19 nguyên tắc cơ bản của hạt điều khiển potx

Fundamentals of
Particulate Control

To understand particulate control, one first must understand some fundamental
concepts and properties of particulate. Figure 19.1 shows common terms associated
with particulate material as a function of particle diameter. Particles of concern to
air pollution are typically measured in microns (i.e., micrometers, or 1

×

10

–6

m).
Large or coarse particles are those considered to be well above 10 microns. Note
for perspective that the diameter of a human hair is approximately 50 to 110 microns.
Very small or fine particles are considered to be those less than one micron, or
submicron. This size range includes smoke and fumes. Also notice that the size
range considered “lung damaging dust” ranges from approximately 0.7 to 7 microns.
Dust in this size range gets into lungs and is the most difficult dust to collect with
particulate control equipment for reasons that will be discussed later in this chapter.

19.1 PARTICLE-SIZE DISTRIBUTION

Particles frequently are described by their diameter. The amount of the particulate
of a given diameter is very informative. But pay attention to the number distribution
and the mass distribution. Table 19.1 illustrates the distinction. Given 100,000 par-
ticles of one micron diameter and assigning each particle a unit mass of one gives
a total mass of 100,000 units. Adding 1,000 particles with a diameter of 10 microns,

plus 10 particles with a diameter of 100 microns provides a size distribution con-
sisting of one, 10, and 100 micron particles. There are 101,010 particles, of which
99% are one micron in diameter. Because the volume, and therefore the mass of
each particle varies with the cube of the diameter, the mass of one-micron particles
is only 9% are the total mass of all particles. Size distributions commonly are
expressed in terms of the mass distribution. It is always best to be very clear whether
the distribution is a mass or a number distribution.
Sample particle size distribution data are listed in Table 19.2. Data are divided
into six size bins, the first being zero to 2 microns, and the last being greater than
25 microns. Note that the last size bin is open ended. The mass fraction of particulate
within each size range is provided. The next column gives the cumulative weight
percent less than the top size listed in each size range.
Cumulative size distributions are commonly plotted on probability paper. Prob-
ability paper is based upon the normal distribution, a bell shaped curve, with the
highest density in the center and the lowest densities at each extreme. The x-axis
on probability paper is different from logarithmic graph paper, where the highest
density would be at the extreme top or right. The y-axis on probability paper may
be either linear or logarithmic. The example data listed in Table 19.2 are plotted on
19

9588ch19 frame Page 279 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

FIGURE 19.1

Common particulate terms and size ranges.

TABLE 19.1
Number Fraction vs. Mass Fraction

d

j

,

␮

m Number Number Fraction Mass of Particle Total Mass Mass Fraction

1 100,000 0.990000 1 10

5

0.009
10 1000 0.009900 1000 10

6

0.090
100 10 0.000099 10

6

10

7

0.900

Total



101,010 1.0 1.11

×

10

7

1.0



TABLE 19.2
Sample Particle Size Distribution Data

Size Range
(

␮

m)
Mass Fraction
in Size Range,
(m

j

)
Cumulative %
Less Than Top Size

0–2 0.005 0.5
2–5 0.195 20.0
5–9 0.400 60.0
9–15 0.300 90.0
15–25 0.080 98.0
>25 0.020 100.0

9588ch19 frame Page 280 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

linear probability paper in Figure 19.2, and on log-probability paper in Figure 19.3.
On probability paper with a linear y-axis, a normal distribution would plot as a
straight line. On log-probability paper, a log normal distribution would plot as a

FIGURE 19.2

Sample particle size distribution on linear-probability plot.

FIGURE 19.3

Sample particle size distribution on log-probability plot.

9588ch19 frame Page 281 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

straight line. The sample particle size distribution in Table 19.2 plots as a straight
line on log-probability paper, so it is a log-normal distribution.
This data can be plotted on linear graph paper giving the mass fraction in equal
micron size range bins, which would show a skewed distribution as shown in
Figure 19.4. The same distribution, but with the mass fraction bins plotted on a log
scale, gives the distribution shown in Figure 19.5. The distribution produces a bell-
shaped curve when plotted on the log-scale, indicative of a log-normal distribution.
When the same data are plotted as a cumulative distribution, i.e., as the total
percentage less than the specified particle size, an S-shaped curve is produced. The
curve for a log-normal distribution is skewed when plotted on linear graph paper,

FIGURE 19.4

Particle size bins plotted on linear graph paper.

