Chapter 3 Particle Sizing

Topics Covered Measurement methods Data analysis

Particle Size and Air Pollution Control

Particle Size?

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

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

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

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

Electronic Microscope Optical Microscope 0.001 0.01 0.1 1 10 100 microns

Optical Particle Counter

Electronic Microscope microns Optical Counter Electronic Microscope Optical Microscope 0.001 0.01 0.1 1 10 100

Electrical Aerosol Analyzer

Electrical Aerosol Analyzer Optical Counter Electronic Microscope microns Electrical Aerosol Analyzer Optical Counter Electronic Microscope Optical Microscope 0.001 0.01 0.1 1 10 100

Bahco Analyzer

Electronic Microscope Optical Microscope Optical Counter Electrical Aerosol Analyzer Bahco Counter 0.001 0.01 0.1 1 10 100 microns

Cascade Impactor

Cascade Impactors

Electrical Aerosol Analyzer Optical Counter Electronic Microscope 0.001 0.01 0.1 1 10 100 microns Inertial Impactor Bahco Counter Electrical Aerosol Analyzer Optical Counter Electronic Microscope Optical Microscope

Data Analysis

Log-Normal Distribution

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

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.

Geometric Mean 50%

Geometric Standard Deviation or

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

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 100.00 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% - 7.25% = 92.25%, the cumulative percent mass less than 4 mm.

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

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

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.

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

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 1 00 . 0 But wait there is more

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

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

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