AEROSOLS An aerosol is a system of tiny particles suspended in a gas Aerosols or particulate matter refer to any substance, except pure water, that exists as a liquid or solid in the atmosphere under normal conditions and is of microscopic or submicroscopic size but larger than molecular dimensions There are two fundamentally different mechanisms of aerosol formation: • • number, tend to coagulate rapidly to form larger particles Surface tension practically limits the smallest size of particles that can be formed by mechanical means to about mm PARTICLE SIZE DISTRIBUTION Size is the most important single characterization of an aerosol particle For a spherical particle, diameter is the usual reported dimension When a particle is not spherical, the size can be reported either in terms of a length scale characteristic of its silhouette or of a hypothetical sphere with equivalent dynamic properties, such as settling velocity in air Table summarizes the physical interpretation for a variety of characteristic diameters The Feret and Martin diameters are typical geometric diameters obtained from particle silhouettes under a microscope nucleation from vapor molecules (photochemistry, combustion, etc.) comminution of solid or liquid matter (grinding, erosion, sea spray, etc.) Formation by molecular nucleation produces particles of diameter smaller than 0.1 mm Particles formed by mechanical means tend to be much larger, diameters exceeding 10 mm or so, and tend to settle quickly out of the atmosphere The very small particles formed by nucleation, due to their large TABLE Measures of particle size Definition of characteristic diameters geometric size Physical meaning and corresponding measuring method (b ϩ l ) / 2, (b ϩ l ϩ t ) / 3,(blt )1 / , /(1 / l ϩ / b ϩ / t ), lb , {(2lb ϩ 2bt ϩ 2lt / 6)} Feret diam Martin diam equivalent projection area diam (Heywood diam.) diameter of the circle having the same area as projection area of particle, corresponding to diam obtained by light extinction diameter of the sphere having the same surface as that of a particle, corresponding to diam obtained by absorption or permeability method equivalent volume diam (6v/p)1/3 diameter of the sphere having the same volume as that of a particle, corresponding to diam obtained by Coulter Counter Stokes diam diameter of the sphere having the same gravitational setting velocity as that of a particle, Dst ϭ [18 mvt/g(rp Ϫ rf)Cc]1/2, obtained by sedimentation and impactor b unidirectional diameter: diameter of particles as the length of a chord dividing the particle into two equal areas equivalent surface area diam (specific surface diam.) (s/p)1/2 equivalent diam unidirectional diameter: diameter of particles at random along a given fixed line, no meaning for a single particle t l breadth: b length: l (continued) 15 © 2006 by Taylor & Francis Group, LLC 16 AEROSOLS TABLE (continued) Measures of particle size Physical meaning and corresponding measuring method Definition of characteristic diameters thickness: t volume: v aerodynamic diam diameter of the sphere having unit specific gravity and having the same gravitational setting velocity as that of a particle, Dae ϭ [18 mut/gCc]1/2, obtained by the same methods as the above surface area: s electrical mobility equivalent diam diameter of the sphere having the same electrical mobility as that of a particle, De = npeCc/3pmBe, obtained by electrical mobility analyzer equivalent diffusion diam diameter of the sphere having the same penetration as that of a particle obtained by diffusion battery equivalent light scattering diam diameter of the sphere having the same intensity of light scattering as that of a standard particle such as a PSL particle, obtained by light scattering method When particles, at total number concentration N, are measured based on a certain