MIXING OF SOLIDS Experiments with Tumbling Blenders A R N0 LD KA U FM A
N, Merck Sharp
&? Dohme Research Laboratories, Rahway, X. J .
The dry mixing of antibiotics was tested in a double-cone blender and three twin-shell blenders of different capacities. The progress of mixing was studied b y measuring the variance of a set of 10 random samples after different numbers of blender revolutions. A comparison of the two blender types showed that the twin-shell blender gave slightly better mixing results than the double-cone blender. Evaluation of various twin-shell blenders ( 1 -pint, 8-quart, 50-cu. foot) indicated greater mixing rates in the larger blenders.
the lead of previous workers in this field (77), a quantitative method for evaluating the progress of mixing of a two-component solids mixture was developed. The sample size was chosen to correspond to the ultimate commercial subdivision of a production-size antibiotic mixture. Ten samples were taken from randomly selected positions in the mixer after different numbers of revolutions. After analyzing for one component, the variance of the set of samples was computed and used as a criterion of homogeneity. The course of mixing was studied in 1-pint and 8-quart twin-shell blenders and in a 1-pint double-cone blender. Limited data were obtained in a 50-cu. foot twin-shell blender. The main purposes of this work were to ascertain whether the tumbling blenders produced satisfactory mixtures, to compare the performance of the double-cone and the twin-shell units, and to obtain information regarding the factors influencing mixer scale-up. The techniques described here can be applied in other solids mixing problems. OLLOWING
Experimental
The twin-shell blenders used were standard units manufactured by the Patterson-Kelley Co., Inc., East Stroudsburg, Pa. (Figure 1). T h e double-cone blender (Figure 2) was constructed to Merck specifications by Patterson-Kelley. In most runs, procaine penicillin G was used as the measured component and dihydrostreptomycin sulfate as the second component. Specially designed rods (7, 72) and guides ( 7 ) were used to obtain random samples of the mixture. Ten samples were selected as a reasonable number to establish a point on the mixing curve. Three coordinate numbers completely describe a sample position within the mixture. Random sample positions were obtained by selecting values for each position from a table of random numbers ( 8 ) . After the mixer had been stopped at the desired number of rotations, the samples were taken with the sampling rod and guide at the positions specified. An attempt was made to maintain a constant ratio of sample volume to mixer volume for all mixer sizes te ted. The value of the ratio was determined by dividing the ultimate subdivision (about 5 grams) by the total weight of a production blend (400 to 600 kg.). Therefore, the ratio of sample weight to mixture weight for the production blender was equal to 0.8 to
1.2
x
10-5.
For each series of 10 samples, the following quantities are calculated : Mean concentration, Absolute deviation,
X
=
ZX
-
[XI= [X - XI
ZlXl Average deviation, a.d. = Unbiased estimate of variance,
Figure 1.
These calculations for the set of 10 samples led to one point on the mixing curve. These simple calculations give the variance at some desired intermediate point during the course of mixing. There are additional relationships that define the end conditions of the mixing process. For the two-component mixture
Twin-shell blenders
uo*=
Discharge nozzle arrangement (not shown) differs with blenders Blender Capacity 1 pint 8 quarts 5 0 cu. ft. 104
Dimensions Inches B C
A 40' 45O
40'
3 7'18 42
I&EC FUNDAMENTALS
2114
6 2281,
2:XZ n-1
s2 = __
- P)
It can be seen that this equation is independent of sample size. Lacey ( 6 ) has shown that
D 5'18 13a/, 72a/,
P(l
=
P(1
- P)
~
n?J
T h e variance,
s2,
measured in our experiments lies between a
~ ~ ~ _ _ _ _ _ _ _
~
~
Table I.
~~
~~~
Sunimary of Laboratory Runs
wt.70
Run NO. 1
2 3 4
7 8 9
10 11 12
13 14
Blende1 Tjje
Fdledo
Measured Component in M a t u r e
Twin-shell, Lucite Twin-shell:, Lucite Twin-shell.,S. S. Twin-shell., S. S. Double-cone, S. S. Twin-shell.,S. S. Twin-shell.,S. S. Double-cone, S. S. Twin- shell^, S. S. Twin-shell.: S. S. Twin-shell, S. S. Twin-shell, S. S.
55 55 55 55 55 55 65 65 71.5 65 65
50 38.8 28.4 28.4 28.4 76.8 50 50 28.4 75 40
65
50
VOl. c
15"
OUTSIDE STRIPS FOR MOUNTING MIXER IN Y O K E
Nominal working capacity. Runs 1 to 12, 1 pint; 13 and 14, 8 quarts. Measured component. Run 1, dyed alumina; all other runs, procaine penicillin G. Second component. Run 1, undyed alumina; run 8, potassium penicillin; all other runs dihydrostreptomycin sulfate.
.
4.6"I . D .
Figure 2.
r
Double-cone blender
1 -pint working capaciiy
IO0
maximum value of u: and a minimum value of u,2. T h e variance is therefore a n accurate indication of the progress of mixing and is used as su'ch in this article.
