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Effect of mixing aids on the transport behavior of particulate solids
Powder Technology. 0 Elsevier Sequoia
Effect
of Mixing
23 (1979) 26X171 S.A., Lausanne -Printed
Aids on the Transport
A.-Z. M. ABOUZIEDDepartment
of Materials
Behavior
of Particulate
Solids
and D. W. FUERSTBNAU Science and MinemZ Engineering,
(Received January 15.1979;
Uniuersity
of CaZifornia. Berkeley,
Calif
94720
(U.S.A.)
in revised form March 30,1979)
SUMMARY Tbe behavior
261
in the Netherlands
of particulate
materials
being
transported through rotary drums is strongly affected by the addition of mixing aids to the system. This effect is reflected in three main dependent parameters: holdup, variance of the residence-time distribution, and extent of particulate segregation in the drum. In addition, the discharge rate of material fluctuates widely due to the presence of mixing aids. The holdup decreases to a limiting value with increasing volume of mixing aids. The dimensionless variance of the residence time distribution increases with increasing volume of mixing aids up to a certain limit, beyond which it remained constant. This is the same limit that controls the constancy of holdup. In a system with segregating components due to differences in such physical properties as density, particle size, particle shape and roughness, the presence of mixing aids virtually eliminates segregation or at least minimizes its effect in all cases. INTRODUCTION The addition of balls as mixing aids to drum mixers accelerates the mixing process and minimizes segregation mainly through
their pronounced effect on convective particle transport within the system. In a similar way, the balls that are used for size reduction in tumbling mills also markedly influence the transport behavior of material flowing through a baU mill. *Resent address: Departmentof Mining, Petroleum and Metallurgy, Faculty or‘ Engineering, Cairo University, Egypt.
Thus far, only limited work has been reported on the effect of mixing aids on such phenomena as the holdup of material in rotating cylinders, the residence time distribution of the material passing through the drum, and mixing kinetics. In 1966 Sawahato [l] experimentally demonstrated the effect of adding rubber balls as aids for the mixing of sand grains that had been dyed with two different colors. That work was followed by a somewhat more quantitative evaluation of the effect of mixing aids by Chaudhuri and Fuerstenau 121, who obtained a quantitative correlation between the diffusion coefficient of one component of a mixture into the other as a function of the number of added balls, with other process variables being kept constant. The diffusion coefficient was observed to increase exponentially with the number of Lucite balls added to the system. By extendinp the work to higher ball fillings in the mixer, Sboji et al. [3] found that the diffusion coefficient increases with the number of balls added up to a certain limit and then remains constant. In an important first study with a continuous drum mixing system, using river sand with a distribution of particle !&es, Sugimoto 143 investigated the effect of mixing aids on the degree of mixedness in the absence of particle breakage. He found that when particles with a continuous size distribution flow through a rotary cylinder, the residence time distributions for each of the particle sizes did not overlap in the absence of mixing aids; but adding rubber balls to his system caused the residence time distributions of different particle sizes to overlap. The extent of overlappi- was observed to increase as the number of ribber balls in the mixer was increased. He also concluded that the apparent axial
dispersion coefficient for the whoIe particulae system flowing through a rotary drum increases when mixing aids are present. Using different tracer materials in a closedcircuit wet ball mil’, Kelsall et al. [ 51 studied both the residence time distribution and the breakage behavior of calcite. They observed that the mean residence time of particles of different sizes in their system did not differ appreciably. Similarly, in a study of the residence time distribution of cement in a tube mill, Austin et al. [6] observed that the average velocity of movement of different particle sizes through the mill is not a strong function of particle size, due to the vigorous mixing action within a tumbling ball mill. The present investigation is concerned with the effect of mixing aids on the holdup of material, as well as on the residence time distribution in a continuous rotary drum. In addition, the effect of mixing aids on segregation phenomena resulting from differences in physical properties of the various components was also investigated_ The operating variables considered in this investigation included the effect of the number of balls, the balI size, the feed rate of material, and the speed of the drum. The material variables included particle size, particle density and particle shape.
EXPERLMENTAL
METHODS
AND
MATERIALS
A horizontal drum, 24 cm long and 8 cm in diameter, was used throughout this investigation. As shown schematically in Fig. 1, the system was designed so that particIes could be fed at a constant rate and the discharge sampled for tracer distribution_ Lucite balls of density 1.2 g/cm3 were used as tine mixing aids. For most of the experiments, the balls had a diameter of 1.25 cm, but for studies of the ball size effect, balls of 1.6, 2.0, and 2.54 cm diam. were also utilized. To prevent the balls &om escaping from the drum exit, a wire grid was attached to the discharge opening. A detailed description of this setup and the general experimental procedure has been recently published elsewhere [?I. The bulk particulate material utilized in these experiments was 3 5 X 48 mesh dolomite. Tracers, which were analyzed by a counting procedure [S], were 28 X 35,48 X 65,
I
CONTINUOUS ROTARt
DRUM
EXPERIYENT*L
.PPAR*TvS
M,XER
i
Fig. 1. A schematic diagram of the experimental setuw It incIudes the feedine! section. the mixer. 24 &n x 8 cm horizontal d&n and the sampling section.
100 X 150, and 35 X 48 mesh dyed dolomite for the series of experiments on the effect of particle size on transport and segregation. For studying the effect of particle density and particle shape on segregation, the tracer comprised 35 X 48 particles of either magnetite, galena, glass beads, or copper shot.
EXPERIMENTAL
RESULTS
Holdup EffectofnumberofbalIsonhoZdup In this series of experiments,
up to 180 Lucite balls of 1.25 cm diameter were used. Them aximum number of balls was controlled by the back-flow of material that resulted from overloading the drum. As the number of balls is increased, the material holdup decreases because of the volume occupied by the added balls, but this decrease is nonlinear, as can be observed in Fig_ 2. At higher ball loadings, the holdup appears to remain constant with increasing number of balls. At this limit (about 160 balls), the volume of mixing aids in the system is about 50% of the total volume of material plus balls. This
263
0
50
100 150 NUMBER OF EzdJ.5
200
Fig. 2_ The holdup (balls and material) of number of balls.
as a function
means that the balls in the system at this limit are almost ELIcontact with each other and the particula e material just fills the voids between the balls. By increasing the number of balls beyond that limit, the additional balls will only “float” on the surface of the bed charge without entrapping material between them. In this same figure the total volume of the charge (material plus balls) is plotted uersus the number of balls. During the addition of the first 20 balls to the system, the total holdup decreases but then increases with further addition of mixing aids. When the first 20 balls are added to the system, they rush with the flowing material towards the discharge end and stay just in front of the wire net at the exit end. At this position, these few balls mainly act as a stirrer that helps in shuffling the particulate material out from the drum. As the volume of mixing aids increases further, they occupy a sufficiently longer portion of the drum length and begiu to hinder the flow of particles through the ball mass. This causes the level of material in the drum to increase and, consequently, also the total volumetric holdup of material plus balls.
