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How do we characterize aerosols?

How do we characterize aerosols?. Size: Monodisperse: All the particles are of the same size Polydisperse: Particles are of more than one size Concentration: Number concentration by counting Mass concentration by weight measurement Ex: Particles in room air: N = 10 4 #/cc

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How do we characterize aerosols?

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  1. How do we characterize aerosols? • Size: • Monodisperse: All the particles are of the same size • Polydisperse: Particles are of more than one size • Concentration: • Number concentration by counting • Mass concentration by weight measurement • Ex: Particles in room air: • N = 104 #/cc • M = 5.23610-6 g/cc • dp = 10-3 cm = 10 m • Q: Does this mean all the 104 particles in 1 cc air are 10 m? • What is the effect if we use this size to represent the system? (e.g. in inhalation system) • How can we better describe this aerosol system? Aerosol & Particulate Research Lab

  2. Particle Size Distribution Reading: Hinds, Chap 4 Typical data from measurement Aerosol & Particulate Research Lab

  3. Histogram of frequency(count) versus particle size Q: Which size range has the most particles? Aerosol & Particulate Research Lab

  4. Frequency/dp (distribution function) vs particle size Q: Total # of particles ? Q: TiO2 pigment is produced by aerosol process in DuPont. If the production rate is increased 10 folds, how do I know the product still maintains the same particle size distribution? Aerosol & Particulate Research Lab

  5. Standardized frequency/dpvs particle size Q: What is the value of the total area? Aerosol & Particulate Research Lab

  6. Continuous Particle Size Distribution If the size range is very small, the discrete PSD will approach continuous PSD. q(dp): q as a function of dp Aerosol & Particulate Research Lab

  7. Cumulative Distribution • Definition: • The fraction that is less than a specific size • Why cumulative distribution? • Provide another viewpoint to observe the distribution. Q: What’s the RED spot? Q: What’s the annual income of a starting engineer? Aerosol & Particulate Research Lab

  8. MEAN (arithmetic average): The sum of all the particle sizes divided by the number of particles • MEDIAN: • The diameter for which 50% of the total are smaller and 50% are larger; the diameter corresponds to a cumulative fraction of 50% • MODE: • Most frequent size; setting the derivative of the frequency function to 0 and solving for dp. • For a symmetrical distribution, the mean, median and mode have the same value. Aerosol & Particulate Research Lab

  9. GEOMETRIC MEAN: • the Nth root of the product of N values • Expressed in terms of ln(dp) • For a monodisperse aerosol, • otherwise, • Very commonly used because an aerosol system typically covers a wide size range from 0.001 to 1000 m n(dp): n as a function of dp Aerosol & Particulate Research Lab

  10. Weighted Distributions • Why do we need other distributions? • Aerosols may be measured in different ways, and in indirect ways (e.g. impactors, light scattering) • What are the other distributions? • Definition: frequency of the property (e.g. mass, number) contributed by particles of the size interval • What is the effect? • Ex. A system containing spherical particles (mode size?) • Number Concentration: Mass Concentration: • 100 #/cc 1m & =1.91g/cm3 10-11 g/cc 1m • 1 #/cc 10m 10-9 g/cc 10m Q: How will the PSD on page 6 look like if plotted as mass distribution? Aerosol & Particulate Research Lab

  11. Number Distribution Mass Distribution Q: What is the mode size of the distribution? Important to clarify the type of distribution reported. Aerosol & Particulate Research Lab

  12. Count Mean Diameter: based on number of particles. • Mass Mean Diameter: based on mass of particles. Conversion Q: In addition to the representative size, what other aerosol property can we use to present the aerosol size distribution in a concise way? Aerosol & Particulate Research Lab

  13. Moments of the PSD • Definition: The quantity proportional to particle size raised to a power; an integral aerosol property Q: What is Mo? n(dp): n as a function of dp Q: What is M1? Q: What is M1/M0? Q: What is M2/M0? M3/M0? Q: Which is larger? M1/M0? (M2/M0)1/2? (M3/M0)1/3? Aerosol & Particulate Research Lab

  14. Volume Moments • Particle volume, instead of particle diameter, is also used as a variable (i.e. the x-axis is particle volume, not size) • Definition: • Conversion of n to ndp: Q: What is M1/M0? (1) (2) (3) (4) Aerosol & Particulate Research Lab

  15. Lognormal PSD • Various distributions: Power law, Exponential, ...etc. Very limited application in aerosol science • Normal Distribution: widely used elsewhere, but typically not for aerosol science, because • most aerosols exhibit a skewed distribution function • if a wide size range is covered, a certain fraction of the particles may have negative values due to symmetry. frequency function standard deviation Aerosol & Particulate Research Lab

  16. Why using Lognormal? • The application of a lognormal distribution has no theoretical basis, but has been found to be applicable to most single source aerosols • Useful for particle of a wide range of values (largest/smaller size > 10) • Its mathematical form is very convenient when handling weighted distributions and moments. • How to use it? Simply replace dp by lndp. geometric mean diameter Aerosol & Particulate Research Lab

  17. geometric standard deviation frequency function Convert dlndp to ddp particle volume based function Aerosol & Particulate Research Lab

  18. Features of Lognormal PSD Q: What is the unit of sg if particles are measured in µm? Q: If sg = 1.5, how much is d84%/d16%? For a given distribution, g remains constant (nondimensional) for all weighted distributions. Aerosol & Particulate Research Lab

  19. Log-Probability Graph Measurement from a cascade impactor Q: Is this a log-normal distribution? What’s its d50%? sg? Get graph paper from http://www.humboldt.edu/geology/courses/geology531/graph_paper_index.html Aerosol & Particulate Research Lab

  20. Aerosol & Particulate Research Lab

  21. Moments for lognormally distributed aerosols: The statistical variables can be easily determined through the moments! Ref: Lee, K. W. and Chen, H., Aerosol Sci. Technol., 3, 1984, 327-334. Lee, K. W., Chen, H. and Gieseke, J. A., Aerosol Sci. Technol., 3, 1984, 53-62. Aerosol & Particulate Research Lab

  22. q: weighted distribution 0: count 1: length 2: area 3: volume/mass p: type of average 0: median/geometric 1: mean 2: area 3: volume/mass Hatch-Choate Conversion Eq. (Table 4.3) b = q + p/2 Q: If CMD = 10 mm and sg = 2, how much is MMD? Diameter of average mass? Aerosol & Particulate Research Lab

  23. Locations of various average diameters CMD = 9 µm g = 1.89 Statistical accuracy: mass average diameters are well out on the tail based on count data. Q: How do we ensure that this region of the number distribution is accurately represented? Aerosol & Particulate Research Lab

  24. Reflection Aerosol & Particulate Research Lab

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