made in 1-liter bottles at 110 r.p.m., and a typical charge of 100 grams of balls and fines occupied perhaps 20Yc of the volume of a 1-liter bottle. T h e disappeatance of fines and rhe densification of the agglomerates in the system \\ere measured after each run. T h e bulk densities of both fines and balls \vere measured in a graduated cylinder. All densities referred to here are therefore bulk densities. 'The \\eight of fines and balls present in the system was determiiied directly after screening. .4s pointed our later, the "rare of fines disappearance." here defined as the loss in weight of fines per revolution per unit mass of bed, is independent of rotational speed, other factors being equal. The effect upon rate of fines disappearance of the follo\ving variables \\vas studied : ball diameter. volume fraction balls, ball density, ball composition, vessrl size, and speed of rotation. 'The volurne fraction balls is the bulk volume of balls originally added to a system, divided by the bulk volume of balls plus the bulk volume of fines originally added. General Observations
'12'ith an initial charge comprised of a mixture of balls and fines, nvo successive stages of operation are observable, characterized by a greater rate of fines disappearance in the first stage (stage 1) than in the second (stage 2). ?'he greater the initial ratio of balls to fines, the briefer stage 1 becomes. In the typical run sho\vn graphically in Figure 1, stage 1 was obviously completed in about 4500 revolutions. Inspection of Figure 2 presenting density changes of both balls and fines for this run s1iow.s that densities increase rapidly a t the outset, but that the rate of increase diminishes \vith increasing total revolutions. T h e quantity of fines present a t the end of stage 1 varies with the ratio of balls to fines and with ball diniensions in the initial charge, and may be as high as 207, by volume for charges \\ith small---e.g., 30Gj,--initia! ball loading, and as low as almost zero for high initial ball loading (such as 67%). During the first stage, the balls grow a t the expense of the fines. but the total number of balls remains very constant. There is usually no formation of agglomerates intermediate in size betxveen the balls and fines of the initial charge. During this period, \Val1 "cake" forms \\.hose \\eight is roughly proportional to the \\eight increases of the balls. 'To minimize such VOL.
5
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wall cake formation in longer runs: a metal bar held magnetically against the inside bottle walls \vas sometimes inserted to act as a scraper. A change in the total number of balls present O C C L I ~ Sin stage 2. Intermediate-sized balls now appear, formed mainly by breakup of larger balls, though some, no doubt, also formed by coalescence of fines. T h e fines remaining a t the o u m t of this second stage are sloivly picked u p by the balls and finally disappear entirely. If rotation of this mass of balls is continued for a longer period of rime, then regardless of the initial size: density? etc., the whole charge is converted to a system of strong, dense (1.5 to 1.6 grams per cc.). free-flolving pellets, all of a diameter of about 0.4 to 0.7m m . ( 2 ) . T h e number of revolutions required to complete the first stage increases Lvirh the weight 7cfines in the charge and decreasing size of the bal s. T h e transition behveen the two stages becomes more difficult to detect as the \\.eight per cent fines increases. \,Vhen only fines are present initially, the rate of change of fines density is slo\\-est, and an alteration in bed properties can be detected only after about lo5 revolutions. Even in this case: ho\vever, balls finally put in an appearance, formed by coalescence of the fines. Rates of change of agglomerate size distribution are slojv during stage 1 even \\hen the initial ball concentration is increased to about 15%. Only after the initial volume concentration of balls exceeds about 3@yc d o the rates become so rapid that the transitions betlveen stages 1 and 2? as discussed above, become marked. This minimum concentration for rapid ball grolvth uill vary \vith the system under consideration.
0
0
0
0 - BALLS A - FINES
-
0 - WALL CAKE
A
0
2
4 THOUSAN35
A
6
8
10
O F REVOLUTIONS
Figure 1 . Relation of weight of balls, fines, and wall cake to number of rotations for run 65 Charge. 50 grams of balls (-40/+50 mesh; 0.59 gram/cc.) and 5 0 grams of fines (--200-mesh; 0.52 gram/cc.). 1 0 0 0 - m l . bottle contained dried air a t room conditions, rotated a t 1 10 r.p.m.
Ball Growth Rates
Experimental study was made primarily of stage 1, since it is here that the highest agglomeration rates occur. \Vhen exploring the effect of one operating variable such as fines density on the rate of fines disappearance, all other variables \yere, of course, kept as constant as possible at knoxvn values. Because of interaction among the different parameters during the progress of a run, these rate calculations \vex made by extrapolating back to the initial time interval in Lvhich all the parameters were controlled. I t \vas found that the rate of fines disappearance per unit bed Lveight and the consequent changes in the system's properties depend only on the total number of revolutions made, independent of the rotational speed between 34 and 110 r.p.m. Thus the rate of fines disappearance is al\vays reported here per revolution, not per unit time. If TITF is the weight of fines per unit \\.eight of bed and +Visthe total revolutions made from the start of the run, then dT17F,1d.V is here called the rate of fines disappearance per unit bed Lveight. T h e rate ~!ll'~,'d.V \vas found to vary in stage 1 as follo\vs:
0 BALLS A FINES
04
1
00
I
20
1
I
I
I
40 THOUSANDS
OF
I
60 REVOLUTIONS
, 80
1
1
10 0
Figure 2. Relation of bulk density of balls and fines to rolling time for run 65 Charge. 50 grams of balls (-40/+50 mesh; 0.59 gram/cc.) and 50 grams of fines ( - ZOO-mesh; 0.52 grarn/cc.). 1000-ml. bottle contained dried oir a t raom Conditions, rotated a t 1 1 0 r.p.m.