1.25,1.6,2.0 and 2.54 cm, the material holdup was found to be 23, 22, 24 and 23 volume percent, respectively, clearly showing that there is no effect of ball size on the amount of material retained in the drum. The scatter of the holdup values can be considered as a characteristic of the presence of the mixing aids in the system. The added mixing aids result in a vigorous stirring effect of the particulate system inside the drum. This stirring action is not regular because in some instances the balls may be packed together and in other instances they may be separated. Due to the contraction and expansion of the assembly of mixing aids within the drum, the discharge of material from the drum is not regular but is affected by these irregular waves of contraction and expansion of the assembly of balls. This effect is reflected as fluctuations in the rate at which material is discharged, as can be seen in Fig. 3_ Figure 3 also shows that the fluctuations depend on ball size, which might be expected because the relative motion by an individual ball is much greater in the case of large bahs as compared with smaller ones. Actually the instantaneous fluctuations are even greater because each sample recorded in Fig. 3 was collected over 10 seconds but is plotted on a per-second basis. It should be pointed out that it would be very difficult to include these non-systematic fluctuations of the discharge material in any distributed parameter model for such system.
Effect of ball size on holdup In this series of experiments,
the same total volume of mixing aids was used in each experiment, with ah the experimental conditions being held constant except for the size of the added balls. With balls of diameters
Fig. 3. Fluctuations drum exit.
of the discharge material at the
Effect of &urn speed on_hoidup At a reasonable feed rate (1.8 g/set), the drum could not be run at speeds less than 42 r-p-m. (28% of the critical speed of the drum) because the material would flow back into the inlet due to the large head between the iniet and the outlet of the drum. The reason for the abnormally high head of material in the drum at such small feed rates and relatively high speed results from the high resistance that the material faces while passing through the assembly of balls within the drum. As can be seen from the results given in Fig. 4, the holdup decreases as the drum speed increases up to 80 r.p_m_ (55% of the critical speed of the drum)_ This may be due to the increase of the number of times the material has been shoveled along the drum axis by the balls (per unit time) as the drum speed increases, resulting in an increase in convective transport. As the drum rotational speed increases to 120 r.p.m. (about 83% of the critical speed of the drum), the hoIdup has increased again due to the cataracting of some of the material within the drum. In the same figure, the effect of the drum speed on the hoIdup without mixing aids is aIso plotted. The general trend of holdup with drum speed in the presence or absence of mixing aids is roughly similar, except for the pronounced shift in drum speed.
Effect
of material feed rate on holdup
The results presented in Fig. 5 show that the holdup increases linearly with feed rate, with the same trend as in the absence of mixing aids. The difference is that the rate of increase of holdup with feed rate is higher when mixing aids are present than in their absence. This probably results from the resistance offered by the mixing aids to the flow of particles through the drum. As a result, the slight increase in feed rate to the system requires a higher head for material to push itself through the mixing aids to reach the discharge end.
FEED RATi. GMSfSEC
Fig. 5. Holdup of material mixing aids - as a function
Residence-time
_ - with and without of material feed rate.
distribution
Effect of number of balls on the residencetime distribution (RTD) In ordinary transport processes in the absence of mixing aids, the most important mechanisms for mixing are dispersion of the individual particles by diffusion and convective dispersion caused by the flow of material
Fig. 4. Holdup of materiai - with aad without mixing aids - as a function of drum speed.
Corn the inlet towards the outlet. In the presence of mixing aids in the system, it appears that there is an additional mechanism of mixing created by the balls. This is the mixing by convection due to the disturbance of the flow of material by the balls. Quantitative evaluation of the effect of each of these three mechanisms (diffusion, convective dispersion, and convection) showed that, if the coefficients of these acting mechanisms are additive,
their relative values under similar conditions are the following: diffusion coefficient = 0.23 cm2/min, convective dispersion coefficient = 11.19 cm2/min, and convection coefficient = 0.81 cm2/min_ Here, however, discussion on the effect of the mixing aids will be based on the resultant effect of all the operative mechanisms. For study of any system to be technically fruitful, it must represent, to some extent, some situations in practice_ For this reason the minimum number of balls used in this investigation was the number that just covers the whole length of the mixer under the required operating conditions. For our experimental setup, the minimum number of balls required for this purpose was about 100 balls of 1.25 cm in diameter, or the volumetric equivalent of the other ball diameters. The first experiment in this series was run with the wire grid on the discharge end without any mixing aids added to the system. The number of balls was increased gradually from 100 to 180, which is the maximum number of balls that can be added without having any back-flow material from the inlet opening_ The variance of the residence-time distribution was used as the dependent variable. It was found that the variance of the residence-time distribution increases linearly with increasing number of balls up to a certain limit, after which it remains constant (Fig. 6). The reasons for increasing the variance with increasing number of balls may be due to the increase of the stirring action in the system as
Fig. 6. The dirpeusionless number of balls.
variance
as a function
of
the number of balls increases, which in turn increases the convection effect in the process. It seems that the critical limit of the number of balls beyond -.vhich the variance remains constant is the stage at which the particulate bed volume is occupied with balls. As discussed already, any extra balls beyond this limit “float” on the surface of the bed without further disturbance of the material. At this limit, the variance of the residence time distribution is about ten times the variance without mixing aids. Effect of ball size on the RTD The dimensionless variance, 002, of the RTD was found to be 10.0,9.9,9.5 and 10.2 X lop2 for balls of diameter 1.25,1.6,2.0 and 2.54 cm, respectively, at constant mixing aid volume. Thus. there is no significant change in the variance with changing the total surface area of the mixing phase. An important conclusion which can be drawn from this result is that the main factor in the effectiveness of mixing aids is their total volume rather than their total surface area. Effect of feed rate on the RTD The feed rate could be increased in this series of experiments only up to 2 g/set because at higher feed rates the material flows back out of the feed Met. It should be mentioned that the limiting feed rate in the presence of mixing aids is half the limiting feed rate in the absence of mixing aids under similar conditions. Figure 7, which gives the relation between the dimensionless variance of the residence-time distribution and the rate of feed to the drum, shows that the variance decreases as feed rate increases. The same trend can also be observed in the absence of mixing aids.
Fig. 7. The dimensionless variance as a fuktion of feed rate in glsec (with and without mixing aids).
266
Effect
of drum speed
on the RTD
It can be seen from Fig. 8 that the dimensionless variance of the residence time distribution increases as the speed of the drum increases_ This may result from the great disturbance caused by the mixing aids as the number of revolutions per unit time increases. But in fact, when the dimensionless variance per revolution is compared at different drum speeds, it is found that the variance decreases linearly with increasing speed (see Fig. 9). This is not the case in the absence of mixing aids, where the variance per revolution is constant in the constant shear zone region [ES] and increases sharply as the material begins to cataract_ If the two curves in Fig. 8 are compared, it will be observed that the rate of increase of the dimensionless variance in the presence of mixing aids is decreasing, while in the absence of mixing aids the rate of increase of the variance is increasing. This may be due to the damping effect of the mixing balls in the
cataracting stage where particles do not have similar chances to fly and collide in the upper space of the mixer. Finally, it should be mentioned that the time ait which tracers first report in the exit age distribution is always earlier in the presence of mixing aids than in their absence. The mixing efficiency of mixing aids As has been mentioned before, mixing aids
act as stirring elements for convective transport inside the system. This increases the particulate dispersion as well as minimizing the segregation tendency of the different components of the particulate system in the drum. The degree to which segregation is minimized depends mainly on the relative volume of the mixer that is occupied by the
mixing
The effect dispersion Fig_ 8. The dimensionless variance as a function drum speed (with and without mixing aids)_
of
Fig. 9. The dimensionless variance per revolution as a function of drum speed (with and without mixing aids)_
aids.
