Aerosol, Fluid ,,Dispersion of Pollutants Introduced into the Atmosphere as Determined by Residence Times (Husar and Patterson, 1980) After formation, the aerosols are mixed and transported by atmospheric motions and are primarily removed by cloud and precipitation processes. Aerosol formation at source: Primary aerosol formation: Product of incomplete combustion Elemental carbon Organic carbo An important assumption of Stokes’s law is the relative velocity of gas right at the surface of the sphere is zero. The assumption is not met for small particles whose size approaches the mean free path of the gas such particles settle faster than predicted by stokes law because there is a slip at the surface of the particle. At standard conditions, this error become significant for particles less than 1 mm in diameter. In 1910 Cunningham derived a correction factor for Stokes’s law to account for effect of slip.

1. Fundamental of aerosol:
Formation and dynamics
By
Gazala Habib
Assistant Professor
Department of Civil Engineering, IIT-Delhi

2. Outline
What is aerosol?
Life time and transport of aerosol
compared to gases.
How do aerosol look like?
Why do we bother about these tiny
particles?
Aerosol formation?
Aerosol size and shape
Forces on Aerosol

3. Suspended particles in
medium
Type of suspended particles
Suspending
medium
gas Liquid solid
Gas - Fog, mist, spray Fume, dust
Liquid Foam Emulsion Colloid, suspension,
slurry
Solid sponge Gel Alloy

4. Sources of Atmospheric
Aerosol

5. Residence time and transport of
aerosol
Dispersion of
Pollutants Introduced
into the Atmosphere
as Determined by
Residence Times
(Husar and Patterson,
1980)
After formation, the
aerosols are mixed
and transported by
atmospheric motions
and are primarily
removed by cloud and
precipitation
processes.

6. Size and Shape of Aerosol
• Size range: 0.001 mm (molecular cluster) to
100 mm (small raindrop)
Fly ash particle
from coal burning
Granite cutting
particle
Iron oxide
particles

7. 0.01 0.1 1.0 10.0
- « nucleation: radius is between
0.002 and 0.05 mm. They result
from combustion processes, photo-
chemical reactions, etc.
- « accumulation: radius is
between 0.05 mm and 0.5 mm.
Coagulation processes.
-« fine: particles (nucleation and
accumulation) result from
anthropogenic activities,
- « coarse: larger than 1 mm. From
mechanical processes like aeolian
erosion.
Aerosol Size Distribution

9. Visibility Degradation from Aerosols
7.6 µgm-3
12.0 µgm-3
21.7 µgm-3 65.3 µgm-3
Glacier National Park, Montana

10. What is radiative forcing by aerosols?
DFl
TOA
DFl
SUR

11. Aerosol and climate change
Cloud with
aerosol
Numerous
cloud nuclei
Small droplets,
Brighter cloud,
less prone to
rain
Annual mean precipitation (1976-2003)
minus (1948-1975): Green/blue (red/Yellow)
decrease (increase)
Drought
Radiative Forcing (Wm-2) due to aerosol
Top of the Atmosphere
(+ve forcing)
Surface (-Ve forcing)
Knowledge gap: Large uncertainty
in quantification of impact of
aerosol on climate [IPCC, 2007].

12. Ship Track Formation – the First
Evidence of Aerosol Indirect Effect
N ~ 40 cm-3
W ~ 0.30 g m-3
re ~ 11.2 µm
N ~ 100 cm-3
W ~ 0.75 g m-3
re ~ 10.5 µm
“Borrowed” from Michael King

13. • Adding CCN makes clouds with more, smaller droplets.
• These clouds are whiter, reflect more sunlight  net
cooling
Aerosol-indirect climate effect Ship
tracks off the Washington coast

14. Formation of aerosol
• Aerosol formation at source:
– Primary aerosol formation: Product of
incomplete combustion
• Elemental carbon
• Organic carbon
Elemental cabon
Organic cabon
EC+OC

15. Formation of aerosol-2
• Aerosols smaller than 1 µm are mostly formed
by condensation processes such as conversion of
sulfur dioxide (SO2) gas (released from volcanic
eruptions) to sulfate particles and by formation of
soot and smoke during burning processes.
• Aerosol particles larger than about 1 mm in size
are produced by windblown dust and sea salt
from sea spray and bursting bubbles

16. Secondary aerosol formation
in the Atmospher
Soil dust
Sea salt
Environmental importance: health (respiration), visibility, climate,
cloud formation, heterogeneous reactions, long-range transport of nutrients…

17. • Can you name the laws of motion for a
moving object?
– Newton’s law
– stokes law

18. Do aerosol follow Newton’s
law?
• Newton’s law
– Inertial force dominates the viscous force
• What is Reynolds number?
• Re>1000
– Large body such as cannonballs (not for particles)
– http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.ht
ml

19. Stokes’s Law
– Viscosity dominates
over Inertia
– http://members.shaw.c
a/gp.lagasse/Centrifug
e%20Training/basic2.ht
ml
– Solution of Navier-
Stokes equations
(differential eqs
describing the fluid
motion)
Navier-Stokes equations are
derived from application of
Newton’s second law to a fluid
element on which the forces
include body forces, pressure, and
viscous forces.

