How to Compute the Mean Particle Diameter from a LISST Volume Distribution
How to Compute the Mean Particle Diameter from a LISST Volume Distribution
[Sequoia, March 26, 2010]
In the table below, the computation of the mean particle size from a LISST volume distribution is outlined.Column A is the size class number, from 1-32.
Column B is the MID POINT of the size bin in µm. In this example we are using the size classes associated with a LISST type B randomly shaped inversion (LISST Bin Sizes).
Column C is the Volume Distribution in µl/l.Each row in column D (dSum) is computed as the size class # for that row multiplied with the volume concentration in the size class. For example, for size class 8, dSum is equal to 8 * 3.035 = 24.28.
A
B
C
D
Size class
Size class mid point (µm)
Volume Distribution (µl l-1)
dSum
(Size class # * VC in size class)
1
1.09
0.190
0.190
2
1.28
0.256
0.512
3
1.51
0.360
1.080
4
1.79
0.616
2.464
5
2.11
0.853
4.265
6
2.49
1.041
6.246
7
2.93
1.429
10.003
8
3.46
3.035
24.280
9
4.09
4.071
36.639
10
4.82
4.419
44.190
11
5.69
4.818
52.998
12
6.71
5.714
68.568
13
7.92
6.218
80.834
14
9.35
6.252
87.528
15
11.03
6.151
92.265
16
13.02
6.360
101.76
17
15.36
6.288
106.896
18
18.13
6.311
113.598
19
21.39
6.732
127.908
20
25.25
7.726
154.52
21
29.79
8.252
173.292
22
35.16
9.573
210.606
23
41.49
10.666
245.318
24
48.96
11.581
277.944
25
57.77
11.843
296.075
26
68.18
12.214
317.564
27
80.45
11.177
301.779
28
94.94
9.434
264.152
29
112.04
6.993
202.797
30
132.21
4.750
142.500
31
156.02
3.128
96.968
32
184.11
2.300
73.600
VD = VC
dSum
180.751
3719.339
By definition, the mean particle size in terms of size class number is now dSum/VD = dSum/VC, in this example 3719.339 / 180.751 = 20.57714.
We can now see that the mean particle size, in terms of size class numbers is somewhere between size class 20 and 21, i.e. somewhere between 25.25 and 29.79 µm.
Now round down dSum/VC to the nearest integer, in this case it would be 20.
Compute the remainder; in this case it would be 20.57714 – 20 = 0.57714.
The mean particle size is now computed as the midpoint of size class 20 (from rounding down dSum/VC) multiplied by the ratio of the bin midpoints (200^(1/32) = 1.1801) raised to the power of the remainder: 25.25 * 1.1801^0.57714 = 27.78µm.
VD = VC