The
experiments
that
were
carried out to prove the effectiveness of mixing aids in minimizing segregation tendencies were designed such that there were sufficient differences in physical properties between the bulk and tracer to cause segregation in the absence of mixing aids. The bulk material was 35 X 48 mesh dolomite and the tracers sizes were 28 X 35,35 X 48,48 X 65 or 100 X 150 mesh dyed dolomite. The tracer density was varied between 2.8 and 8.7 g/cm’ and particle shapes ranged from irregular to spherical In all segregation experiments, the drum was run at 42 r-p-m. with 160 Lucite balls 1.25 cm in diameter at a cons’mnt bulk material feed rate of 1.8 -+ 0.1 g/set. of mixing aids on the extent
of
Figure 10 shows two C-curves: one, when mixing aids were used and the other without
Fig- 10. C-sxuves for 35 x 48 mesh dolomite rrarer flowing in dolomite bulk of the same particle size in the presence and in the absence of mixing aids.
267
using mixing aids. In the presence of mixing aids, the tracer is more dispersed; and the dimensionless start time, 0 s, and the mode of the C-curve are less. From this figure it is clear that the disturbance of the material flow by the mixing aids causes more dispersion and hence much more efficient mixing_ In fact, this effect is clearer when the relative concentration of the tracer is plotted uersus real time in the exit age distribution (Fig. 11).
Fig_ 11. Dimensional residence time distribution for 35 x 48 mesh dolomite tracer flowing in dolomite bulk of the same particle size in the presence and in the absence of mixing aids.
Segregation
Segregation is a serious problem that exists in the processes of mixing and/or transporting particulates whose components differ in their physical characteristics, such as their size [ 8, 91, density [S] , or shape [ 31. To show how serious this problem is, experiments were carried out using bulk and tracer materials of different physical properties. The dimensionless variance and the dimensionless as well as dimensional residence-time distributions were used to illustrate this effect. To determine how effective the mixing aids are in eliminating or minimizing segretation, the same series of experiments was repeated l&singmixing aids. The results will be discussed in detail in this section. Effect of tracer particle bulk size on segregation
material is discharged under-roasted while the larger sizes are over-roasted_ The reasons were not known. In fact, the main reason is that in the case of two or more different sizes inside a drum, segregation takes place because coarser particles tend to ‘float’ on the surface of the bed and fine particles segregate at the core of the bed. So, from the transport point of view, the floating material, Le. the coarse particles, always remain in the most active zone in the kiln (the shear zone), while the fine particles move in the least active zone (the core zone). Hence, the coarser particles on the surface are always subjected to the fresh current of gases and higher temperature, while the finer particles are mostly inside the moving bed away from the favorable conditions for roasting. Figure 12 shows the C-curves for the different dolomite tracer sizes in the absence of mixing aids. When plastic balls were added as mixing aids, segregation due to difference in particle size between the bulk and tracer was almost eliminated. Figure 13 shows the response curves for different tracer sizes in a bulk of 35 X 48 meshEffect of tracer particle density on segregation In this series of experiments, dolomite
(sp. g-r. 2.8), magnetite (sp. gr. 5.2) and galena (sp. g-r. 7.8) particles were used as tracers in dolomite as the bulk. The particle
size at constant
With the bulk size being kept constant, a series of experiments was run in which the tracer size was changed. Under these conditions, the variance decreases as the particle size of the tracer increases. In practice, the results of this phenomenon have been observed in the roasting process where the finer size
Fig. 12. Dimensional residence time distributions for dolomite tracers of different particle size flowing in dolomite bulk of 35 x 48 mesh size.
268
an indication of increased mixedness, but it is really a measure of the extent of segregation. Once again, when mixing aids were used in the system, segregation was eliminated and all the tracers, regardless of their densities, show the same response (see Fig. 17). Effect of particle segrega f ion 04
06
OS
LO
D*HENSIONLESS
12 TIME.
14
16
6
Fig. 13. C-curve for different tracer particle sizes flowing in 35 X 48 mesh dolomite in the presence of mixing aids.
size for the different tracers, as well as the bulk material, was 35 X 48 mesh. Here we are considering that particle shape does not differ significantly between the three different minerals. Figure 14 shows the C-curves of the response of the different tracers in absence of mixing aids. It can be seen that the modes of the curves are close to each other, but the starting time, to, and the spread are different. The starting time and the spread of the RTD increase as the density of the tracer particles increases. Table 1 illustrates the relationship between the dimensionless variance of the C-curves and the tracer particle dens&y. Again, as the density of the tracer exceeds that of the bulk, it can be observed that the dimensionless variance increases. In such cases of segregated systems, the increase in variance over the standard variance (i.e. when bulk and tracer have identical specific gravities) is not
shape and density
on
In this series of experiments two groups of tracers were used. Tn one of these groups the density of the tracers was approximately equal to that of the bulk material (dolomite), and in the other group the density of the tracer materials was about three times higher than that of the bulk material. In the first group, glass beads and dolomite particles of 35 X 48 mesh size were used to represent tracer particles of spherical and irregular shapes having a density of about 2.8 g/cm3 flowing in dolomite bulk of the same particle size (35 X 48 mesh). Figure 15 presents the C-curves for both glass beads and dolomite tracers in absence of Lucite balls. From this figure it can be seen that glass beads first accumulated at the discharge end of the drum, and finally, when their concentration became relatively high, they discharged mostly at once, with the rest coming out gradually by the random movement of the particles. In contrast, the dolomite discharged smoothly. The reasons for the abnormal
35 F
0
OLAsf-
26
6
0 Ito
140
60
160
Fig. 15. Dimensional Fig. 14_ Dimensional residence time distribution for tracers of different densities flowing in 35 x 48 mesh doIox+e (no mixii aids present)_
200 220 TIME. SECONDS
240
260
280
residence time distribution for tracer materials of different particle shape (dolomite uld glass beads) flowing in 35 x 48 mesh dolomite (no mixing aids present).
0
cubca
36 x 46 207
36 x 48 a.7
GhlU bonda
Coppar shot
2.60
2-48
2.42
2836
2,68 2046 2066
412
411
403
406
416 410 410
283
181
193
186
168 166 176
hod rate Holdup rT (ccc) (g/W (8)
166
166
169
172
6.96
0.72
1.89
1.22
0.64 0.77 0.91
(x1o-2)
(sac) 161 167 160
0;
7~
Dopondontpnrametorein abeeucoof mixingnids
22
276
106
164
364 266 200
PC
66
0.7
1.7
181
OS 0,a 1,o
(cm’/mln)
D
1.66
1.70
l-82
1.76
1.80 1.77 1076
232
236
237
236
241 242 244
138
136
132
133
137 140 138
Feed rate Holdup 7~ (SW) (glaec) (g)
140
136
130
136
134 137 139
10,a
9,t?
