How do we characterize aerosols

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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?

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Particle Size Distribution
Reading Hinds, Chap 4
Typical data from measurement
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Histogram of frequency(count) versus particle size
Q Which size range has the most particles?
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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?
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Standardized frequency/?dp vs particle size
Q What is the value of the total area?
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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
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Cumulative Distribution

• Definition
• The fraction that is less than a specific size
• Why cumulative distribution?
• Provide another viewpoint to observe the
  distribution.

Q Whats the RED spot?
Q Whats the annual income of a starting
engineer?
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• MEAN (arithmetic average)
• The sum of all the particles 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.

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• 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
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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?
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Number Distribution
Mass Distribution
Q What is the mode size of the distribution?
Important to clarify the type of distribution
reported.
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• 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?
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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?
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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)
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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
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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 gt 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
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geometric standard deviation
Q Whats the unit of ?g?
frequency function
Convert dlndp to ddp
particle volume based function
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• Features of Lognormal PSD

For a given distribution, the geometric standard
deviation remains constant (nondimensional) for
all weighted distributions.
Q If sg 1.5, how much is d84/d16?
Log-Probability graph
Measurement from a cascade impactor
Is this a log-normal distribution? Whats its
d50? sg?
Get graph paper from http//sorrel.humboldt.edu/g
eodept/geology531/graph_paper_index.html
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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.
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Hatch-Choate Conversion Eq.
(Table 4.3)

• p type of average
• 0 median/geometric
• 1 mean
• 2 area
• 3 volume/mass

• q weighted distribution
• 0 count
• 1 length
• 2 area
• 3 volume/mass

b q p/2
Q If CMD 10 mm and sg 2, how much is
MMD? Diameter of average mass?
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Reflection