characteristic diameter as shown in Table and the number of particles, dn, having diameters between Dp and Dp ϩ dDp are counted, the normalized particle size distribution f(Dp) is defined as follows: 0.1 D4 D3 D2 Dv ( ) (1) where ( ) D8 30 Dh Dmode 50 Dg 70 NMD ( ) f Dp ϭ ⌬n N ⌬D p (2) 99.9 0.1 is x2 g σ ma ss b 99 nu mb er ba sis 90 The discrete analog which gives a size distribution histogram is Dg MMD f D p dD p ϭ1 F = 84.13% D1 as ∫ 100-F (%) 10 dn f Dp ϭ , N dD p 0.5 10 50 Dp ( µm) where ⌬n is the particle number concentration between Dp Ϫ ⌬Dp/2 and Dp ϩ ⌬Dp/2 The cumulative number concentration of particles up to any diameter Dp is given as ( ) F Dp ϭ ∫ Dp ( ) f D p dD p ϭ Ϫ ∫ ( ) dF ϭ f Dp dD p Dp ( ) f D p dD p (3) The size distribution and the cumulative distribution as defined above are based on the number concentration of particles If total mass M and fractional mass dm are used © 2006 by Taylor & Francis Group, LLC FIGURE Log-normal size distribution for particles with geometric mean diameter of µm and geometric standard deviation of 2.0 The different average particle diameters for this distribution are defined in Table instead of N and dn, respectively, the size distributions can then be defined on a mass basis Many particle size distributions are well described by the normal or the log-normal distributions The normal, or Gaussian, distribution function is defined as, ( ⎛ D Ϫ Dp p f Dp ϭ exp ⎜Ϫ ⎜ 2s 2ps ⎝ ( ) )⎞ ⎟ ⎟ ⎠ (4) AEROSOLS Ϫ where Dp and s are, respectively, the mean and standard deviϪ ation of the distribution The mean diameter Dp is defined by Dp ϭ ∫ Ϫ ( ) Ϫ In the practical measurement of particle sizes, Dp and s are determined by Dp ϭ (5) D p f D p dD p Ϫ (D p Ϫ Dp ) f ( D ) dD p i pi N ( )⎞ ⎟ 1ր ⎟ ⎠ TABLE Names and defining equations for various average diameters Defining equations General case number mean diam D1 In the case of log-normal distribution ln D1 ϭ A ϩ 0.5C ϭ B Ϫ 2.5C ⌺⌬nD p N length mean diam D2 ln D2 ϭ A ϩ 1.5C ϭ B Ϫ 1.5C ⌺⌬nD p ⌺⌬nD p surface mean, Sauter or mean volume-surface diam D3 ⌺⌬nD p volume or mass mean diam D4 ⌺⌬nD p ⌺⌬nD p ϭ ⌺⌬nD p ϭ ⌺⌬sD p ln D3 ϭ A ϩ 2.5C ϭ B Ϫ 0.5C S ⌺⌬mD p ln D4 ϭ A ϩ 3.5C ϭ B ϩ 0.5C M ln Ds ϭ A ϩ 1.0C ϭ B Ϫ 2.0C ⌺⌬nDp ln Dv ϭ A ϩ 1.5C ϭ B Ϫ 1.5C ⌺⌬nD p diam of average surface Ds N diam of average volume or mass Dv N harmonic mean diam Dh ln Dh ϭ A Ϫ 0.5C ϭ B Ϫ 3.5C N ⌺(⌬/D p ) number median diam or geometric mean diam NMD volume or mass median diam MMD ⎡ ⌺⌬n ln D p ⎤ ⎥ N ⎣ ⎦ NMD ⎡ ⌺⌬nD ln D p ⎤ p ⎥ ⎣ ⌺⌬nD p ⎦ ln MMD ϭ A ϩ 3C exp ⎢ exp ⎢ ⎡ ⌺⌬m ln D p ϭ exp ⎢ ⎣ M A ϭ ln NMD, B ϭ ln MMD, C ϭ (ln sg)2 N(total number) ϭ ⌺⌬n, S(total surface) ϭ ⌺⌬s, M(total mass) ϭ ⌺⌬m © 2006 by Taylor & Francis Group, LLC (7) where ni is the number of particles with diameter Dpi and N is the total particle number measured (6) p ∑n D ⎛ n D Ϫ Dp i pi sϭ⎜ ⎜ N ⎝ and the standard deviation, indicating the dispersion of the distribution, is given by s2 ϭ ∫ 17 18 The log-normal distribution is particularly useful for representing aerosols because it does not allow negative particle sizes The log-normal distribution function is obtained by substituting ln Dp and ln ␴g for Dp and s in Eq (4), ( ( ⎛ lnD Ϫ ln D p p f ln D p ϭ exp ⎜Ϫ ⎜ ln s g π ln s g ⎝ ) ) ⎞ ⎟ ⎟ ⎠ (8) The log-normal distribution has the following cumulative distribution, Fϭ 2p ln s g ∫ Dp ( ⎛ ln D Ϫ ln D p g exp ⎜Ϫ ln s g ⎜ ⎝ ) ⎞ d ln D ⎟ ( ) ⎟ p (9) ⎠ The geometric mean diameter Dg, and the geometric standard deviation sg, are determined from particle count data by (∑ n ln D ) N ϭ ⎡ ∑ n ( ln D Ϫ ln D ) ⎢ ⎣ ln Dg ϭ ln s g i pi g N⎤ ⎥ ⎦ (10) 1ր D p at F ϭ 84.13% D p at F ϭ 50% ϭ D p at F ϭ 50% D po at F ϭ 15.7% The rapid graphical determination of the geometric mean diameter Dg as well as the standard deviation sg is a major advantage of the log-normal distribution It should