FIGURE 19.5

Particle size bins plotted on semi-logarithmic graph paper.

9588ch19 frame Page 282 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

as shown in Figure 19.6. But when plotted on semi-logarithmic paper, the curve is
symmetrical, as shown in Figure 19.7.
Log-normal distributions are common for many particulate emission sources
because a large amount of mass is concentrated in a very few large particles. While
common, other distributions are certainly found. Bimodal distributions, those with
a large mass of particles in two different size fractions, sometimes are found. They
may be indicative of two different mechanisms for generating the particles. For
example, larger particles in the distribution may have formed from a grinding

process, while smaller particles may have formed from a condensation process.

FIGURE 19.6

Sample cumulative size distribution on linear paper.

FIGURE 19.7

Sample cumulative size distribution on semi-logarithmic paper.

9588ch19 frame Page 283 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

19.2 AERODYNAMIC DIAMETER

The diameter of the particle is a common descriptor. But there are two diameters
that are commonly used as descriptors: physical diameter and aerodynamic diameter.
The physical diameter, of course, is the actual diameter of a spherical or nearly
spherical particle. The aerodynamic diameter is the diameter of a spherical particle
with the density of one gram per cubic centimeter that behaves aerodynamically in
the same manner as the subject particle. That is, the actual particle and the spherical
particle with density of 1 g/cm

3

have the same momentum and drag characteristics.
As a practical example, they have the same terminal settling velocity, which is an
aerodynamic property. Remember that terminal settling velocity results from simple
force balance between the force of gravity and resisting drag force.

19.3 CUNNINGHAM SLIP CORRECTION

When airborne particles are so small that the particle size approaches the mean free
path of gas molecules, less than 5 microns, drag on on the particles tends to be
reduced. Drag is created as gas molecules impact a moving particle. But when the
mean free path is approached, a moving particle will tend to “slip” between the gas
molecules with less resistance. This phenomena is of importance to particulate
collection devices and the term Cunningham slip correction factor will be found in
many small particle correlations. The following empirical correlation for the Cun-
ningham slip correction factor was developed by Davies:

1

(19.1)
where
C

′

= cunningham slip correction factor

λ

= mean free path, meters
d

p

= particle diameter, microns
The mean free path,

λ

, is given by:
(19.2)
where

µ

= gas viscosity, kg/m-s

ρ

g

= gas density, kg/m

3

u

m

= mean molecular speed, m/s
The mean molecular speed, u

m

, is given by:
′

=+ + −












C
d
d
p
p
1 2 1257 04 055
λ
λ
. . exp .
λ
µ
ρ
=
0 499.
gm
u

9588ch19 frame Page 284 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

(19.3)
where
MW = molecular weight of the gas
R = universal gas constant, 8315 g m

2

/gmole-°K-s

2

T = absolute temperature, °K
By the ideal gas law, density is
(19.4)
So the gas mean free path can also be expressed as:
(19.5)
where P = Pressure, Pa
The Cunningham slip correction factor for air at 1.0 atm is plotted in Figure 19.8.
It can be seen that the correction factor has a major effect when the particle diameter
is less than 1 micron.

FIGURE 19.8

Cunningham slip correction factor for air at 1 atm.
u
RT
MW

m
=
8
π
ρ
g
m
V
PMW
RT
==
λ
µ
π
=
0 499
8
.P
MW
RT

9588ch19 frame Page 285 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

19.4 COLLECTION MECHANISMS
19.4.1 B

ASIC

M

ECHANISMS

: I

MPACTION

, I

NTERCEPTION

, D

IFFUSION

Consider a particle in a gas stream moving toward or being carried toward a target.
If the particle touches the target, it likely will stick to the target due to intersurface
forces. The target may be a liquid droplet, as in the case of wet scrubbers, or a fiber,
as in a fabric filter baghouse. Three mechanisms by which the particle touches the
target are illustrated in Figure 19.9. Small, medium, and large size particles are
depicted as being carried by the gas stream toward round targets. The gas flow
streamlines are shown as diverging as they approach the target, then moving around
the target.
In each of these mechanisms, a large number of targets will increase the prob-
ability that a particle will touch a target. Therefore, having abundant targets enhances
collection efficiency.