Directlv \vith the square of D g , the ball diameter, as sho\vn in Figure'3. Directly with p B , the ball density, as sho\+n in Figure 4. Directly ivith the cube of V B , the volume fraction balls, as sho\\n in Figure 5. for systems in Lvhich V B lies bet\veen 33 and 62Tp. I
"
Inversely Lvith a function of p F , the fines density. T h e form of this function has not yet been established; holvever: p r increases linearly with decreases in TITF, as shoxvn in Figure 6. T h e foregoing findings can he expressed analytically : (INITIAL BALL DIAMETER)'
Figure 3. pearance
T h r rate of fines disappearance \\as observed in bottles of three different sizes, \\ith the ratio of po\\der volume to vessel volume kept constant T h e rate of fines disappearance peI 12
l&EC
PROCESS DESIGN
AND DEVELOPkENT
IN (MM)'
Effect of ball diameter on rate of fines disap-
Charge. 5 0 groms of balls and 5 0 grams of fines, having densities, respectively, of 0.6 and 0.52 gram/cc. 1000-ml. bottle not equipped with scraper, rotated a t 1 1 0 r.p.m. Dried air used a t room temperature and pressure
t
t o 5
L
00
-
IO 20 13ALL DENSITY, G R / C M 3
30
I
Figure 4. Effect of ball density on rate of fines disappearance Charge. 6 5 grams of tines having a volume o f 1 2 5 cc., and 6 0 cc. of bails of 0.35-mm. diameter. Total number o f balls, 1.56 X lo6. 1000-ml. battle rotated without scraper a t 110 r.p.m. Glass spheres had a diameter of 0.39 mm. but paint reported was corrected to a diameter o f 0.35 mm., because assumption made that rate varies as diameter squared
t z
I 0-5 0 10
unit bed weight was found to be the same for the 1000-ml. and the 4000-ml. bottles, but smaller for the 500-ml. bottles. Ho\vever, \\hen beds of different weights were tumbled in a 1000-ml. bottle, the rate of disappearance of fines per unit \\eight of powder was found to increase as the total weight of the powder charge decreased.
10 INITIAL VOLUME FRACTION
BALLS
Figure 5. Effect of volume fraction balls on rate of fines disappearance Charge weighed 100 grams, consisted of balls (-40/+50 mesh, Operations 0.6 gram/cc.) and tines (- 200-mesh, 0.52 gram/cc.). in a 1000-ml. bottle containing dry air, no scraper
Mechanism of Growth
When a cylinder partly filled with powder is rotated, the powder bed is observed to rotate with the cylinder. As the bed turns at low speeds of rotation, miniature avalanches develop as gravitational forces overcome frictional and cohesive forces acting on bed layers lying close to the tilted bed surface. At these low speeds, there is little of the cataracting of the falling particles that v;ould occur if the powder mass were placed in a rapidly rotating cylinder. When fines are present in considerable proportions, making the bed sticky, a succession of po\vder packets of finite thickness shear off near the bed surface and strike the toe of the bed. When relatively few fines are present, balls roll down the tilting bed surface and again strike the toe of the bed. In the first case, sliding is intermittent, while in the latter, balls roll doivn the face continuously. In either case, the material ne\\ly arrived a t the toe is reincorporated into the main bed mass as rotation proceeds. There is relative motion of agglomerates in a rotating bed only along the interface between the main bed and the material avalanching down its surface, and a t the toe of the bed \\here the avalanche is rapidly brought to a halt. Transfer of particles from one agglomerate to another appears to occur by crushing caused by the impact of agglomerates colliding \\ ith each other or with the vessel \\all when a do\\n\4ard-moving packet is suddenly brought to a halt at the toe of the b e d Fragments formed are picked up by the surviving agglomerates. Transfer of particles also appears to occur by abrasion betneen moving and stationary agglomerates along the bed-avalanche interface
01.001 Y
I
I
I
I
,
I
,
,
,
I
,
Figure 6. Relation of bulk density of surviving fines to weight of surviving fines for several runs Total charge in ail runs 100 grams, with initial fines weight o f 35, 50, and 6 5 grams as shown. Operations in 1000-ml. bottle turning at 1 IO r.p.m.