10.0
10.0
9,a lo,3 9,o
rg 0: (WC) (x10-2)
19
20
20
20
22 19 22
PC
DopondontpnromotomIn prosonccof mixingnlds**
*Bulkmatorinlwns dolomlto(sp, gr, 2.86 g/cm’) of pnrticloslzo 36 x 46 mesh, tha drum apcodwan42 r.p.m. (28%of its crrticnlspcod). **160 Lucite bnllaof 1.26 cm dlamotorand donalty1.2 g/cm3,
ephoroe
aphoras
irrrg.
96 x 40 7,0
irrag. irrog. irrog,
Partic ahapo
Galonn
28 x 36 2,86 36 x 48 2086 48 x 66 286
Pnrticle Pnrticlo danait{ tJiZ0 (mash) (g/cm )
Physicalproportlce
Magnotlto 96 x 48 6,2
Dolomlto
matorinl
TraCOr
TABLE1 Effect of physicalpropertiesof the tracer materialson their transportbehaviorin the presenceand in the nbsenceof mixingaids*
12.7
12.1
12.3
i2,a
11,6 12,7 11,l
(cm*/mln)
D
270 hand, our findings show that in the presence of mixing aids, segregation due to differences in particle shape and density is virtually eliminated, as shown in Fig. 17, which presents the response curves for tracers of different particle shapes and densities passing through the rotary drum under similar conditions. Table 1 summarizes the effect of the physical properties of the tracer materials on their transport behavior in a rotary drum in the presence and in the absence of mixing aids_ It is clear that in a nonsegregating system the effective dispersion coefficient, D, in the presence of mixing aids is more than ten times the dispersion coefficient in the absence of mixing aids. In the case of segregating systems, any segregation is almost eliminated by the addition of mixing aids to the system.
behavior of the glass beads can be explained as follows: beginning at the moment of injection, the tracer beads start percolating by gravity to the core of the bed because of the lower friction of the glass spheres. When almost all the tracer particles have accumulated at the end constriction, most of the spheres suddenly pour out and then the rest continue coming out randomly. This is mainly the reason that the MRT, the maximum concentration, C,,, , and the variance of the C-curve have higher values for glass beads than for dolomite_ In the second group of tracers, galena and copper spheres of densities about 7.8 and 8.7 g/cm3, respectively, and g/cm3 particle size of 35 X 48 mesh were used in dolomite bulk without mixing aids. Clearly, both of these tracers have a great tendency for segregation. Even though the intensity of segregation due to particle shape difference between galena and copper spheres can be observed in Fig. 15, the MRT and the estent of dispersion for copper spheres are much higher than the corresponding ones for galena. The reason may be drle to the fact that the irregulariy shaped galena particles are picked up more frequently by the flowing bulk particles than the smooth copper spheres. The same phenomenon was found by Kelsall et aZ_ [5], where they observed that steel spheres as tracer in calcite bulk behave completely differently from any other tracer. On the other
1
Fig. 17. Dimensionless residence time distribution for tracer materials of different particle shape and density each flowing in 35 x 48 mesh dolomite bulk in the presence of mixing aids.
SUMMARY
1 500
Fig. 16. DimensionaI residence time distribution for tracers of different particle shape and density (galena, copper shot and dolomite) flowing in 35 x 48 mesh dolomite in the absence of mixing aids.
AND
CONCLUSION
This study of the effect of mixing aids in the continuous flow of particulates through a rotating drum shows that the two main dependent variables are the holdup of material in the drum and the residence-time distribution of the discharge material. With respect to holdup, it was found that the material holdup decreases with increasing volume of mixing aids in the system up to a certain limit, beyond which it remains constant due to the total impregnation of the particulate bed with balls and the floating of the extra balls on the surface of the bed. An important observation is that the discharge of material fluctuates widely due to the presence
271
of balls even though the feed rate to the drum is essentially constant. The fluctuation range increases with increasing ball size, whereas the holdup is not affected by ball size. The dimensionless variance of the residence time distribution was used as a tool for studying the effect of the mixing aids on the transport behavior of materials in rotary drums. It was found that the variance increases with increasing number of balls up to a limit beyond which the variance remains constant. This iimit is the same one beyond which the holdup also remains constant. The variance is independent of the size of balls as long as the total ball volume is the same. As the feed rate increases, the variance decreases due to the decrease in retention time with increasing feed rate_ The variance increases with increasing speed, but the rate of increase of the variance decreases as speed increases. The most important effect of mixing aids is the elimination, or at least the minimizing, of the segregation of the particulate components in a system that is subject to segregation. It was found that the difference in physical properties (size, density, and/or shape) among the components flowing has no effect on the transport behavior of these components in the presence of the mixing aids. In contrast, these differences in physical properties, in the absence of mixing aids, have a serious effect on the flow properties of the different components. As a result of the presence of mixing aids, the dispersion of the various components in the particulate system increases markedly, which in turn is reflected in improved mixing_
ACKNOWLEDGEMENTS
The authors wish to acknowledge the National Science Foundation for the support of this research.
LIST OF SYMBOLS co
C(t)
average concentration of the tracer in the drum tracer concentration in the residence thne distribution at time t
c(e 1
c max D H J Pe t
to V 8 00 iB =T
d P
dimensionless concentration maximum concentration in the residence time distribution effective dispersion coefficient holdup of material in the drum fractional ball filling Peclet number time, set starting time of the tracer to report in the exit age distribution, set volume of the rotating drum dimensionless time, t/r dimensionless starting time, to /r mean residence time of the bulk material mean residence time of the tracer material dimensionless variance of the residence time distribution bulk density of the flowing material
REFERENCES Y. Sawahato, On mixing of solids with mixing aids, Kagaku Kogaku, 30 (1966) 178. P. K. Chaudhuri and D. W_ Fuerstenau, The effect of mixing aids on the kinerics of mixing in a rotating drum, Powder Technol., 4 (1970/71) 146. K. Shoji, R. Hogg and C. G. Austin, Axial mixing of partictes in batch ball mills, Powder Technol., 7 (1973) 331. M. Sugimoto, Effect of the ball Filling on the residence time distribution of particles flowing through a rotary cylinder, Kagaku Kogaku, 32 (1968) 196. D. F. Kelsall, K. J. Reid and C. J_ Restarick, Continuous grinding in a small wet ball mill. Part III. A study of distribution of residence time, Powder Technol., 4 (1969/70) 170. L. G. Austin, P. T. Luckie and B. G. Ateya, Residence time distribution in mills, Gem_ Concr_ Res., 1 (1971) 241. A.-Z. Abouzeid, T. S. Mika, K. V. S. Sastry and D. W. Fuerstenau, The influence of operating variables on the residence time distribution For material transport in a continuous rotary drum, Powder Technol., 10 (1974) 273. A.-Z. Abouzeid, Transport and mixing behavior of particulate solids through rotary drums, Ph_D_ Diss.. Univ. of California, Berkeley, 1973. A_ Men and O_ Molerus, Ermittlung der Transportkoeffizienten van Schiittfiitern in einem Drehrohr und ihre Abhsngigkeit von Korngrosse und MarkierungsFunktion,Dechema-Monographien, Symposium, Cannes, Band 69, Nr. 1292 - 1326, Tei12 (1971) 675.