FIGURE 19.9

Basic particle collection mechanisms.

9588ch19 frame Page 286 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

19.4.1.1 Impaction

In the mechanism called impaction, large particles moving toward the target have
mass, and therefore momentum, which causes each particle to travel in a straight
line toward the target. The particle leaves the streamline as the streamline bends to
move around the target. The greater the mass of the particle, the more likely that it
will travel in a straight line. Also, as the velocity difference between the particle
and the target increases, the particle will have increased momentum and will be
more likely to be carried into the target.
The radius of curvature of the bend in the streamline has a very important effect
on the probability that a particle will be carried into the target. The smaller the radius
of curvature, the less likely that a particle will follow the streamline. Therefore,
small targets are more likely to be impacted than large targets.

19.4.1.2 Interception

Interception is the mechanism by which particles of roughly 0.1 to 1 micron diameter
are carried by the gas streamline sufficiently close to the surface of the target that
the particle touches the target. These particles have insufficient inertia to leave the
gas streamline and are carried with the streamline. Some gas will flow very close
to the particle.
Interception is a relatively weak mechanism for particle collection compared to
impaction and, as discussed in the next section, diffusion. It is coincidental that the
path of the streamline and the particle happens to be close to the target. It is for this
reason that particles in this size range are difficult to collect compared to larger and
smaller particles. For the same reason, particles in this size range are not collected

by natural cleaning mechanisms in nasal and tracheobronchial passages, and enter
the lungs where they can lodge in the alveoli.

19.4.1.3 Diffusion

Diffusion of extremely small, submicron particles is a result of Brownian motion.
These particles are so small that the mass of the particles is very small and the
number of collisions with air molecules is low. Therefore, random collisions with
air molecules cause the particle to bounce around. They are moved from one gas
streamline to the next by random motion. If sufficient time is allowed, and if the
distance to the target is small, then diffusion can be an effective collection mecha-
nism. This is why fabric filter baghouses can be effective for collecting submicron
particles, and why it is difficult for wet venturi scrubbers to collect these particles.

19.4.2 O

THER

M

ECHANISMS

19.4.2.1 Electrostatic Attraction

If particles acquire a charge and are placed in an electric field, the electrostatic force
will move the particles across gas flow streamlines. Electrostatic forces on small

9588ch19 frame Page 287 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC

particles can be quite large, making this a very effective mechanism for particle
collection. This mechanism is utilized in electrostatic precipitators.

19.4.2.2 Gravity

The force of gravity is sufficient to pull very large particles out of a gas stream.
Some mechanical separators are designed to slow a gas stream to allow particles to
settle. However, gravity is a weak mechanism for all but the heaviest particles.

19.4.2.3 Centrifugal Force

Centrifugal force is the basis for cyclonic separation as a dusty gas is spun into a
circle. Cyclones are discussed in Chapter 21.

19.4.2.4 Thermophoresis

When a temperature gradient exists across a gas space, there will be a small tem-
perature difference from one side of a particle to the other side. Gas molecules on
the high-temperature side of the particle collide with the particle with more energy
than gas molecules on the cooler side. This causes the particle to move slightly
toward the cold side. Thermophoresis is a relatively weak mechanism for particle
collection, but it can have a small effect on collection efficiency.

19.4.2.5 Diffusiophoresis

Diffusiophoresis can be illustrated by considering the example of water vapor in a
gas stream condensing on a cold target. As water vapor molecules are removed from
the gas stream by condensation in the vicinity of the target, the concentration of
water molecules, and hence the partial pressure of water vapor, is decreased. The
concentration gradient causes water molecules from the bulk gas space move toward

the cold target. The moving water vapor molecules collide with particles, causing
them to be driven slightly toward the cold target. Again, this is a relatively weak
mechanism that can have a small effect on particulate collection efficiency.

REFERENCE

1. Davies, C. N., Definitive equations for the fluid resistance of spheres,

Proc. Phys.
Soc.,

57, 259, 1945.

9588ch19 frame Page 288 Wednesday, September 5, 2001 10:03 PM
© 2002 by CRC Press LLC