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 . 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. 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. 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