1. Chapter 3
Particle Sizing

2. Topics Covered
Measurement methods
Data analysis

3. Particle Size and Air Pollution Control

4. Particle Size?

5. Aerodynamic Diameter
The diameter of a sphere with a density of 1 g/cm3 that has the same falling velocity in air as the actual particle

6. Measurement Methods Microscopy Optical counters
Electrical aerosol analyzer
Bahco analyzer
Cascade impactors

7. Ideal Measuring Device
Measure the exact size of each particle
Determine the composition of each particle
Report real-time data instantaneously

9. Microscopy Polarized Light Microscopy Scanning Electron Microscopy
Energy Dispersive X-Ray
Spectroscopy

10. Electronic Microscope
Optical Microscope
microns

12. Optical Particle Counter

13. Electronic Microscope
microns
Optical Counter
Electronic Microscope
Optical Microscope

15. Electrical Aerosol Analyzer

16. Electrical Aerosol Analyzer Optical Counter Electronic Microscope
microns
Electrical Aerosol Analyzer
Optical Counter
Electronic Microscope
Optical Microscope

18. Bahco Analyzer

19. Electronic Microscope Optical Microscope
Optical Counter
Electrical Aerosol Analyzer
Bahco Counter
microns

21. Cascade Impactor

22. Cascade Impactors

23. Electrical Aerosol Analyzer Optical Counter Electronic Microscope
microns
Inertial Impactor
Bahco Counter
Electrical Aerosol Analyzer
Optical Counter
Electronic Microscope
Optical Microscope

24. Data Analysis

25. Log-Normal Distribution

26. Log-Probability Plots
(log probability paper) dp
(log scale)
1% 10% 50% 90% 99%
% mass smaller dp

27. There is a .pdf of the log probability paper on the instructor CD for class use. Recommend instructor to make printouts and use in class freely.

28. Geometric Mean 50%

29. Geometric Standard Deviationor

30. Example 3-1
Determine the mass mean diameter and the geometric standard deviation of the particle collection represented by the following distribution:
Size Range (gm)
Mass (mg)
<2
1.0
2 to 4
14.5
4 to 6
24.7
6 to 10
59.8
10 to 20
68.3
20 to 40
28.9
>40
2.8

31. Example Particle Size Data
Solution…
Refer to the table. Determine the total mass and calculate the percentage in each size range.
Starting with the size range for the smallest particles (<2 mm), subtract the percent mass in that range (0.50%) from to determine the cumulative percent mass greater than 2 mm (99.50%).
3. For each subsequent size range, subtract the percent mass in that range from the cumulative percent mass of the previous size range to determine the cumulative percent mass less than dp max for that size range.
Example Particle Size Data
Size Range (mm)
Mass (mg)
% Mass in
Size Range
Cumulative %
Mass Less
Than dp max
<2
1.0
0.50
99.50
2 to 4
14.5
7.25
92.25
4 to 6
24.7
12.35
79.90
6 to 10
59.8
29.90
50.00
10 to 20
68.3
34.15
15.85
20 to 40
28.9
14.45
1.40
>40
2.8
--‑
TOTAL
200.0
100.0
For example, for the 2-4 mm size range, 99.50% % = 92.25%, the cumulative percent mass less than 4 mm.

32. And then…
Plot dpmax versus Cumulative Percent Mass Smaller Than dpmax on log-probability paper:
Geometric Mean 50%

33. Finally…
The mass mean particle diameter is found at the 50th percentile and is 10 mm. The geometric standard deviation is calculated from: or

34. Assume that the Cunningham slip correction factor is 1.
Review Questions
1. Calculate the aerodynamic diameter of a spherical particle having a true diameter of 2 mm and a density of 2.7 g/cm3.
Solution:
Assume that the Cunningham slip correction factor is 1.

35. Review Questions 2. Given the following distributions:
Is either distribution lognormal?
If yes, what is the geometric mass mean diameter and the geometric standard deviation?
Size Range (mm)
Sample A Mass (mg)
Sample B Mass (mg)
<0.6
25.50
8.50
0.6 to 1.0
33.15
11.05
1.0 to 1.2
17.85
7.65
1.2 to 3.0
102.00
40.80
3.0 to 8.0
63.75
15.30
8.0 to 10.0
5.10
1.69
>10.0
0.01

36. Solution #2 (a) Size Range (gm) Mass (mg) Percent Mass in Size Range
Cumulative Percent
Mass Less
Than dpmax
<0.6
25.50 10 90
0.6 to 1.0
33.15 13 77
1.0 to 1.2
17.85 7 70
1.2 to 3.0
102.00 40 30
3.0 to 8.0
63.75 25 5
8.0 to 10.0
5.10 2 3
>10.0
7.65
--‑
TOTAL
255.0
But wait there is more

37. Solution #2 (b) Size Range (gm) Mass (mg) Percent Mass in Size Range
Cumulative Percent
Mass Less
Than dpmax
<0.6
8.50 10 90
0.6 to 1.0
11.05 13 77
1.0 to 1.2
7.65 9 68
1.2 to 3.0
40.80 48 20
3.0 to 8.0
15.30 18 2
8.0 to 10.0
1.69
1.99
0.01
>10.0
--‑
TOTAL
85.0
100.0
But wait there is more

38. Finally, Plot them Is lognormal Is not lognormal
But wait there is more

39. And finally…
The geometric mass mean diameter and the geometric standard deviations for Sample A are: