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Module 3: Characteristics of Particles - Review Exercises

Features
Instructions:
Work these problems on a sheet of paper and check your answers against those provided below.

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Use the following information and Figure 1 to answer Questions 1 through 3.


Aggregate, including stone, sand and mineral dust, is divided into separate barrels of the feed bins. The aggregate is proportioned and blended in a cold feed system. The other aggregate, reclaimed asphalt pavement (RAP), is stored separately. The aggregates are then introduced into the drum mixer through vibrating screens.
Fuel is fired in the burner heating the drum mixer. The aggregate from the feed bins is dried and heated in the drum mixer prior to coating. The RAP is also added to the drum mixer. As the RAP is heated to temperatures of 250-350°F, organics are vaporized and the gas is released and cooled as drum exhaust gas.
The asphalt cement is added to the drum mixer from an asphalt tank. The asphalt cement coats and bonds the aggregate. The resultant asphalt mixture is then carried to a storage silo by an elevator.

Figure 1

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Q icon #1
The following questions refer to the section of Figure 1 where the aggregate is loaded, blended, and introduced into the drum mixer via vibrating screens.
  1. What particle formation mechanism is most likely to be present here?
  1. Physical attrition
  2. Combustion particle burnout
  3. Homogeneous and/or heterogeneous nucleation
  4. Droplet evaporation

  1. How would you categorize the particles formed with respect to size?
  1. Supercoarse
  2. Coarse
  3. Fine
  4. Ultrafine

  1. Under what category are these particles regulated?
  1. TSP
  2. PM10
  3. PM5
  4. Condensable particulate

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Answer: i. a. Physical attrition
Physical attrition occurs when the aggregate grinds and rubs together as it is loaded, blended, and fed through the vibrating screens.

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Answer: ii. a. Supercoarse
Physical attrition generally produces particulate in the 10 to 1000 micrometer size range, which is classified as supercoarse.

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Answer: iii. a. TSP
TSP or total suspended particulate refers to particles greater than 0.1 micrometer and less than approximately 30 micrometers. The other categories are incorrect because they represent particles that are smaller than 10 micrometers.
To review material, see Module 3 lessons on Particle Size Categories and Particle Formation.

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Q icon #2
What particulate formation mechanism occurs as a result of the burner shown in Figure 1?
  1. Physical attrition
  2. Combustion particle burnout
  3. Homogeneous and/or heterogeneous nucleation
  4. Droplet evaporation

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Answer: b. Combustion particle burnout
When fuel particles are injected into the hot furnace area of the drum mixer, most of the organic compounds in the fuel are vaporized and oxidized in the gas stream. Fuel particles get smaller as the volatile matter leaves and they are quickly reduced to only the incombustible matter (ash) and the slow burning char composed of organic compounds. Eventually, most of the char will also burn leaving primarily the incombustible material. As combustion progresses, the fuel particles, which started as 10 to 1000 micrometer particles, are reduced to ash and char particles that are primarily in the 1 to 100 micrometer range.
To review material, see Module 3 lesson on Particle Formation.

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Q icon #3
The following questions refer to the section of Figure 1 where organic vapors from RAP are released from the drum mixer.
  1. What particle formation mechanism is most likely to be present here?
  1. Physical attrition
  2. Combustion particle burnout
  3. Homogeneous and/or heterogeneous nucleation
  4. Droplet evaporation

  1. How would you categorize the particles formed with respect to size?
  1. Supercoarse
  2. Coarse
  3. Fine
  4. Ultrafine

  1. Under what category are these particles regulated?
  1. TSP
  2. PM10
  3. Condensable particulate matter
  4. None of the above

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Answer: i. c. Homogeneous and/or heterogeneous nucleation
Nucleation occurs when the organic vapors begin to condense in areas downstream from the drum mixer where the gas temperatures are cooler.
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Answer: ii. c. Fine
Nucleation creates particles in the 0.1-1.0 micrometer size range. These particles would be classified as fine because the size range for fine particles is 0.1-2.5 micrometers.
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Answer: iii. c. Condensable particulate matter
For regulation purposes, particles that form upon cooling are classified as condensable particulate matter.
To review material, see Module 3 lessons on Particle Size Categories and Particle Formation.

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Use Table 1 to answer Questions 4 and 5.


Table 1

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Q icon #4
What is the Stokes diameter for the size range having the highest concentration for Stack #1 (see Table 1 above)? The density of the particles collected at Stack #1 is 2.1 gm/cm3.
  1. 0.6 to 3.0
  2. 0.82 to 2.05
  3. 1.2 to 3.0
  4. 1.75 to 4.39

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Answer: b. 0.82 to 2.05
Solution:
For Stack #1, the size range >1.2 - 3.0 micrometers has the highest mass concentration. Since the data was obtained using a cascade impactor, the size range determines the aerodynamic diameter (dpa). Use the following equation to determine the Stokes particle diameter.
Equation 4

Where:

  1. Calculate the Stokes diameter for a particle at the lower end of the size range.
    Equation 4(1)

  2. Calculate the Stokes diameter for a particle at the upper end of the size range.
    Equation 4(2)

    To review material, see Module 3 lessons on Aerodynamic Diameter and Size Distribution.

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Q icon #5
Use the distribution data from Table 1 to answer the following questions. Link to Appendix C (Blank Log-Probability Graph).
  1. Which source produced a lognormal distribution?
  1. Stack #1
  2. Stack #2
  3. Stack #3
  4. No source produces a lognormal distribution.

  1. What is the mass median particle size for the lognormal distribution?
  1. 1.2 micrometer
  2. 1.8 micrometer
  3. 2.2 micrometer
  4. 3.0 micrometer

  1. What is the geometric standard deviation for the lognormal distribution?
  1. 0.4
  2. 1.8
  3. 2.5
  4. 4.8

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Answer: i. b. Stack #2
Solution:
Step 1. For each stack, calculate the cumulative percentage mass that is less than the minimum particle sizes in each size range.

Table2

Table3

Table4

Step 2. For each stack, plot the cumulative percent mass less than the minimum particle diameter (on the abscissa) vs. the minimum particle diameter (on the ordinate). Use the logarithmic scale provided in Appendix C.

Figure 2

Step 3. Determine which stack has a lognormal particle distribution.
From Figure 2, only the particle distribution data for Stack #2 is linear (i.e. lognormal).
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Answer: ii. b. 1.8 micrometer
Solution:
For Stack #2, determine the mass median particle diameter of the particle distribution, which is the 50% probability point on graph below.

Figure 3

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Answer: iii. c. 2.5
Solution:
Determine the geometric standard deviation by using a ratio of the 50% probability with either the 15.83% or 84.13% points.
Calculate the geometric standard deviation of the particle distribution from Stack #2. Two ways are provided below.
Equation 5iii

To review material, see Module 3 lesson on Size Distribution.

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Q icon #6
Match the particle formation process with the particle size range usually generated by that process.
Equation 6

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Answer:
  1. b. 1.0 to 100
  2. c. 10 to 1000
  3. a. 0.1 to 1.0

To review material, see Module 3 lessons on Aerodynamic Diameter and Size Distribution.

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Q icon #7
For nucleation to occur:
  1. The particle-containing gas stream must heat to the flash point.
  2. The gas stream temperature must be higher than 212°F.
  3. The gas stream temperature must be lower than 212°F.
  4. The vapor-containing gas stream must cool to the dew point.

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Answer: d. The vapor-containing gas stream must cool to the dew point.
For nucleation to occur the vapor-containing gas stream must cool to the dew point.
To review material, see Module 3 lesson on Particle Formation.

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Q icon #8
Select the correct particle collection mechanism for items (i) through (viii) below.
Collection Mechanisms
  1. Inertial impaction and interception
  2. Brownian diffusion
  3. Gravitational settling
  4. Electrostatic attraction
  5. Thermophoresis
  6. Diffusiophoresis

  1. This collection mechanism is the only significant one for fine particles.
  2. This collection mechanism assists in the collection of supercoarse particles that have a relatively fast terminal settling velocity.
  3. This collection mechanism is dependent on the composition and temperature of the gas stream and the composition of the particles.
  4. This mechanism can be important when water evaporation or condensation is involved due to the formation of high concentration gradients.
  5. This collection mechanism operates on the principle that rapidly moving gas molecules transfer kinetic energy to particles in the gas stream, causing the particles to deflect slightly and impact the target (e.g. liquid droplet).
  6. This collection mechanism usually affects particles larger than 10 micrometers and occurs as particles strike slowly moving or stationary objects in their paths.
  7. This collection mechanism, which employs a relatively small force, causes particle movement due to thermal differences on two sides of the particle.
  8. This collection mechanism is affected by particle resistivity.