Effect
of Mixing
23 (1979) 26X171 S.A., Lausanne -Printed
Aids on the Transport
A.-Z. M. ABOUZIEDDepartment
of Materials
Behavior
of Particulate
Solids
and D. W. FUERSTBNAU Science and MinemZ Engineering,
(Received January 15.1979;
Uniuersity
of CaZifornia. Berkeley,
Calif
94720
(U.S.A.)
in revised form March 30,1979)
SUMMARY Tbe behavior
261
in the Netherlands
of particulate
materials
being
transported through rotary drums is strongly affected by the addition of mixing aids to the system. This effect is reflected in three main dependent parameters: holdup, variance of the residence-time distribution, and extent of particulate segregation in the drum. In addition, the discharge rate of material fluctuates widely due to the presence of mixing aids. The holdup decreases to a limiting value with increasing volume of mixing aids. The dimensionless variance of the residence time distribution increases with increasing volume of mixing aids up to a certain limit, beyond which it remained constant. This is the same limit that controls the constancy of holdup. In a system with segregating components due to differences in such physical properties as density, particle size, particle shape and roughness, the presence of mixing aids virtually eliminates segregation or at least minimizes its effect in all cases. INTRODUCTION The addition of balls as mixing aids to drum mixers accelerates the mixing process and minimizes segregation mainly through
their pronounced effect on convective particle transport within the system. In a similar way, the balls that are used for size reduction in tumbling mills also markedly influence the transport behavior of material flowing through a baU mill. *Resent address: Departmentof Mining, Petroleum and Metallurgy, Faculty or‘ Engineering, Cairo University, Egypt.
Thus far, only limited work has been reported on the effect of mixing aids on such phenomena as the holdup of material in rotating cylinders, the residence time distribution of the material passing through the drum, and mixing kinetics. In 1966 Sawahato [l] experimentally demonstrated the effect of adding rubber balls as aids for the mixing of sand grains that had been dyed with two different colors. That work was followed by a somewhat more quantitative evaluation of the effect of mixing aids by Chaudhuri and Fuerstenau 121, who obtained a quantitative correlation between the diffusion coefficient of one component of a mixture into the other as a function of the number of added balls, with other process variables being kept constant. The diffusion coefficient was observed to increase exponentially with the number of Lucite balls added to the system. By extendinp the work to higher ball fillings in the mixer, Sboji et al. [3] found that the diffusion coefficient increases with the number of balls added up to a certain limit and then remains constant. In an important first study with a continuous drum mixing system, using river sand with a distribution of particle !&es, Sugimoto 143 investigated the effect of mixing aids on the degree of mixedness in the absence of particle breakage. He found that when particles with a continuous size distribution flow through a rotary cylinder, the residence time distributions for each of the particle sizes did not overlap in the absence of mixing aids; but adding rubber balls to his system caused the residence time distributions of different particle sizes to overlap. The extent of overlappi- was observed to increase as the number of ribber balls in the mixer was increased. He also concluded that the apparent axial
dispersion coefficient for the whoIe particulae system flowing through a rotary drum increases when mixing aids are present. Using different tracer materials in a closedcircuit wet ball mil’, Kelsall et al. [ 51 studied both the residence time distribution and the breakage behavior of calcite. They observed that the mean residence time of particles of different sizes in their system did not differ appreciably. Similarly, in a study of the residence time distribution of cement in a tube mill, Austin et al. [6] observed that the average velocity of movement of different particle sizes through the mill is not a strong function of particle size, due to the vigorous mixing action within a tumbling ball mill. The present investigation is concerned with the effect of mixing aids on the holdup of material, as well as on the residence time distribution in a continuous rotary drum. In addition, the effect of mixing aids on segregation phenomena resulting from differences in physical properties of the various components was also investigated_ The operating variables considered in this investigation included the effect of the number of balls, the balI size, the feed rate of material, and the speed of the drum. The material variables included particle size, particle density and particle shape.
EXPERLMENTAL
METHODS
AND
MATERIALS
A horizontal drum, 24 cm long and 8 cm in diameter, was used throughout this investigation. As shown schematically in Fig. 1, the system was designed so that particIes could be fed at a constant rate and the discharge sampled for tracer distribution_ Lucite balls of density 1.2 g/cm3 were used as tine mixing aids. For most of the experiments, the balls had a diameter of 1.25 cm, but for studies of the ball size effect, balls of 1.6, 2.0, and 2.54 cm diam. were also utilized. To prevent the balls &om escaping from the drum exit, a wire grid was attached to the discharge opening. A detailed description of this setup and the general experimental procedure has been recently published elsewhere [?I. The bulk particulate material utilized in these experiments was 3 5 X 48 mesh dolomite. Tracers, which were analyzed by a counting procedure [S], were 28 X 35,48 X 65,
I
CONTINUOUS ROTARt
DRUM
EXPERIYENT*L
.PPAR*TvS
M,XER
i
Fig. 1. A schematic diagram of the experimental setuw It incIudes the feedine! section. the mixer. 24 &n x 8 cm horizontal d&n and the sampling section.
100 X 150, and 35 X 48 mesh dyed dolomite for the series of experiments on the effect of particle size on transport and segregation. For studying the effect of particle density and particle shape on segregation, the tracer comprised 35 X 48 particles of either magnetite, galena, glass beads, or copper shot.
EXPERIMENTAL
RESULTS
Holdup EffectofnumberofbalIsonhoZdup In this series of experiments,
up to 180 Lucite balls of 1.25 cm diameter were used. Them aximum number of balls was controlled by the back-flow of material that resulted from overloading the drum. As the number of balls is increased, the material holdup decreases because of the volume occupied by the added balls, but this decrease is nonlinear, as can be observed in Fig_ 2. At higher ball loadings, the holdup appears to remain constant with increasing number of balls. At this limit (about 160 balls), the volume of mixing aids in the system is about 50% of the total volume of material plus balls. This
263
0
50
100 150 NUMBER OF EzdJ.5
200
Fig. 2_ The holdup (balls and material) of number of balls.
as a function
means that the balls in the system at this limit are almost ELIcontact with each other and the particula e material just fills the voids between the balls. By increasing the number of balls beyond that limit, the additional balls will only “float” on the surface of the bed charge without entrapping material between them. In this same figure the total volume of the charge (material plus balls) is plotted uersus the number of balls. During the addition of the first 20 balls to the system, the total holdup decreases but then increases with further addition of mixing aids. When the first 20 balls are added to the system, they rush with the flowing material towards the discharge end and stay just in front of the wire net at the exit end. At this position, these few balls mainly act as a stirrer that helps in shuffling the particulate material out from the drum. As the volume of mixing aids increases further, they occupy a sufficiently longer portion of the drum length and begiu to hinder the flow of particles through the ball mass. This causes the level of material in the drum to increase and, consequently, also the total volumetric holdup of material plus balls.