be emphasized that the size distribution on a number basis shown by the solid line in Figure differs significantly from that on a mass basis, shown by the dashed line in the same figure The conversion from number median diameter (NMD) to mass median diameter (MMD) for a log-normal distribution is given by ln(MMD) ϭ ln(NMD) ϩ 3(ln sg)2 (11) If many particles having similar shape are measured on the basis of one of the characteristic diameters defined in Table 1, a variety of average particle diameters can be calculated as shown in Table The comparison among these diameters is © 2006 by Taylor & Francis Group, LLC VOLCANIC PLUMES FOREST FIRE PLUMES DUST STORMS INTENSE SMOG 104 103 HEAVY AUTO TRAFFIC SAND STORMS 102 101 100 INDUSTRY TYPICAL URBAN POLLUTION CONTINENTAL BACKGROUND SEA SALT SOUTH ATLANTIC BACKGROUND NORTH ATLANTIC BACKGROUND 10–1 10–3 10–2 10–1 100 101 102 103 FIGURE Surface area distributions of natural and anthropogenic aerosols Figure shows the log-normal size distribution for particles having Dg ϭ mm and sg ϭ 2.0 on a log-probability graph, on which a log-normal size distribution is a straight line The particle size at the 50 percent point of the cumulative axis is the geometric mean diameter Dg or number median diameter, NMD The geometric standard deviation is obtained from two points as follows: sg ϭ 105 Dp (mm) pi i SURFACE AREA DISTRIBUTION, ∆S/∆log Dp(mm2 cm–3) AEROSOLS shown in Figure for a log-normal size distribution Each average diameter can be easily calculated from sg and NMD (or MMD) Figure indicates approximately the major sources of atmospheric aerosols and their surface area distributions There tends to be a minimum in the size distribution of atmospheric particles around mm, separating on one hand the coarse particles generated by storms, oceans and volcanoes and on the other hand the fine particles generated by fires, combustion and atmospheric chemistry The comminution processes generate particles in the range above mm and molecular processes lead to submicron particles PARTICLE DYNAMICS AND PROPERTIES Typical size-dependent dynamic properties of particles suspended in a gas are shown in Figure together with defining equations (Seinfeld, 1986) The solid lines are those at atmospheric pressure and the one-point dashed lines are at low pressure The curves appearing in the figure and the related particle properties are briefly explained below Motion of Large Particles A single spherical particle of diameter Dp with a velocity u in air of density rf experiences the following drag force, Fd ϭ CD Ap(rf u2/2) (12) 19 AEROSOLS 100 e a dis bso pla lu ce te v m alu en t in e of 1s Bro ,∆ w X nia in n air In 4D/p (cm), D ic ctr Ele ) =1 (n p ff., coe mo 10–3 Be ty, bili Vth 102 τg gc m –3 p =1 ρ tim f., C 10–8 0.001 lax Re Kelvin effect, (water droplet) ati c 0.01 Pulse (exam height ple) ef 10–7 100 e co on ip τg 10–6 m m 10 at Hg 0.1 101 1000 10 100 10–1 (3.1) Cc = + 2.514 λ + 0.80 Dp 10–2 10 Dp λ ) exp (–0.55 Dp λ Cc =1+(2 / pDp) [6.32 + 2.01 exp (–0.1095pDp)] p in cm Hg, Dp in mm ∆x = Pd / P FIGURE (3.4) D= (3.6) Be = p ρpDpCc 18m τg = 4Dt = exp ( 4Mσ ) RTρlDp kTCc 3pmDp np e Cc 3pmDp (3.2) (3.3) (3.5) (3.7) (3.8) Fundamental mechanical and dynamic properties of aerosol particles suspended in a gas © 2006 by Taylor & Francis Group, LLC Dp (mm) (ρp –ρf)gDpCc Vt = 18m Increase in vapor pressure by Kelvin effect, pd / p Hg 10–5 Sl Pulse height (light scattering) 1°C/cm C c a t1 0m m Slip coefficient, Cc 10–4 Thermophoretic velocity vth (cm/s) Average absolute value of Brownian displacement in 1s ∆x = al Relaxation time τg(s), Electrical mobility Be (cm2 V–1 s–1), ion fus Dif Settling velocity vt (cm/s), Diffusion coefficient D (cm2/s), Se ttlin gv air elo (ρ city p =1 , gc m –3 Vt ) Av er ag 10–1 10–2 20°C in air 1atm 10 mm Hg 20 AEROSOLS where Ap is the