20. Stoke’s Law: Assumptions for solving
Navier-Stoke equtions
• Resulting equations are very difficult to solve because they are nonlinear partial
differential equations.
• Therefore, Stoke’s solution involved the assumptions
– Inertial force is negligible compared to viscous force: this eliminates the higher
order terms in Navier-Stokes equation and yield linear equation that can be
solved.
– Fluid is incompressible.
– There are no wall or other particles nearby
– The motion of the particle is constant
– The particle is rigid sphere
– The fluid velocity at the particle surface is zero.
The net force acting on the particle is obtained by integrating the normal and
tangential forces over the surface of the particle.
Re<1.0 (error in the drag force will be 12% error at Re=1.0 and 5% error at Re=0.3)

21. Stokes’s law: Assumptions
valid or invalid
• Fluid is incompressible
– Air around the particle can not be compressed
significantly when particle moves through it. Valid
– Presence of the wall within 10 diameters of
particle will modify the drag coefficient . Aerosols
are of small size therefore only a tiny fraction of
aerosol will be within 10 particle diameters in any
real container or tube. Valid

22. Stokes Law: Non-rigid particle
– What if it is water droplet (non rigid sphere)?
• Settle 0.6% faster than predicted
• Reason circulation develop within the droplet caused
by resisting force at drop let surface

24. Aerosol settling by gravity
• Drag force (FD) = Inertial force (FG=mg)
pg
For water droplet
settling in air
Not valid for particles
less than 1.0 mm size.

25. Aerosol settling by gravity
…contd.
• 10% accurate for particle with standard
density having diameter of 1.5-75 mm.
• Mechanical mobility of particle (for d>1.0 mm)
– Ratio of terminal velocity of particle to the steady
force producing that velocity.

26. • Example 1: What are the terminal velocity
drag force and mobility of a 2.5 mm diameter
iron-oxide sphere settling in still air? The
density of iron oxide is 5200 kg/m3.
η=1.81X10-5

27. • An important assumption of Stokes’s law is the
relative velocity of gas right at the surface of the
sphere is zero. The assumption is not met for
small particles whose size approaches the mean
free path of the gas such particles settle faster
than predicted by stokes law because there is a
slip at the surface of the particle. At standard
conditions, this error become significant for
particles less than 1 mm in diameter.
• In 1910 Cunningham derived a correction factor
for Stokes’s law to account for effect of slip.
What about Particles 0.1 mm
to 1.0 mm diameter?

28. What about Particles 0.1 mm
to 1.0 mm diameter?
Particle dp<1.0 mm
Particle dp>1.0 mm
Include slip correction factor
or Cunningham correction
factor (Cc)
l= Mean free path (For
air at 1 atm 0.066 mm)
Slip correction factors for particles 1.0 mm size is 1.15 that means
the particle settles 15% faster than predicted by stokes equ

29. Particles less than 0.1 mm
diameter
• For particle less than 0.1 mm
• Settling velocity (V): When Re<1.0

30. Slip correction factor
• Slip correction
factor decreases
with increase in
particle diameter.

31. Nonspherical Aerosol
• Liquid droplets less than 1 mm
and some solid particle are
spherical. Most other type of
particles are non spherical.
• Some have regular geometric
shapes, such as cubic (sea salt
particles), cylindrical (bacteria
and fibers).
• Agglomerated particles,
crushed material have
irregular shape.
• Dynamic shape factor (α) is
applied to Stoke’s Law to
account for effect of shape on
particle motion.
α is the ratio of actual
resistance force of the
nonspherical particle to the
resistance force of sphere
having the same volume
and velocity as
nonspherical particle.
de = equivalent volume
diameter

32. Aerodynamic diameter
Aerodynamic diameter always greater than stokes’s equivalent dia.

33. When particle is travelling
in accelerated field
• This is important for understanding the collection
mechanism of aerosols. Such as cascade
impactor.
• Relaxation time and stopping distance are
important
• Relaxation time characterizes the time required
by the particle to adjust or relax its velocity to
anew condition of force.
• Relaxation time (τ) = mass X mobility=mB

34. Stopping Distance
• Maximum distance a particle with an initial
velocity V0 will travel in still air in the absence of
external force.
– S= V0*τ
• Velocity of the particle at any time t in
accelerating field
– V(t)=Vf-(Vf-V0)e-t/τ
– For the particle released in still air and accelerating to its
terminal velocity Vf is settling velocity.
How long will it take a 30 mm glass sphere (p =
2500 kg/m3) to reach a velocity equal to 50%
of settling velocity if it is released from rest in
still air.

35. Thermal and radiometric forces
• When the temperature gradient is established in a
gas, an aerosol particle in that gas experience a
force in the direction of decreasing temperature. The
movement of the particle that results from this force
is called thermophoresis.
• The magnitude of the thermal force depends on gas
and particle properties, as well as temperature
gradient.
• Thermal precipitators are used for aerosol collection.
Example in real life: heated metal rod
immersed in smoke.
The aerosol move away from the rod

36. Thermal precipitator

37. Radiometry force
• Photophoresis is a special case of
thermophoresis in which the absorption of
light by particle creates a temperature
gradient in the particle. The gas immediately
around the particle takes on the same
gradient and establishes the radiometric force.
•

38. References
• Hinds, W. C. (1999) Aerosol Technology:
Properties, Behavior, and measurement of air
born particles. John Willey & Sons Inc.
• Friedlander S. K. (2000) Smoke, dust, and haze:
fundamentals of aerosol dynamics. Oxford
University Press.