1.25,1.6,2.0 and 2.54 cm, the material holdup was found to be 23, 22, 24 and 23 volume percent, respectively, clearly showing that there is no effect of ball size on the amount of material retained in the drum. The scatter of the holdup values can be considered as a characteristic of the presence of the mixing aids in the system. The added mixing aids result in a vigorous stirring effect of the particulate system inside the drum. This stirring action is not regular because in some instances the balls may be packed together and in other instances they may be separated. Due to the contraction and expansion of the assembly of mixing aids within the drum, the discharge of material from the drum is not regular but is affected by these irregular waves of contraction and expansion of the assembly of balls. This effect is reflected as fluctuations in the rate at which material is discharged, as can be seen in Fig. 3_ Figure 3 also shows that the fluctuations depend on ball size, which might be expected because the relative motion by an individual ball is much greater in the case of large bahs as compared with smaller ones. Actually the instantaneous fluctuations are even greater because each sample recorded in Fig. 3 was collected over 10 seconds but is plotted on a per-second basis. It should be pointed out that it would be very difficult to include these non-systematic fluctuations of the discharge material in any distributed parameter model for such system.
Effect of ball size on holdup In this series of experiments,
the same total volume of mixing aids was used in each experiment, with ah the experimental conditions being held constant except for the size of the added balls. With balls of diameters
Fig. 3. Fluctuations drum exit.
of the discharge material at the
Effect of &urn speed on_hoidup At a reasonable feed rate (1.8 g/set), the drum could not be run at speeds less than 42 r-p-m. (28% of the critical speed of the drum) because the material would flow back into the inlet due to the large head between the iniet and the outlet of the drum. The reason for the abnormally high head of material in the drum at such small feed rates and relatively high speed results from the high resistance that the material faces while passing through the assembly of balls within the drum. As can be seen from the results given in Fig. 4, the holdup decreases as the drum speed increases up to 80 r.p_m_ (55% of the critical speed of the drum)_ This may be due to the increase of the number of times the material has been shoveled along the drum axis by the balls (per unit time) as the drum speed increases, resulting in an increase in convective transport. As the drum rotational speed increases to 120 r.p.m. (about 83% of the critical speed of the drum), the hoIdup has increased again due to the cataracting of some of the material within the drum. In the same figure, the effect of the drum speed on the hoIdup without mixing aids is aIso plotted. The general trend of holdup with drum speed in the presence or absence of mixing aids is roughly similar, except for the pronounced shift in drum speed.
Effect
of material feed rate on holdup
The results presented in Fig. 5 show that the holdup increases linearly with feed rate, with the same trend as in the absence of mixing aids. The difference is that the rate of increase of holdup with feed rate is higher when mixing aids are present than in their absence. This probably results from the resistance offered by the mixing aids to the flow of particles through the drum. As a result, the slight increase in feed rate to the system requires a higher head for material to push itself through the mixing aids to reach the discharge end.
FEED RATi. GMSfSEC
Fig. 5. Holdup of material mixing aids - as a function
Residence-time
_ - with and without of material feed rate.
distribution
Effect of number of balls on the residencetime distribution (RTD) In ordinary transport processes in the absence of mixing aids, the most important mechanisms for mixing are dispersion of the individual particles by diffusion and convective dispersion caused by the flow of material
Fig. 4. Holdup of materiai - with aad without mixing aids - as a function of drum speed.
Corn the inlet towards the outlet. In the presence of mixing aids in the system, it appears that there is an additional mechanism of mixing created by the balls. This is the mixing by convection due to the disturbance of the flow of material by the balls. Quantitative evaluation of the effect of each of these three mechanisms (diffusion, convective dispersion, and convection) showed that, if the coefficients of these acting mechanisms are additive,
their relative values under similar conditions are the following: diffusion coefficient = 0.23 cm2/min, convective dispersion coefficient = 11.19 cm2/min, and convection coefficient = 0.81 cm2/min_ Here, however, discussion on the effect of the mixing aids will be based on the resultant effect of all the operative mechanisms. For study of any system to be technically fruitful, it must represent, to some extent, some situations in practice_ For this reason the minimum number of balls used in this investigation was the number that just covers the whole length of the mixer under the required operating conditions. For our experimental setup, the minimum number of balls required for this purpose was about 100 balls of 1.25 cm in diameter, or the volumetric equivalent of the other ball diameters. The first experiment in this series was run with the wire grid on the discharge end without any mixing aids added to the system. The number of balls was increased gradually from 100 to 180, which is the maximum number of balls that can be added without having any back-flow material from the inlet opening_ The variance of the residence-time distribution was used as the dependent variable. It was found that the variance of the residence-time distribution increases linearly with increasing number of balls up to a certain limit, after which it remains constant (Fig. 6). The reasons for increasing the variance with increasing number of balls may be due to the increase of the stirring action in the system as
Fig. 6. The dirpeusionless number of balls.
variance
as a function
of
the number of balls increases, which in turn increases the convection effect in the process. It seems that the critical limit of the number of balls beyond -.vhich the variance remains constant is the stage at which the particulate bed volume is occupied with balls. As discussed already, any extra balls beyond this limit “float” on the surface of the bed without further disturbance of the material. At this limit, the variance of the residence time distribution is about ten times the variance without mixing aids. Effect of ball size on the RTD The dimensionless variance, 002, of the RTD was found to be 10.0,9.9,9.5 and 10.2 X lop2 for balls of diameter 1.25,1.6,2.0 and 2.54 cm, respectively, at constant mixing aid volume. Thus. there is no significant change in the variance with changing the total surface area of the mixing phase. An important conclusion which can be drawn from this result is that the main factor in the effectiveness of mixing aids is their total volume rather than their total surface area. Effect of feed rate on the RTD The feed rate could be increased in this series of experiments only up to 2 g/set because at higher feed rates the material flows back out of the feed Met. It should be mentioned that the limiting feed rate in the presence of mixing aids is half the limiting feed rate in the absence of mixing aids under similar conditions. Figure 7, which gives the relation between the dimensionless variance of the residence-time distribution and the rate of feed to the drum, shows that the variance decreases as feed rate increases. The same trend can also be observed in the absence of mixing aids.
Fig. 7. The dimensionless variance as a fuktion of feed rate in glsec (with and without mixing aids).
266
Effect
of drum speed
on the RTD
It can be seen from Fig. 8 that the dimensionless variance of the residence time distribution increases as the speed of the drum increases_ This may result from the great disturbance caused by the mixing aids as the number of revolutions per unit time increases. But in fact, when the dimensionless variance per revolution is compared at different drum speeds, it is found that the variance decreases linearly with increasing speed (see Fig. 9). This is not the case in the absence of mixing aids, where the variance per revolution is constant in the constant shear zone region [ES] and increases sharply as the material begins to cataract_ If the two curves in Fig. 8 are compared, it will be observed that the rate of increase of the dimensionless variance in the presence of mixing aids is decreasing, while in the absence of mixing aids the rate of increase of the variance is increasing. This may be due to the damping effect of the mixing balls in the
cataracting stage where particles do not have similar chances to fly and collide in the upper space of the mixer. Finally, it should be mentioned that the time ait which tracers first report in the exit age distribution is always earlier in the presence of mixing aids than in their absence. The mixing efficiency of mixing aids As has been mentioned before, mixing aids
act as stirring elements for convective transport inside the system. This increases the particulate dispersion as well as minimizing the segregation tendency of the different components of the particulate system in the drum. The degree to which segregation is minimized depends mainly on the relative volume of the mixer that is occupied by the
mixing
The effect dispersion Fig_ 8. The dimensionless variance as a function drum speed (with and without mixing aids)_
of
Fig. 9. The dimensionless variance per revolution as a function of drum speed (with and without mixing aids)_
aids.
