Motion of Aerosol

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Motion of Aerosol
Reading Chap. 3.3-3.4

• Newtons Resistance Law and Stokes Law
• Cunningham Slip Correction Factor
• Settling Velocity, Mechanical Mobility
• Particle Acceleration
• Aerodynamic Diameter
• Settling Chamber
• Brownian Motion Diffusion

http//aerosol.ees.ufl.edu/aerosol_trans/section01
.html
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History
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Q Plot CD as a function of Rep for Newtons Law
Q Plot CD as a function of Rep for Stokes Law
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Q What is the max velocity of a particle to be
in the Stokes regime? 1 mm, 10 mm, 100 mm
(rg 1.2 kg/m3 m 1.8110-5 Pas)
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Categorize aerosol movement based on interaction
between the particle and gas molecules
http//aerosol.ees.ufl.edu/aerosol_trans/section06
.html
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Settling Velocity

• When the drag force is equal and opposite to the
  gravitational force
• Particle Mechanical Mobility

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Q What is the impact of considering Cc on a
particles settling velocity? Why?
Q What is the physical meaning of B? Q Does a
smaller or a larger particle have larger mobility?
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Relaxation Time indication of the time required
for a particle to adjust/relax its velocity to a
new condition of force Terminal/Settling
Velocity
Transition Regime
Turbulent Regime
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If flow regime is unknown because VTS is unknown
--gt K factor
Laminar Klt 3.3 Turbulent K gt 43.6
Q For a 100 µm unit-density particle, which flow
regime is applicable?
Fig 5-8 on P.9
Q Can we clean the dust in this classroom by
waiting them to settle down? How long will it
take? Assume the particle size is 1 mm, 10 mm,
100 mm. The room is 3 m high.
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Particle Acceleration

• Newtons law

http//aerosol.ees.ufl.edu/aerosol_trans/section04
.html
FD3??VTSdp
FD3??V(t)dp
FGmg
FGmg
FGmg
t? V(t)?
tgt3? V(t)VTS
t0 V(t)0
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Non-zero Initial velocity
Stopping Distance
For Re0 lt 1
Small aerosols adapt to the new environment (i.e.
following the flow well) in a very short time,
almost instantly!!!
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Aerodynamic Diameter

• The Stokes diameter, ds, is the diameter of the
  sphere that has the same density and settling
  velocity as the particle.
• The aerodynamic diameter, da, is the diameter of
  the unit density (?01 g/cm3) sphere that has the
  same settling velocity as the particle.

Q PM10 and PM2.5 are aerodynamic diameters.
Why? Is optical diameter or aerodynamic
diameter more relevant?
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Horizontal Elutriator/Settling Chamber(Plug flow
model no radial or axial mixing)
Q If monodisperse aerosols are uniformly
distributed at the entrance, what is the
collection efficiency as a function of VTS
(dp)?
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Brownian Motion Diffusion
http//galileo.phys.virginia.edu/classes/109N/more
_stuff/Applets/brownian/brownian.html
http//www.geocities.com/piratord/browni/Difus.htm
l

• The primary transport mechanism for small
  particles (lt 0.1 ?m) Important when transport
  distance is small e.g. filter, airway in human
  lung
• Definition
• Brownian motion irregular wiggling motion of a
  particle caused by random bombardment of gas
  molecules against the particle
• Diffusion the net transport of the particles
  from a region of higher concentration to a region
  of lower concentration

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Ficks First Law of Diffusion
The net flux of aerosols (the net number of
particles traveling through a unit area per unit
time) is proportional to the concentration
gradientJ flux (/area/time)D diffusion
coefficient (area/time)n particle number
concentration (/cm3)
driving force
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Spread of particles over time and space

• Solve 1-D equation

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Solution
Mean Square Displacement of particles
Result
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Quick Reflection