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Powder sampling

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```with the
results shown in Table 1.7 and the tolerable sampling error for each
fraction is ±5%. The amount required for each fraction, in order to keep
within this limit, equation (1.15) is given in column 4.
F^ or a sieve analysis, in order to reduce the errors at the coarse end of
the distribution, repeat analyses should be made using only the coarsest
sieves. For the example above an error of 100% in the coarsest size range
may be acceptable, i.e. (0.1 ±0.10) g; this reduces the required weight to
94 g.
Table 1.8. Minimum incremental mass required for sampling from a
stream of powder
Maximum particle size (mm)
250-150
150-100
100-50
50-20
20-10
10- 0
Minimum mass of increment (kg)
40.0
20.0
12.0
4.0
0.8
0.3
1.14.2 Sampling by increments
For sampling a moving stream of powder the gross sample is made up of
increments. In this case the minimum incremental weight is given by:
M^ = l^ o^fo (1.16)
52 Powder sampling and particle size determination
where:
M- is the average mass of the increment,
//Q is the average rate of flow,
WQ is the cutter width for a traversing cutter,
VQ is the cutter velocity.
If M^o is too small, a biased sample deficient in coarse particles, results. For
this reason w^ should be at least ?>d where d is the diameter of the largest
particle present in the bulk. ISO 3081 suggests a minimum incremental
mass based on the maximum particle size in mm. These values are given
in Table 1.8. Secondary samplers then reduce this to analytical quantities.
Example 10
Determine the minimum increment weight for a powder falling from a belt
conveyer at a rate of 3 metric tons per hour if the size of the largest
particle is 1.0 mm and the sampling cutter speed is 6 cm s~^
M^
r . . . . n 3 . . u - i V 3 ^ 1 0 - ^ m ^ 3x10^ kgh&quot;
3600 s h~^ 0.06 ms&quot;*
M, -42g
Since the flowrate is 833 g s~^ this is not a practical amount, hence a two-
stage sampler is required. Sampler 1, say, can sample for 2 s to generate
1.67 kg of powder, which is fed to a hopper to provide a feed to a second
sampler that reduces it by a factor of 40 to generate the required 42 g.
The minimum number of increments required to give an acceptable
accuracy for the sampling period is 35, hence, the gross sample weight is
given by:
A/,.= 1.47 kg
The gross sample can be reduced to a laboratory sample of about 10 g,
using a Vezin type sampler for example, and finally to a measurement
sample of about 1 g using a rotary riffler. If the particle size analysis is
carried out on less than 1 g the final reduction is usually effected by
dispersing the powder in a liquid and pipetting out the required aliquot.
Powder sampling 53
Gy [45] proposed an equation relating the standard deviation, which he
calls the fundamental error a)r, to the sample size:
-I- \w W Cd^ (1.17)
where Wis the mass of the bulk and w = nco is the mass of « increments,
each of weight &> which make up the sample, C is the heterogeneity
constant for the material being sampled and d is the size of the coarsest
element.
For the mining industry [46] he expressed the constant C in the form
C = clfg where:
\-P C = p (1.18)
P is the investigated constant; p is the true density of the material; / is the
relative degree of homogeneity, for a random mixture / = 1, for a perfect
mixture / == 0; / is a shape factor assumed equal to 0.5 for irregular
particles and 1 for regular particles; g is a measure of the width of the size
distribution, g = 0.25 for a wide distribution and 0.75 for a narrow
distribution (i.e. d^^^y^ < 2d^^^).
For the pharmaceutical industry Deleuil [35] suggested C = 0.1/c with
the coarsest size being replaced by the 95% size. For W»w equation
(1.17) can be written.
w(9^-0.1/ ]-P
IP' ,
.3 T3 pfd' (1.19)
where: 0 = t^-^ and t = 3, (99.9% confidence level) for total quality,
\u2022 For t/95 = 100 )im, p = \.5, P = 10-^ (1000 ppm), 6 = 0.2, / = 0.03
(random), w = 1000 g.
\u2022 For dg^ = 100 |Lim, /? - 1.5, P = 0.05, 0= 0.05, / = 1 (homogeneous),
w = 4 g.
\u2022 For 9^5 = 20 |um, p^ 1.5, P - 10&quot;^ (100 ppm), 0 = 0.05, / - 0.03
(random), w = 8000 g.
54 Powder sampling and particle size determination
Deleuil points out that a sample of this weight is never prepared because
the lot is considered to be perfectly homogeneous (/ = 1).
The product from industrial grinding circuits oscillates due to
variation in hardness and particle size distribution of feed.
Heiskanen and Niemelia [47] demonstrated that, using automatic
sampling, on-line analysis and autocorrelation procedures, they could
map out a frequency of oscillation.
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Powder sampling 55
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