projected area of the particle on the flow (ϭ pD2/4), and CD is the drag coefficient of the particle The p drag coefficient CD depends on the Reynolds number, Re ϭ ur D p rf /m The motion of a particle having mass mp is expressed by the equation of motion mp (13) where ur is the relative velocity between the particle and air ( ϭ |u Ϫ v|, u ϭ velocity of air flow, v ϭ particle velocity), and m is the viscosity of the fluid dv ϭ∑F dt (14) where v is the velocity of the particle and F is the force acting on the particle, such as gravity, drag force, or electrical force Table shows the available drag coefficients depending on TABLE Motion of a single spherical particle Rep Ͻ (Stokes) drag coefficient, CD Ͻ Rep Ͻ 104 104 Ͻ Rep (Newton) 0.44 24/Rep drag force, R f ϭ C D A p rf v ⎛ 4.8 ⎞ ⎟ ⎜ 0.55 ϩ ⎜ Re p ⎟ ⎠ ⎝ 3pmDpv ⎛ ⎞ pmD p v vD p rf ϩ 4.8⎟ ⎜ 0.55 m ⎠ ⎝ 2 gravitational settling equation of motion mp 0.055prf (vDp)2 ⎛ rf ⎞ dv ϭ m p ⎜ Ϫ ⎟ g Ϫ R f or, dt rp ⎠ ⎝ rf ⎞ 3rf dv ⎛ ϭ ⎜1Ϫ ⎟ g Ϫ C v2 dt ⎝ rp D p D rp ⎠ terminal velocity, vt (dv/dt ϭ 0) ( ) D p rp Ϫ rf g 18m ⎛ A2 + A Ϫ A ⎞ ⎜ ⎟ ⎜ ⎟ 1.1 ⎝ ⎠ ⎛ D p ( rp Ϫ rf )g ⎞ ⎟ ⎜ rf ⎠ ⎝ m rf D p A1 ϭ 4.8 A2 ϭ 2.54 rp Ϫ rf rf unsteady motion time, t velocity, v ⎛ v Ϫ vt ⎞ t ϭ t g 1n ⎜ ⎝ v Ϫ vt ⎟ ⎠ t ϭ 24t g ∫ falling distance, S ⎡ ⎤ ⎛ t ⎞ vt t ϭ t g (vt Ϫ v0 ) ⎢exp ⎜Ϫ ⎟ Ϫ 1⎥ tg ⎠ ⎝ ⎢ ⎥ ⎣ ⎦ gD p vt t g ∫ Re p dt t S ϭ ∫ vdt Re p ϭ vD p rf m , tg ϭ rp D p 18m , v0: initial velocity, vt : terminal velocity Rep0, Rept: Rep at v0 and at vt respectively, CDt: drag coefficient at terminal velocity © 2006 by Taylor & Francis Group, LLC 1/ Re p Re p d Re p C Dt Re Ϫ C D Re t t t ϭ t / t g , Re p ϭ Re p / Re p p not simple because of Rep ϽϽ 104 at initiation of motion AEROSOLS Reynolds number and the basic equation expressing the particle motion in a gravity field The terminal settling velocity under gravity for small Reynolds number, v t , decreases with a decrease in particle size, as expressed by Eq (3.1) in Figure The distortion at the small size range of the solid line of vt is a result of the slip coefficient, Cc, which is size-dependent as shown in Eq (3.2) The slip coefficient Cc increases with a decrease in particle size suspended in a gaseous medium It also increases with a decrease in gas pressure p as shown in Figure The terminal settling velocities at other Reynolds numbers are shown in Table tg in Figure is the relaxation time and is given by Eq (3.6) It characterizes the time required for a particle to change its velocity when the external forces change When a particle is projected into a stationary fluid with a velocity vo , it will travel a finite distance before it stops Such a distance called the stop-distance and is given by v0tg Thus, tg is a measure of the inertial motion of a particle in a fluid Motion of a Small Diffusive Particle When a particle is small, Brownian motion occurs caused by random variations in the incessant bombardment of molecules against the particle As the result of Brownian motion, aerosol particles appear to diffuse in a manner analogous to the diffusion of gas molecules The Brownian diffusion coefficient of particles with diameter Dp is given by D ϭ Cc kT/3pmDp (15) where k is the Boltzmann constant (ϭ1.38 ϫ 10Ϫ16 erg/K) and T the temperature [K] The mean square displacement of a particles Ϫᎏ in a certain time interval t, and its absolute value ⌬ x2 Ϫ of the average displacement Ϫx , by the Brownian motion, are ⌬ given as follows ⌬x ϭ Dt ⌬x ϭ Dt p (16) The number concentration of small particles undergoing Brownian diffusion in a flow with velocity u can be determined by solving the following equation of convective diffusion, ѨN ϩ ٌ ⋅ u N ϭ D ٌ N Ϫ ٌ ⋅ vN Ѩt (17) v ϭ τg ∑ F mp (18) where N is the particle number concentration, D the Brownian diffusion coefficient, and v the particle velocity due to an external