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CE 583 – The Nature of Particulate Pollutants
Jeff Kuo, Ph.D., P.E. [email protected]
1
Content
Primary and Secondary Particles
Settling Velocities and Drag Forces
 Stokes’ law
 Stokes’ stopping distance
 Aerodynamic particle diameter
 Diffusion of particles
Particle Size Distribution Functions
 Gaussian and log-normal
 By weight and by number
Behavior of Particles in the Atmosphere
2
Primary and
Secondary
Particles
ballmill
Particulates make an air stream visible and hazy.
Particulates are not chemically uniform (sizes, shapes,
chemical compositions).
Some are more harmful and visible.
Not all particles are spherical (rod-like asbestos) 
diameter of sphere of equal volume.
Micron () means micrometer (m)
Ones cause significant problems: 0.01 – 10 .
Particles >100  will not pass a Tyler 150 mesh
screen.
Most mechanical processes will not create particles <
10  (except paint pigments and ground talc).
3
Primary and
Secondary Particles
Most fine particles (0.1 to 10 ) are formed by
combustion, evaporation or condensation.
Directly above a burning tobacco is a
transparent zone (gaseous HC), above it is
visible smoke (condensed HC – tars, oils of
0.01 to 1 ).
Smokes from tailpipe of an “oil-burning” car
are all high MW hydrocarbon.
Uncommon in air pollution to distinguish fine
particles that are liquids or solids.
Ash – incombustible materials left behind
after burning (oxides of silicon, calcium,
aluminum,..)
4
Primary and
Secondary
Particles
char
soot
Fly ash in coal burning contain two groups:
 ~0.02 : contains high % of volatile materials (P,
Mg, Na, K, Cl, Zn, Cr, As, Co, and Sb) – formed by
condensation of vaporized materials.
 ~10 : those not vaporized (oxides of Si, Al, Ca,…)
Coal char: porous residue (HC gases were driven off by
high T) from incomplete burning. blue= N; red = O
Soot: long, lacy filaments up to a few mm long.
Soot is actually agglomerate of fine particles - formed
in flames from vaporizing HC.
Spherical metal ash particles –
chars & soot were burned
5
Rain drop
6
7
Primary and
Secondary
Particles
V  D3
A  D2
A
1

V
D
When two fine particles are brought into contact,
they will stick by electrostatic and van der Waals
forces.
These forces are ~ area of particle (or D2)
Gravity and inertial forces are ~ mass of particle (or
D3)
As D, D3  faster than D2 (surface forces become
important).
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Primary and
Secondary
Particles
V  D3
A  D2
A
1

V
D
Thus, the basic strategy for particulate control is
to agglomerate them into larger ones for removal
 forcing the contact (settling chamber, cyclone,
ESP, or filters) or contact with water (scrubber).
Some particulates can be formed in the
atmosphere from gaseous pollutants – secondary
particles (from HC, oxides of N, oxides of sulfur)
vs. primary particles – emitted as particles.
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Primary and
Secondary
Particles
Particles efficient in scattering the light are those with
D close to wavelength of light (0.4 to 0.8 ) – mostly
by secondary particles.
The Great Smoky Mountains National Park of
Tennessee got its name from secondary particles
formed from the HC emitted from the forests.
Inhalable particles (< 10 ); respirable particles (<
3.5 ); fine particles (< 2.5 )
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Settling Velocity
and Drag Forces
The “terminal gravitational settling” velocity for
1-mm sand grain (1000-,SG =2) in air is 600
cm/s, and that for 1- is 0.006 cm/s. One will
settle, the other won’t.
Dusts (settle quickly) vs. suspendable particles –
arbitrary definition: ~ 10.
Aerosols – particles small enough to remain
suspended in the atmosphere/gases for long
times (as if they were dissolved).
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Settling Velocity and Drag
Forces – Stokes’ Law
Balance between gravity and drag forces
At the “terminal gravitational settling” velocity,
the sum of the forces acting is zero.
Can be used to determine the size of settling
chambers for removing dust particles from gas
or liquid streams.
(  part   fluid )
2
Stokes’ law:
V  gD
18
Ex. 8.1: 1 micron particle
3
(
2000

1
.
2
kg
/
m
)
2
6
2
V  (9.81m / s )(10 m)
18(1.8 10 5 kg / m  s)
 6.05 10 5 m / s  1.99 10 4 fps
12
Settling Velocity and Drag Forces – Stokes’ Law
Particle moving
through fluid

C
v
A

F
2
D
p
F
D
Drag force, FD
d v
FD 3
CD = drag coefficient
Ap = projected area of particle
rF = density of fluid
vr = relative velocity
p
r


d
v
Re 
p
 =particle shape factor (=1 for sphere)
r

Stokes Regime
 Rigid spheres
 10-4 < Re < 1
dp = particle diameter
 = fluid viscosity
r
2
F
24