The
experiments
that
were
carried out to prove the effectiveness of mixing aids in minimizing segregation tendencies were designed such that there were sufficient differences in physical properties between the bulk and tracer to cause segregation in the absence of mixing aids. The bulk material was 35 X 48 mesh dolomite and the tracers sizes were 28 X 35,35 X 48,48 X 65 or 100 X 150 mesh dyed dolomite. The tracer density was varied between 2.8 and 8.7 g/cm’ and particle shapes ranged from irregular to spherical In all segregation experiments, the drum was run at 42 r-p-m. with 160 Lucite balls 1.25 cm in diameter at a cons’mnt bulk material feed rate of 1.8 -+ 0.1 g/set. of mixing aids on the extent
of
Figure 10 shows two C-curves: one, when mixing aids were used and the other without
Fig- 10. C-sxuves for 35 x 48 mesh dolomite rrarer flowing in dolomite bulk of the same particle size in the presence and in the absence of mixing aids.
267
using mixing aids. In the presence of mixing aids, the tracer is more dispersed; and the dimensionless start time, 0 s, and the mode of the C-curve are less. From this figure it is clear that the disturbance of the material flow by the mixing aids causes more dispersion and hence much more efficient mixing_ In fact, this effect is clearer when the relative concentration of the tracer is plotted uersus real time in the exit age distribution (Fig. 11).
Fig_ 11. Dimensional residence time distribution for 35 x 48 mesh dolomite tracer flowing in dolomite bulk of the same particle size in the presence and in the absence of mixing aids.
Segregation
Segregation is a serious problem that exists in the processes of mixing and/or transporting particulates whose components differ in their physical characteristics, such as their size [ 8, 91, density [S] , or shape [ 31. To show how serious this problem is, experiments were carried out using bulk and tracer materials of different physical properties. The dimensionless variance and the dimensionless as well as dimensional residence-time distributions were used to illustrate this effect. To determine how effective the mixing aids are in eliminating or minimizing segretation, the same series of experiments was repeated l&singmixing aids. The results will be discussed in detail in this section. Effect of tracer particle bulk size on segregation
material is discharged under-roasted while the larger sizes are over-roasted_ The reasons were not known. In fact, the main reason is that in the case of two or more different sizes inside a drum, segregation takes place because coarser particles tend to ‘float’ on the surface of the bed and fine particles segregate at the core of the bed. So, from the transport point of view, the floating material, Le. the coarse particles, always remain in the most active zone in the kiln (the shear zone), while the fine particles move in the least active zone (the core zone). Hence, the coarser particles on the surface are always subjected to the fresh current of gases and higher temperature, while the finer particles are mostly inside the moving bed away from the favorable conditions for roasting. Figure 12 shows the C-curves for the different dolomite tracer sizes in the absence of mixing aids. When plastic balls were added as mixing aids, segregation due to difference in particle size between the bulk and tracer was almost eliminated. Figure 13 shows the response curves for different tracer sizes in a bulk of 35 X 48 meshEffect of tracer particle density on segregation In this series of experiments, dolomite
(sp. g-r. 2.8), magnetite (sp. gr. 5.2) and galena (sp. g-r. 7.8) particles were used as tracers in dolomite as the bulk. The particle
size at constant
With the bulk size being kept constant, a series of experiments was run in which the tracer size was changed. Under these conditions, the variance decreases as the particle size of the tracer increases. In practice, the results of this phenomenon have been observed in the roasting process where the finer size
Fig. 12. Dimensional residence time distributions for dolomite tracers of different particle size flowing in dolomite bulk of 35 x 48 mesh size.
268
an indication of increased mixedness, but it is really a measure of the extent of segregation. Once again, when mixing aids were used in the system, segregation was eliminated and all the tracers, regardless of their densities, show the same response (see Fig. 17). Effect of particle segrega f ion 04
06
OS
LO
D*HENSIONLESS
12 TIME.
14
16
6
Fig. 13. C-curve for different tracer particle sizes flowing in 35 X 48 mesh dolomite in the presence of mixing aids.
size for the different tracers, as well as the bulk material, was 35 X 48 mesh. Here we are considering that particle shape does not differ significantly between the three different minerals. Figure 14 shows the C-curves of the response of the different tracers in absence of mixing aids. It can be seen that the modes of the curves are close to each other, but the starting time, to, and the spread are different. The starting time and the spread of the RTD increase as the density of the tracer particles increases. Table 1 illustrates the relationship between the dimensionless variance of the C-curves and the tracer particle dens&y. Again, as the density of the tracer exceeds that of the bulk, it can be observed that the dimensionless variance increases. In such cases of segregated systems, the increase in variance over the standard variance (i.e. when bulk and tracer have identical specific gravities) is not
shape and density
on
In this series of experiments two groups of tracers were used. Tn one of these groups the density of the tracers was approximately equal to that of the bulk material (dolomite), and in the other group the density of the tracer materials was about three times higher than that of the bulk material. In the first group, glass beads and dolomite particles of 35 X 48 mesh size were used to represent tracer particles of spherical and irregular shapes having a density of about 2.8 g/cm3 flowing in dolomite bulk of the same particle size (35 X 48 mesh). Figure 15 presents the C-curves for both glass beads and dolomite tracers in absence of Lucite balls. From this figure it can be seen that glass beads first accumulated at the discharge end of the drum, and finally, when their concentration became relatively high, they discharged mostly at once, with the rest coming out gradually by the random movement of the particles. In contrast, the dolomite discharged smoothly. The reasons for the abnormal
35 F
0
OLAsf-
26
6
0 Ito
140
60
160
Fig. 15. Dimensional Fig. 14_ Dimensional residence time distribution for tracers of different densities flowing in 35 x 48 mesh doIox+e (no mixii aids present)_
200 220 TIME. SECONDS
240
260
280
residence time distribution for tracer materials of different particle shape (dolomite uld glass beads) flowing in 35 x 48 mesh dolomite (no mixing aids present).
0
cubca
36 x 46 207
36 x 48 a.7
GhlU bonda
Coppar shot
2.60
2-48
2.42
2836
2,68 2046 2066
412
411
403
406
416 410 410
283
181
193
186
168 166 176
hod rate Holdup rT (ccc) (g/W (8)
166
166
169
172
6.96
0.72
1.89
1.22
0.64 0.77 0.91
(x1o-2)
(sac) 161 167 160
0;
7~
Dopondontpnrametorein abeeucoof mixingnids
22
276
106
164
364 266 200
PC
66
0.7
1.7
181
OS 0,a 1,o
(cm’/mln)
D
1.66
1.70
l-82
1.76
1.80 1.77 1076
232
236
237
236
241 242 244
138
136
132
133
137 140 138
Feed rate Holdup 7~ (SW) (glaec) (g)
140
136
130
136
134 137 139
10,a
9,t?