force F acting on the particle The average absolute value of Brownian displacement Ϫ in one second, Ϫx , is shown in Figure 3, which is obtained ⌬ © 2006 by Taylor & Francis Group, LLC 21 Ϫ from t ϭ 1s in Eq (3.4) The intersection of the curves Ϫx ⌬ and vt lies at around 0.5 mm at atmospheric pressure If one observes the settling velocity of such a small particle in a short time, it will be a resultant velocity caused by both gravitational settling and Brownian motion The local deposition rate of particles by Brownian diffusion onto a unit surface area, the deposition flux j (number of deposited particles per unit time and surface area), is given by j ϭ –DٌN ϩ vN ϩ uN (19) If the flow is turbulent, the value of the deposition flux of uncharged particles depends on the strength of the flow field, the Brownian diffusion coefficient, and gravitational sedimentation Particle Charging and Electrical Properties When a charged particle having np elementary charges is suspended in an electrical field of strength E, the electrical force Fe exerted on the particle is npeE, where e is the elementary charge unit (e ϭ 1.6 ϫ 10Ϫ19C) Introducing Fe into the right hand side of the equation of particle motion in Table and assuming that gravity and buoyant forces are negligible, the steady state velocity due to electrical force is found by equating drag and electrical forces, Fd ϭ Fe For the Stokes drag force (Fd ϭ 3pmveDp/Cc), the terminal electrophoretic velocity ve is given by ve ϭ npeECc /3pmDp (20) Be in Figure is the electrical mobility which is defined as the velocity of a charged particle in an electric field of unit strength Accordingly, the steady particle velocity in an electric field E is given by Ebe Since Be depends upon the number of elementary charges that a particle carries, np , as seen in Eq (3.7), np is required to determine Be np is predictable with aerosol particles in most cases, where particles are charged by diffusion of ions The charging of particles by gaseous ions depends on the two physical mechanisms of diffusion and field charging (Flagan and Seinfeld, 1988) Diffusion charging arises from thermal collisions between particles and ions Charging occurs also when ions drift along electric field lines and impinge upon the particle This charging process is referred to as field charging Diffusion charging is the predominant mechanism for particles smaller than about 0.2 mm in diameter In the size range of 0.2–2 mm diameter, particles are charged by both diffusion and field charging Charging is also classified into bipolar charging by bipolar ions and unipolar charging by unipolar ions of either sign The average number of charges on particles by both field and diffusion charging are shown in Figure When the number concentration of bipolar ions is sufficiently high with sufficient charging time, the particle charge attains an equilibrium state where the positive and negative charges in a unit volume are approximately equal Figure shows the charge distribution of particles at the equilibrium state 22 AEROSOLS In the special case of the initial stage of coagulation of a monodisperse aerosol having uniform diameter Dp, the particle number concentration N decreases according to 103 Field charging by unipolar ions E = 3ϫ105 V/m NSt = 1013 s/m dN dt ϭϪ 0.5 K N ϱ ϱ n␳ = ⌺ n␳ n(n␳) / ⌺ n(n␳) n␳= –ϱ n␳= –ϱ 102 ( K ϭ K Dp , Dp 101 where K(Dp, Dp) is the coagulation coefficient between particles of diameters Dp and Dp When the coagulation coefficient is not a function of time, the decrease in particle number concentration from N0 to N can be obtained from the integration of Eq (21) over a time period from to t, Diffusion charging by unipolar ions NSt=1013 s/m3 100 Equilibrium charge distribution by bipolar ions N ϭ N0/(1 ϩ 0.5K0N0t) 10–1 NS : ion number concentration : charging time 