8 QT. W.C. TWIN SHELL BLENDER 6 5 % FILL
Summary of Results
Table I summarizes the laboratory runs that \'r ere carried out. The most convenient representation of results was a modification of Gray's method ( 3 ) . Log variance was plotted us. log (number of mixer rotations fl). Typical results are shown by Figure 3. where it is seen that the variance among the random samples decreases rapidly as the mixing progresses. At least during the initial stages of the mixing operation and probably throughout it, no significant difference is found between the variances observed on the charge containing 40% penicillin and one contai ning 50%. Discussion of Results The true variance of the mixture can be obtained only by sampling and analyzing it in its entirety. There is, however, a practical method of using the estimated variance to define a range in which the true variance lies. If the degree of certainty required for this range is specified, the necessary calculations can be performed using the experimentally determined variance, s2, and the statistical quantity. x2. Herdan ( I ) defines x2 a s
For any desired probability, the range within which 2 lies is determined from the ,$ table ( 5 ) . Stange's method ( 9 ) may be used on the graphs showing the experimental variances to plot a band in which the true variance lies. For exam,ple, with 10 samples at a probability of 9070 loglo 0.591
+ loglo .r2 < loglo
o2
< loglo 3.01
+ log13
Examination of Figures 3 and 4 will show the utility of this method. T h e area in which the confidence bands for the two runs overlap is shaded. The acceptable degree of homogeneity for the mixture being produced must be arbitrarily specified. For the purpose of this discussion, let the penicillin concentration in the final product subdivisions vary from the target (mean) value by not more than a standard deviation of i5 7 c . This is equivalent to
IO' 0 RUN 13- 40% PENICILLIN -RUN
14- 5 0 % PENICILLIN
IO2
w sz 0-
z 5 u lo-! a >
I O4
10'
Ibo
IO'
Ib
~b
As to scale-up, Figure 5 compares the 8-quart blender with the very limited amount of data from the 50-cu. foot production blender (1500 x scale-up). These results, as well as the comparison of the 1-pint and 8-quart mixers (16x scale-up), again indicate a significant difference, and show the larger blenders to be more effective. I t is suggested ( 2 ) that the improvement in larger blenders is caused by the greater distance traveled by the particles per rotation.
Conclusions
The progress of mixing in the tumbling blender was very rapid. About 50 to 250 rotations were sufficient to achieve the specified degree of uniformity. Comparative study of blender types showed the twin-shell blender to give slightly better mixing results than the double-cone blender. Evaluation of various twin-shell blenders (1-pint, %quart, 50-cu. ft.) indicated increased mixing rates with the larger blenders. The techniques described here make it possible to design and control solids mixing processes with greater accuracy. In carrying out this type of evaluation, it is important that: The sample size be directly related to the final Droduct subdivision. The number of samoles be determined bv the degree of u confidence desired. The samples be withdrawn from randomly selected positions within the mixer. If these conditions are met, optimum mixing times can be chosen and segregation can be avoided. The major economic value of these techniques is in giving statistical assurance that a mixture will meet specifications. Nomenclature n = no. of samples n, = no. of particles in sample
Ar
= =
P RUN 9
- I PT, W.C. TWIN S H E L L
RUN I O
- I PT, W . C DOUBLE CONE
s = s2 =
X
=
2
=
no. of rotations theoretical (or target) weight fraction of active component in two-component mixture unbiased estimate of standard deviation unbiased estimate of variance experimentally determined weight fraction of active component in sample of two-component mixture mean of series of X values
GREEKLETTERS = true value of variance = statistical quantity chi-squared
g2
x*
rb
Ib’ N t I
1‘0
N U M B E R O F ROTATIONS Figure
1ooj
4.
=
unmixed condition
s = specified condition
Effect of mixer type
r
=
random (completely mixed) condition
Acknowledgment
,
The author thanks John Pekarsky for helping with the analytical work and the Merck Sharp & Dohme Research Laboratories Division of Merck & Co., Inc., for permission to publish this material. literature Cited (1) Blumberg, R., Maritz, J. S.,Chem. Eng. Sci.2 , 240 (1953). (2) . , Fischer, J. J., Tenth Annual Symposium, New Jersey Section, Am. Inst. Chem. Engrs., May 12, 1959. (3) Gray, J. B., Chem. Eng. Progr. 53, 255-325 (1957). (4) Herdan, G., “Small Particle Statistics,” Elsevier, Amsterdam,
z“
10-4-
5x
>
B
R \;!U *.‘\N
RUN C RUN D
b d o
hi
I 7 O/O
97 ‘10 77%
28 O/O RUNF
162
5VO
1b3
N+I NUMBER O F ROTATIONS Figure 5.
Comparison of blender effectiveness
A lo F. 50-cu. ft. twin-shell production blender Run 14. 8-quart laboratory twin-shell blender Percentages refer to procaine penicillin content of charge
106
SUBSCRIPTS o
lo-‘-
;-s2
true value of standard deviation
=
(T
l&EC FUNDAMENTALS
I
nc,
1‘13.2.
( 5 ) Hodgman, C. D., et al., eds., “Handbook of Chemistry and
Physics,” 40th ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1958. (6) Lacey, P. M. C., Trans. Znst. Chem. Engrs. (London) 21, 53-9 (1943). (7)’ Makra, N. K., Coulsen, J. M., J . Imp. (2011. Chem. Eng. SOC.4, 133-56 (1958). (8) Rand Corp., “A Million Random Digits with 100,000 Normal Deviates,” Free Press, New York, 1955. (9) Stange, K., Chem. Zngr. Tech. 26, 150-5 (1954). (10) Zbid., pp. 331-7. (11) Weidenbaum, S. S., “Mixing of Solids. Ad\ rances in Chemical Engineering,” Vol. 11, Academic Press, New York, 1958. (12) Weidenbaum. S.S.. Bonilla. C. F., Chem. En&:. Progr. 51, 27536J (1955). RECEIVED for review October 27, 1960 ACCEPTED August 21, 1961