Effect of Operating Variables on d W , / d N
Rotational Speed. Agglomerate properties, and therefore bed properties. are evidently determined b) the number and violence of the various types of collisions occurting. Collision violence in a s) stem like this is independent (within limits) of the speed of rotation. since the speed of the avalanches VOL. 5
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1
JANUARY
1966
13
appears relatively constant. Similarly, the total number of collisions is determined solely by the total number of completed revolutions. Fines crushing and ball growth are therefore proportionate to the total number of rotations and the total number of effective ball-ball contacts existing in the bed. Effect of Bottle Diameter. T h e rate of fines disappearance per unit bed weight was found to be independent of bottle size when larger bottles were used. This can be explained by assuming bed movements to be symmetrical in bottles of different sizes, so that for the same per cent bottle filling, the volume of avalanching powder is a constant fraction of the bed volume. If sliding speeds are equal, then collision effectiveness is the same in the two bottles and the fines disappearance rate per unit bed mass is the same in the two cases. I t is indicated by the results of the experiments in vessels of three different sizes, all with the same volume percentage loading, that the sliding packets were still accelerating when they hit the toe of the bed in the same case of the 500-ml. bottle, but had reached maximum velocity before they hit the vessel wall in the case of the 1000-ml. and 4000-ml. bottles. Effect of Powder Loading. For a given bottle size, the bed “turns over” a greater number of times per rotation as the size of the bed is decreased. In consequence, there is a n increase in the number of collisions which a n agglomerate experiences during each rotation of the bottle. Thus the smaller the loading, the greater the rate of fines disappearance. Ball Concentration. By analogy with the work of Thomas (6) on aqueous suspensions of finely divided solids, the numbers of ball-to-ball contacts per unit volume of static agglomerate system is assumed to be proportional to the cube of V B , the volume fraction balls in the system. As a bed rotates in a cylinder these ball-to-ball contacts are constantly being made and broken, and so the number of new contacts formed per revolution is taken as proportional to V B 3 . Since these new contacts are more or less violent, they may be considered as collisions \vhich then in turn are proportional to V B 3 . I h e ZnO balls discussed here are reasonably spherical. If the number of particle contacts per ball is assumed to remain constant as the ball diameter changes for a given volume yo balls, the contacts (and collisions) between balls per unit volume must be proportional to l / B 3 / 0 B 3 . Ball-to-ball contacts are assumed the primary source of fines crushing and growth. T h e amount of crushing per contact depends upon the number of fines pinched between the balls, and this must be some fraction of the effective projected ball area, hence proportional to DBz. Finally, the violence of the collisions is determined by the ball mass or p B D B 3 . ‘To summarize, the rate of loss of fines is proportional to:
14
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
the number of ball-to-ball collisions formed per rotation, or vB3/‘DB3;the ball-to-ball contact area causing crushing, or D B 2 / and the collision violence, or pBDB3. The product of these three terms results in the expression V B 3 D B 2 p B : which is the numerator of Equation 1. Seeds a n d Wall Cake. Growth occurred in the mass of tumbling powder studied on all seeds, regardless of their composition, and also on the wall as wall cake because the attractive forces acting on the particles are nonspecific. T h e finding that the wall cake growth rate is proportional to VB is consistent with the fact that relatively violent collisions are required for fines crushing and growth of both balls and wall cake. Fines Density. Fines (being themselves agglomerates) must first be crushed or deformed before they can be joined to balls. However, fines become stronger as their density increases, hence more difficult to crush ( 3 ) . Growth rates diminish as fines density increases since few collisions are violent enough to crush strong fines. I n consequence, as shown in Equation 1, the growth rate varies inversely with a function of the fines density. Acknowledgment
T h e authors are grateful to the National Science Foundation for fello\yships granted the junior author and to the S e w Jersey Zinc Co. for providing zinc oxide powders needed for this work. Nomenclature
DB K
= diameter of balls, cm. = constant
.V
=
total rotations of tumbling drum
V B = bulk volume fraction balls W F = weight of fines per unit weight system pB pF
= =
bulk density of balls, grams per cc. bulk density of fines, grams per cc.
literature Cited
(1) Billings, E., Offutt, H. H. (to Godfrey L. Cabot, Inc.), U. S . Patents 2,120,540 (June 14, 1938), 2,120,541 (June 14, 1938), 2,316,043 (.4pril 6, 1943), Reissue 19,750 (Nov. 12, 1935). (2) Meissner, H. P., Michaels, A. S., Kaiser, R., ISD. END.CHEM. PROCESS DESEXDEVELOP. 3.197 (1964). (3) Ibzd., p. 202. (4) New Jersey Zinc Co., Inc., Palmerton, Pa., personal communications, April 2, 1959. (5) Studebaker, Merton, Division of Colloid Chemistry, 123rd Meeting, ACS, Los Angeles, Calif., March 1953. (6) Thomas, D. G., .4. I. Ch. E. J . 7, 431 (1961). (7) Voyutski, S. S., Zaionchkovskii, A. D., Rubina, S. I., Kollotd Zh. 14, 28-36 (1952). RECEIVED for review lMarch 8, 1965 ACCEPTED July 12, 1965 ,
\
,