10–2 10–2 10–1 100 101 Dp (mm) Ѩn ( v , t ) np м5 Ϯ4 Ϯ3 –1 Ϯ2 Ϯ1 0 0.5 FIGURE Equilibrium charge distribution through bipolar ion charging The height of each section corresponds to the number concentration of particles containing the indicated charge Brownian Coagulation Coagulation of aerosols causes a continuous change in number concentration and size distribution of an aerosol with the total particle volume remaining constant Coagulation can be classified according to the type of force that causes collision Brownian coagulation (thermal coagulation) is a fundamental mechanism that is present whenever particles are present in a background gas © 2006 by Taylor & Francis Group, LLC Knudsen number Kn 20 0.5KB (Dp, Dp) (cm3 / s) Charge distribution Particle number concentration on 0.2 Dp (mm) uti rib 0.1 ist –1 ed siz Ϯ1 0 0.02 0.04 –1 np м4 +3 –3 +2 –2 +1 The first term on the right-hand side represents the rate of formation of particles of volume v due to coagulation, and the second term that rate of loss of particles of volume v by coagulation with all other particles The Brownian coagulation coefficient is a function of the Knudsen number Kn ϭ 2l/Dp, where l is the mean free path of the background gas Figure shows the values of the Brownian coagulation coefficient of mono-disperse particles, 0.5 K(Dp, Dp), as a function of particle diameter in cle np м2 +1 –1 +1 v K ( v , v Ϫ v ) n ( v t ) n ( v Ϫ v t ) dv ∫0 (23) r ti Pa +1 Ѩt ϭ Ϫn ( v , t ) ∫ K ( v , v ) n ( v t ) dv np м4 +3 –3 +2 –2 (22) The particle number concentration reduces to one-half its initial value at the time 2(K0N0)Ϫ1 This time can be considered as a characteristic time for coagulation In the case of coagulation of a polydisperse aerosol, the basic equation that describes the time-dependent change in the particle size distribution n(v, t), is FIGURE The average number of charges on particles by both field and diffusion charging np м3 +2 –2 (21) ) 10–9 10–10 0.001 ρ p= 10 54 0.5 0.1 0.2 0.5 1.0 2.5 5.00 10 0.01 0.1 Dp (mm) 1.0 FIGURE Brownian coagulation coefficient for coagulation of equal-sized particles in air at standard conditions as a function of particle density AEROSOLS air at atmospheric pressure and room temperature There exist distinct maxima in the coagulation coefficient in the size range from 0.01 mm to 0.01 mm depending on particle diameter For a particle of 0.4 mm diameter at a number concentration of 108 particles/cm3, the half-life for Brownian coagulation is about 14 s Kelvin Effect pd /pϱ in Figure indicates the ratio of the vapor pressure over a curved droplet surface to that over a flat surface of the same liquid The vapor pressure over a droplet surface increases with a decrease in droplet diameter This phenomenon is called the Kelvin effect and is given by Eq (3.8) If the saturation ratio of water vapor S surrounding a single isolated water droplet is larger than pd /pϱ, the droplet grows If S < pd /pϱ, that is, the surrounding saturation ratio lies below the curve pd /pϱ in Figure 3, the water droplet evaporates Thus the curve pd /pϱ in Figure indicates the stability relationship between the droplet diameter and the surrounding vapor pressure Phoretic Phenomena Phoretic phenomena refer to particle motion that occurs when there is a difference in the number of molecular collisions onto the particle surface between different sides of the particle Thermophoresis, photophoresis and diffusiophoresis are representative phoretic phenomena When a temperature gradient is established in a gas, the aerosol particles in that gas are driven from high to low temperature regions This effect is called thermophoresis The curve vth in Figure is an example (NaCl particles in air) of the thermophoretic velocity at a unit temperature gradient, that is, K/cm If the temperature gradient is 10 K/cm, vth becomes