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Answer: i. b. Brownian diffusion
Brownian diffusion is the dominant particle collection mechanism in the size range of 0.3 micrometer and less.
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Answer: ii. c. Gravitational settling
Gravitational settling is only effective if the particles are very large and have a fast settling velocity.
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Answer: iii. d. Electrostatic attraction
Gas composition and temperature and particle composition all influence resistivity. The ability to collect particles using electrostatic attraction is directly related to particle resistivity. If the particle resistivity is outside the generally preferred range of 108 to 1010, particle collection efficiency is reduced.
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Answer: iv. f. Diffusiophoresis
Diffusiophoresis is caused by large concentration differences on two sides of a particle.
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Answer: v. b. Brownian diffusion
Brownian diffusion occurs when gas molecules transfer kinetic energy to small particles causing the particles to move in a random motion across the gas flow.
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Answer: vi. a. Inertial impaction and interception
Impaction and interception can occur when a rapidly moving particle, usually larger than 10 , strikes a slow moving or stationary object in the particle's path.
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Answer: vii. e. Thermophoresis
Thermopheresis is particle movement caused by temperature differences on two sides of the particle.
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Answer: viii. d. Electrostatic attraction
The ability to collect particles using electrostatic attraction is directly related to particle resistivity.
To review material, see Module 3 lessons on Particle Size Categories and Collection Mechanisms.

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Q icon #9
Calculate the surface area and volume of a spherical particle having a diameter of 3 micrometers and a density of 1 gm/cm3.
Figure 4

  1. What is the surface area of the particle?
  1. 2.83 10-7 cm2
  2. 2.83 10-5 cm2
  3. 1.13 10-6 cm2
  4. 1.13 10-4 cm2

  1. What is the volume of the particle?
  1. 1.13 10-10 cm3
  2. 1.13 10-8 cm3
  3. 1.41 10-9 cm3
  4. 1.41 10-11 cm3

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Answer: i. a. 2.83 10-7 cm2
Solution:
D = 3 = 0.0003 cm
Equation 9i

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Answer: ii. d. 1.41 10-11 cm3
Solution:
Equation 9ii

To review material, see Module 3 lesson on Surface Area and Volume.

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Q icon #10
How long (to the nearest half minute) will it take a 3.0-micrometer particle to settle 2 meters in still air? Use Figure 4 and Appendix B (Cunningham Slip Correction Factors for Air) as needed.
Equation 10a
  1. 48 min 30 sec
  2. 1 hr 50 min 30 sec
  3. 2 hr 20 min 30 sec
  4. 4 hr 5 min

Figure 5

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Answer: b. 1 hr 50 min 30 sec
Solution:
Since the particle density equals 1 in this problem, the Stokes particle diameter is equivalent to the aerodynamic diameter.
Use the following equation to determine the terminal settling velocity.
Equation 10b

Where:Equation 10c

Step 1. Determine the Cunningham slip correction factor from Appendix B.
For a particle with a 3.0 diameter, Cc = 1.056
Step 2. Determine the air viscosity, , using Figure 5.

  1. Convert temperature from Kelvin to Fahrenheit.
    Equation 10(2)(1)

  2. Find the viscosity of the flue gas, , at 77°F using Figure 5.
    Equation 10(2)(2)

  3. Convert viscosity from American Engineering units to Cgs units.
    Equation 10(2)(3)

Step 3. Calculate the terminal settling velocity of the particle.
Equation 10(3)

Step 4. Calculate how long it will take for the particle to settle 2 meters in still air.
  1. Convert the settling velocity, vt, into units of meters/hour.
    Equation 10(4)(1)

  2. Calculate the length of time for the particle to settle.
    Equation 10(4)(2)

    Rounded to the nearest half minute, the answer is 1 hr 50 min 30 sec.


To review material, see Module 1 lesson on Temperature, Module 2 lesson on Viscosity, and Module 3 lessons on Aerodynamic Diameter and Collection Mechanisms.

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