CD
Re
For large particles
(0.3  Re  1000)
24
CD 
(1  0.14 Re 0.7 )
Re
13
Settling Velocity and Drag
Forces – Stokes’ Law
V  gD
2
(  part   fluid )
18
Ex. 8.2: 200 micron particle. How fast would it be
falling and what would be the Reynolds number be?
2
 200 
V  6.05 10 5 m / s 
 2.42m / s

 1 
DV fluid (200 10 6 m)( 2.42m / s )(1.20kg / m 3 )
Re 


(1.8 10 5 kg / m  s )
 32.3  0.3
14
Settling Velocity and
Drag Forces – Particles
too large for Stokes’ Law
At large particle sizes,
the flow of fluid around
the sphere becomes
turbulent.
Ex. 8.3 shows that the
settling velocity for 200 particle can be 50% of
that calculated by
Stokes’ law.
Stokes’ law does not
apply for particles much
greater than 50-.
For large particles
(0.3  Re  1000)
CD 
24
(1  0.14 Re 0.7 )
Re
15
Settling Velocity and Drag Forces –
Particles too small for Stokes’ Law


8MW
RT
Mean free path of gas molecules
0.499 P
As d particle  
gas no longer looks like continuum,
but rather like discrete particles.
The particles may slip and reduce the drag force.
CD
CD 
C
C  Cunningham correction factor
'
C =1+ A

d particle
A : a constant determined experiment ally,
for specific particle fluid combinatio n
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Settling
Velocity
17
Settling Velocity and Drag Forces – Particles
too small for Stokes’ Law
Ex. 8-4: A 0.1- particle is settling in still air. What
is its terminal settling velocity?
V  VStokes (1  A / D)
At 1 atm and room temp,   0.07 
Assume A  1.728 (derived for oil droplets)
1  A/D  1  1.728 (0.07/0.1)  2.21
V  (6.05 10-7 )( 2.21)  1.34 10 6 m / s
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Settling Velocity and Drag Forces –
Stokes stopping distance
Ex. 8-5: A 1- particle with SG =2 is ejected into air
with V = 10 m/s. How far can it travel before it is
stopped by viscous friction (ignore the gravity)?
xStokes stopping 
Vo D 2  partC
18
(10)(10 6 ) 2 (2000)(1.12)
5


6
.
9

10
m  69 
5
18(1.8 10 )
The value is very small. For particles of this size, air
is a very viscous fluid.
In the next chapter, we will see the Stokes stopping
distance in a natural distance scale and they are
related to control efficiencies.
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Settling Velocity and Drag
Forces – Aerodynamic
particle diameter
xStokes stopping 
Vo D 2  partC
18
Two particles have the same value of D2partC will
have the same stopping distance for any initial
velocity.
Later will show that any two particles with the same
value of this set will behave identically in several
kinds of control devices – same aerodynamic
behavior.
20
Settling Velocity and Drag
Forces – Aerodynamic
particle diameter
Aerodynamic particle diameter for the particle in ex.
8.5:
Da  D  partC  D  part
3 1/ 2
[( L)( M / L ) ]
The symbol a stands for “microns, aerodynamic”.
g
g 0.5
Da  0.1 (2 3 )( 2.21)  0.21 ( 3 )  0.21a
cm
cm
21
Settling Velocity and Drag Forces –
Aerodynamic particle diameter (PE
Sample Exam Question)
The size and density of two particles are 10  & 1
g/cm3 and 5  & 4 g/cm3. The aerodynamic
diameter (), respectively, of the particles are most
nearly:
(a) 10 and 20
(b) 10 and 10
(c) 10 and 5
(d) none of the above
Da  10 (1)  10 a
Da  5 (4)  10 a
22
Settling Velocity and Drag Forces –
Diffusion of particles
kTC
D
3d p
Note: D here is
diffusivity
Ex. 8.6: Estimate the diffusivity of a 1- particle in
air at 20 oC and 1 atm.
(1.38 10 23 kg  m 2 / s 2  K )( 293)(1.16)
D
3 (1.8 10 5 )(10 6 )
 2.8 10 11 m 2 / s
Most gases diffuse in air with D of ~10-5 m2/s and D
of solute in liquids are ~ 10-9 m2/s.
Thus, particles on the order of a few microns do not
diffuse rapidly.
23
PSD Function - Gaussian
(normal) distribution
  variance
  standard deviation
2
250
200
n(ln(dp))
 x  xmean 2 
d
1