ten times higher than shown in the figure If a particle suspended in a gas is illuminated and nonuniformly heated due to light absorption, the rebound of gas molecules from the higher temperature regions of the particle give rise to a motion of the particle, which is called photophoresis and is recognized as a special case of thermophoresis The particle motion due to photophoresis depends on the particle size, shape, optical properties, intensity and wavelength of the light, and accurate prediction of the phenomenon is rather difficult Diffusiophoresis occurs in the presence of a gradient of vapor molecules The particle moves in the direction from higher to lower vapor molecule concentration OPTICAL PHENOMENA When a beam of light is directed at suspended particles, various optical phenomena such as absorption and scattering of the incident beam arise due to the difference in the refractive index between the particle and the medium Optical phenomena can be mainly characterized by a dimensionless parameter defined as the ratio of the particle diameter Dp to the wavelength of the incident light l, a ϭ pDp/l © 2006 by Taylor & Francis Group, LLC (24) 23 Light Scattering Light scattering is affected by the size, shape and refractive index of the particles and by the wavelength, intensity, polarization and scattering angle of the incident light The theory of light scattering for a uniform spherical particle is well established (Van de Hulst, 1957) The intensity of the scattered light in the direct u (angle between the directions of the incident and scattered beams) consists of vertically polarized and horizontally polarized components and is given as I ϭ I0 l2 (i1 ϩ i2 ) 8p r (25) where I0 denotes the intensity of the incident beam, l the wavelength and r the distance from the center of the particle, i1 and i2 indicate the intensities of the vertical and horizontal components, respectively, which are the functions of u, l, Dp and m The index of refraction m of a particle is given by the inverse of the ratio of the propagation speed of light in a vacuum k0 to that in the actual medium k1 as, m ϭ k1/k0 (26) and can be written in a simple form as follows: m ϭ n1 Ϫ in2 (27) The imaginary part n2 gives rise to absorption of light, and vanishes if the particle is nonconductive Light scattering phenomena are sometimes separated into the following three cases: (1) Rayleigh scattering (molecular scattering), where the value of a is smaller than about 2, (2) Mie scattering, where a is from to 10, and (3) geometrical optics (diffraction), where a is larger than about 10 In the Rayleigh scattering range, the scattered intensity is in proportion to the sixth power of particle size In the Mie scattering range, the scattered intensity increases with particle size at a rate that approaches the square of particle size as the particle reaches the geometrical optics range The amplitude of the oscillation in scattered intensity is large in the forward direction The scattered intensity greatly depends on the refractive index of the particles The curve denoted as pulse height in Figure illustrates a typical photomultiplier response of scattered light from a particle The intensity of scattered light is proportional to the sixth power of the particle diameter when particle size is smaller than the wavelength of the incident light (Rayleigh scattering range) The curve demonstrates the steep decrease in intensity of scattered light from a particle Light Extinction When a parallel beam of light is passed through a suspension, the intensity of light is decreased because of the scattering and absorption of light by particles If a parallel light 24 AEROSOLS beam of intensity I0 is applied to the suspension, the intensity I at a distance l into the medium is given by, I ϭ I0 exp(Ϫgl) (28) where g is called the