10.0
10.0
9,a lo,3 9,o
rg 0: (WC) (x10-2)
19
20
20
20
22 19 22
PC
DopondontpnromotomIn prosonccof mixingnlds**
*Bulkmatorinlwns dolomlto(sp, gr, 2.86 g/cm’) of pnrticloslzo 36 x 46 mesh, tha drum apcodwan42 r.p.m. (28%of its crrticnlspcod). **160 Lucite bnllaof 1.26 cm dlamotorand donalty1.2 g/cm3,
ephoroe
aphoras
irrrg.
96 x 40 7,0
irrag. irrog. irrog,
Partic ahapo
Galonn
28 x 36 2,86 36 x 48 2086 48 x 66 286
Pnrticle Pnrticlo danait{ tJiZ0 (mash) (g/cm )
Physicalproportlce
Magnotlto 96 x 48 6,2
Dolomlto
matorinl
TraCOr
TABLE1 Effect of physicalpropertiesof the tracer materialson their transportbehaviorin the presenceand in the nbsenceof mixingaids*
12.7
12.1
12.3
i2,a
11,6 12,7 11,l
(cm*/mln)
D
270 hand, our findings show that in the presence of mixing aids, segregation due to differences in particle shape and density is virtually eliminated, as shown in Fig. 17, which presents the response curves for tracers of different particle shapes and densities passing through the rotary drum under similar conditions. Table 1 summarizes the effect of the physical properties of the tracer materials on their transport behavior in a rotary drum in the presence and in the absence of mixing aids_ It is clear that in a nonsegregating system the effective dispersion coefficient, D, in the presence of mixing aids is more than ten times the dispersion coefficient in the absence of mixing aids. In the case of segregating systems, any segregation is almost eliminated by the addition of mixing aids to the system.
behavior of the glass beads can be explained as follows: beginning at the moment of injection, the tracer beads start percolating by gravity to the core of the bed because of the lower friction of the glass spheres. When almost all the tracer particles have accumulated at the end constriction, most of the spheres suddenly pour out and then the rest continue coming out randomly. This is mainly the reason that the MRT, the maximum concentration, C,,, , and the variance of the C-curve have higher values for glass beads than for dolomite_ In the second group of tracers, galena and copper spheres of densities about 7.8 and 8.7 g/cm3, respectively, and g/cm3 particle size of 35 X 48 mesh were used in dolomite bulk without mixing aids. Clearly, both of these tracers have a great tendency for segregation. Even though the intensity of segregation due to particle shape difference between galena and copper spheres can be observed in Fig. 15, the MRT and the estent of dispersion for copper spheres are much higher than the corresponding ones for galena. The reason may be drle to the fact that the irregulariy shaped galena particles are picked up more frequently by the flowing bulk particles than the smooth copper spheres. The same phenomenon was found by Kelsall et aZ_ [5], where they observed that steel spheres as tracer in calcite bulk behave completely differently from any other tracer. On the other
1
Fig. 17. Dimensionless residence time distribution for tracer materials of different particle shape and density each flowing in 35 x 48 mesh dolomite bulk in the presence of mixing aids.
SUMMARY
1 500
Fig. 16. DimensionaI residence time distribution for tracers of different particle shape and density (galena, copper shot and dolomite) flowing in 35 x 48 mesh dolomite in the absence of mixing aids.
AND
CONCLUSION
This study of the effect of mixing aids in the continuous flow of particulates through a rotating drum shows that the two main dependent variables are the holdup of material in the drum and the residence-time distribution of the discharge material. With respect to holdup, it was found that the material holdup decreases with increasing volume of mixing aids in the system up to a certain limit, beyond which it remains constant due to the total impregnation of the particulate bed with balls and the floating of the extra balls on the surface of the bed. An important observation is that the discharge of material fluctuates widely due to the presence
271
of balls even though the feed rate to the drum is essentially constant. The fluctuation range increases with increasing ball size, whereas the holdup is not affected by ball size. The dimensionless variance of the residence time distribution was used as a tool for studying the effect of the mixing aids on the transport behavior of materials in rotary drums. It was found that the variance increases with increasing number of balls up to a limit beyond which the variance remains constant. This iimit is the same one beyond which the holdup also remains constant. The variance is independent of the size of balls as long as the total ball volume is the same. As the feed rate increases, the variance decreases due to the decrease in retention time with increasing feed rate_ The variance increases with increasing speed, but the rate of increase of the variance decreases as speed increases. The most important effect of mixing aids is the elimination, or at least the minimizing, of the segregation of the particulate components in a system that is subject to segregation. It was found that the difference in physical properties (size, density, and/or shape) among the components flowing has no effect on the transport behavior of these components in the presence of the mixing aids. In contrast, these differences in physical properties, in the absence of mixing aids, have a serious effect on the flow properties of the different components. As a result of the presence of mixing aids, the dispersion of the various components in the particulate system increases markedly, which in turn is reflected in improved mixing_
ACKNOWLEDGEMENTS
The authors wish to acknowledge the National Science Foundation for the support of this research.
LIST OF SYMBOLS co
C(t)
average concentration of the tracer in the drum tracer concentration in the residence thne distribution at time t
c(e 1
c max D H J Pe t
to V 8 00 iB =T
d P
dimensionless concentration maximum concentration in the residence time distribution effective dispersion coefficient holdup of material in the drum fractional ball filling Peclet number time, set starting time of the tracer to report in the exit age distribution, set volume of the rotating drum dimensionless time, t/r dimensionless starting time, to /r mean residence time of the bulk material mean residence time of the tracer material dimensionless variance of the residence time distribution bulk density of the flowing material
REFERENCES Y. Sawahato, On mixing of solids with mixing aids, Kagaku Kogaku, 30 (1966) 178. P. K. Chaudhuri and D. W_ Fuerstenau, The effect of mixing aids on the kinerics of mixing in a rotating drum, Powder Technol., 4 (1970/71) 146. K. Shoji, R. Hogg and C. G. Austin, Axial mixing of partictes in batch ball mills, Powder Technol., 7 (1973) 331. M. Sugimoto, Effect of the ball Filling on the residence time distribution of particles flowing through a rotary cylinder, Kagaku Kogaku, 32 (1968) 196. D. F. Kelsall, K. J. Reid and C. J_ Restarick, Continuous grinding in a small wet ball mill. Part III. A study of distribution of residence time, Powder Technol., 4 (1969/70) 170. L. G. Austin, P. T. Luckie and B. G. Ateya, Residence time distribution in mills, Gem_ Concr_ Res., 1 (1971) 241. A.-Z. Abouzeid, T. S. Mika, K. V. S. Sastry and D. W. Fuerstenau, The influence of operating variables on the residence time distribution For material transport in a continuous rotary drum, Powder Technol., 10 (1974) 273. A.-Z. Abouzeid, Transport and mixing behavior of particulate solids through rotary drums, Ph_D_ Diss.. Univ. of California, Berkeley, 1973. A_ Men and O_ Molerus, Ermittlung der Transportkoeffizienten van Schiittfiitern in einem Drehrohr und ihre Abhsngigkeit von Korngrosse und MarkierungsFunktion,Dechema-Monographien, Symposium, Cannes, Band 69, Nr. 1292 - 1326, Tei12 (1971) 675.