exp  

2
dx  2
2



  cumulative fraction in the size range of interest
150
sigma=1.2
sigma=1.5
sigma=2.0
100
50
0
0.01
0.1
diameter (um)
Plot d/dx vs. x  symmetrical about xmean, the
max occurs at x = xmean. It approaches zero
asymptotically (bell-shape curve).
A larger value of  spreads the values over a wide
range of x.
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The area under the curve = 1.
1
PSD Function - Gaussian
(normal) distribution
No one has found a way
to integrate the equation.
The integration has been
done numerically. Also a
new variable, z (# of
probits from the mean),
is defined.
 z2 
1
exp   
2
2
  cumulative fraction between 0 and x
z  number of standard deviations from the mean
x  xmean 
z=
d

dz

25
PSD Function - Gaussian
(normal) distribution
‘Probability scale’ a scale linear in z (the values of
 corresponding to z are shown, instead.
Gaussian distribution gives linear plot on normal vs.
probability coordinates.
Mean value is at z = 0
1
s = standard deviation
xmean   xi
n
1
s
[ ( xi  xmean ) 2 ]1/ 2
n 1
As n becomes large, the s, sample standard
deviation, becomes , or the (variance)0.5.
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PSD Function – Lognormal distribution
 ln D  ln Dmean 2 
d
1

exp  

2
d ln D  2
2



  cumulative fraction for particles
with diameter between 0 and D
ln D  ln Dmean
z

Many authors write the above equation with  replaced
by ln as
 ln D  ln Dmean 2 
d
1

exp  

2
d ln D ln  2
2
(ln

)


27
PSD Function – Lognormal distribution
Log-normal distribution gives linear plot on
logarithmic vs. probability coordinates
Mean value is at z = 0. Typical  for PSD = 0.5 to 2,
which corresponds to g, logarithmic standard
deviation or geometric standard deviations, for the
last equation (previous slide) of 1.64 to 7.39.
The smallest possible value for g is 1.0,
corresponding to a  of zero.
 = ln(g)
1
Arithmetic mean diameter   Di
n
1
Log mean diameter  exp(  ln Di )  ( D1  D2    DN )1/ N
28
n
PSD Function – Log-normal distribution
How to get
Dmean and 
from the line?
Dmean = 20
From table, z
=1 
=0.8413
Z=1 =(x0.84 –
xmean)/
 = lnD0.84 –
lnDmean =
ln(70/20) =
1.25
g = exp1.25
=3.49
29
PSD Function – Log-normal distribution
(PE Sample Exam Question)
A log normally distributed particle mass has a
geometric standard deviation g of 2.0
microns and a geometric mean diameter of 4
microns. A total of 84.1 of the particles are
likely to have sizes (microns) less than (a) 2,
(b) 4, (c) 6, (d) 8
  ln  g  ln 2  ln( D84.1 / D50 )
D84.1  8
30
PSD Function – Distribution by weight and
by number
It is possible to define different mean diameters
based on the type of cumulative fraction we use.
if  for D a is log normal, then  for Db is log normal

Db  Da exp b  a  2
V  D3
A D
2
V
 D (Sauter)
A
N  D 0 (Number)

Say D3  20m (mass mean)
and   1.25


D0  (20) exp 0  31.252  0.18m
(number mean)
For any particle size distribution,
dnumber  d Sauter  darea  dvolumemass
31
Types of Size Distributions
Typical Rural distribution
Typical Urban distribution
#
A
V or M
Volume and mass distributions are related by particle
density (same shape!)
Typically, environmental engineers are interested in mass
32
distributions.
PSD Function
Distribution function parameters (mean and
standard deviation) are obtained by fitting the data
They generally do a good job in the middle of the
range.
Beware of extrapolating beyond the data range (Ex.
8.8, predicts 6 men taller than 10 feet (3 m) in the
United States based on height distribution statistics.
For distribution functions having same  (previous
slide), we can compute Dmean, number, then draw a
parallel line to find its distribution function.
33
Behavior of
Particles in the
Atmosphere
The plot is for
dby area/dD. If
dby mass/dD was
plotted  the
peak to the right
would be larger.
If dby number/dD
were presented,
then?
34
Behavior of Particles
in the Atmosphere
Finest (0.005 to 0.1): enter
the atmosphere mostly by
condensation of hot vapors
from combustion.
Midsize (0.1 to 1):formed
by agglomeration of finer
particles and by chemical
conversion of gases and
vapors to particles. They
will then captured by drops
in clouds (rainout) or by
falling raindrops (washout).
Larger (2 to 100):
mechanically generated
or industrial particle
source – removed mainly
by settling.
35
Behavior of Particles in the Atmosphere
The first two peaks (last slide) are mainly secondary
particles from gaseous precursors, SO2, NOx, NH3, & HC.
NH3 is mainly from the biological sources.
36
The third peak is mainly primary particles.