Single Particle Motion

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Single Particle Motion
Reading Chaps 3 5
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engineering because you surely need to know how
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• Newtons Resistance Law The force is proportional
  to the gas pushed away and the relative velocity
  between the sphere and the gas (negligible
  viscous force)

CD 0.44 (sphere) for 103 lt Rep lt 2105
Delivery van 0.04 Sports car 1.0 Airplane 0.
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?

• Reynolds Number ratio of inertial forces to
  frictional forces (Chap.2.5)

For a spherical particle, L dp,
Q Choose a combination of dp and V when the
Newtons Law can be applied.
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• Stokes Law negligible inertial force compared
  to viscous force (Rep lt 1) in a laminar flow for
  a spherical particle

Q How does FD change wrt V and dp in the laminar
regime? Q Under what scenario will you expect to
apply Newtons law instead of Stokes Law?
Q How does CD change wrt Re from 10-3 to 105?
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Transition Regime
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Settling Velocity

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

0
Q What is the physical meaning of B? Q Does a
smaller or a larger particle have larger
mobility?
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Terminal Settling Velocity of unit-density spheres

• Cunningham Slip Correction Factor gas velocity
  at the surface of small particles is not zero --gt
  slip

? mean free path (Chap 2.3) 0.066 mm for air
_at_STP
(Re lt 1)
Q So is the corrected VTS larger or smaller?
Appendix A11
Q How long do you have to wait for 0.1 mm
particles to completely settle in this classroom
(4 m high)?
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Knudson Number
Kn 2?/dp

• A dimensionless number for the relative size of a
  particle in the system
• Continuum regime Kn ltlt 1. Gas molecules
  striking the particle surface are strongly
  affected by those leaving.
• Free Molecular regime Kn gtgt 1. The gas molecule
  movement is rarely affected by the presence of
  the particle.

Q Kn for a 10 mm particle? In which regime?
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Nonspherical Particles

• Dynamic shape factor the ratio of the actual
  resistance force of the nonspherical particle to
  the resistance force of a sphere having the same
  volume and velocity
• Drag force
• Settling velocity

de equivalent volume diameter
Q Does an irregular particle experience a larger
or smaller force (compared to a particle with the
same volume)?
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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 (?0 1 g/cm3) sphere that has
  the same settling velocity as the particle.

Cunningham factor should be included if dp lt 1 mm
Q Can we design an instrument by applying
settling velocity?
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Horizontal Elutriator (settling chamber,
spectrometer)
Q Can it be vertical? Q Can we make the
acceleration gt g?
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Centrifuge Separator
Cheng et al., 1988
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Particle Acceleration

• Newtons law

Q What is the physical meaning of relaxation
time?
? mB relaxation time
FGmg
FGmg
FGmg
t0 V(t)0
t? V(t)VTS
tgt3? V(t)VTS
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Non-zero Initial velocity
Displacement
Stopping Distance
Time for unit density particles to reach their
terminal velocity

• An aerosol can adjust itself very quickly to a
  new environment!!!

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Inertial Impaction

• Stokes number the ratio of the stopping distance
  of a particle to a characteristic dimension of
  the obstacle
• For an impactor

Q Stk ltlt 1? Stk gtgt 1?
http//aerosol.ees.ufl.edu/
Q Criteria to determine the impaction/collection
efficiency
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Assumptions of Simplified Theory Uniform
streamlines in the jet Streamlines are arcs of a
circle with the centers at A
h
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Stk50 for 2 impactors
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Determine dp50
Q How to collect smaller particles using
an impactor?
Downstream pressure
(Chap 3.4, Pd in kPa, dp in um)
Q (low pressure impactor) Advantages?
Disadvantages?
Q Again, how to collect smaller particles using
an impactor?
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Cascade Impactor
Aerosol flow In
http//aerosol_beta.ees.ufl.edu/instrumentation/se
ction04.html
Clean air out
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Q Advantages? Disadvantages?
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Virtual Impactor
Collection efficiency internal loss curves for
a virtual impactor
Aerosol concentrator? Cyclone?
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CYCLONE
Outlet
http//aerosol.ees.ufl.edu
Inlet
Vortex Finder
Cyclone body
Cylinder
Cone
Dust Discharger
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Time of Flight
Q Comparison with an impactor?
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Aerodynamic Focusing Lens
Time of Flight (TOF) vs Time in Beam (TIB)
TSI Operating Manual, 2004
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Quick Reflection