extinction coefficient, ( ) g ϭ ∫ Cext n D p dD p (29) n(Dp) is the number distribution function of particles, and Cext is the cross sectional area of each particle For a spherical particle, Cext can be calculated by the Mie theory where the scattering angle is zero The value of Cext is also given by Cext ϭ Csca ϩ Cabs (30) where Csca is the cross sectional area for light scattering and Cabs the cross sectional area for light absorption The value of Csca can be calculated by integrating the scattered intensity I over the whole range of solid angles The total extinction coefficient g in the atmosphere can be expressed as the sum of contributions for aerosol particle scattering and absorption and gaseous molecular scattering and absorption Since the light extinction of visible rays by polluted gases is negligible under the usual atmospheric conditions and the refractive index of atmospheric conditions and the refractive index of atmospheric aerosol near the ground surface is (1.33 ∼ 1.55) Ϫ (0.001 ∼ 0.05)i (Lodge et al., 1981), the extinction of the visible rays depends on aerosol particle scattering rather than absorption Accordingly, under uniform particle concentrations, the extinction coefficient becomes a maximum for particles having diameter 0.5 mm for visible light VISIBILITY For aerosol consisting of 0.5 mm diameter particles (m ϭ 1.5) at a number concentration of 104 particles/cm3, the extinction coefficient g is 6.5 ϫ 10Ϫ5 cm and the daylight visual range is about 6.0 ϫ 104 cm (ϭ0.6 km) Since the extinction coefficient depends on the wavelength of light, refractive index, aerosol size and concentration, the visual range greatly depends on the aerosol properties and atmospheric conditions MEASUREMENT OF AEROSOLS Methods of sizing aerosol particles are generally based upon the dynamic and physical properties of particles suspended in a gas (see Table 4) Optical Methods The light-scattering properties of an individual particle are a function of its size, shape and refractive index The intensity of scattered light is a function of the scattering angle, the intensity and wavelength of the incident light, in addition to the above properties of an individual particle An example of the particle size-intensity response is illustrated in Figure Many different optical particle sizing devices have been developed based on the Mie theory which describes the relation among the above factors The principle of one of the typical devices is shown in Figure The particle size measured by this method is, in most cases, an optical equivalent diameter which is referred to a calibration particle such as one of polystyrene latex of known size Unless the particles being measured are spheres of known refractive index, their real diameters cannot be evaluated from the optical equivalent diameters measured Several light-scattering particle counters are commercially available Inertial Methods (Impactor) The visible distance that can be distinguished in the atmosphere is considerably shortened by the light scattering and light extinction due to the interaction of visible light with the various suspended particles and gas molecules To evaluate the visibility quantitatively, the visual range, which is defined as the maximum distance at which the object is just distinguishable from the background, is usually introduced This visual range is related to the intensity of the contrast C for an isolated object surrounded by a uniform and extensive background The brightness can be obtained by integrating Eq (28) over the distance from the object to the point of observation If the minimum contrast required to just distinguish an object from its background is denoted by C*, the visual range Lv for a black object can be given as Lv ϭ Ϫ(1/g)ln(ϪC*) © 2006 by Taylor & Francis Group, LLC Stk ϭ (32) rpCc D p u0 18m (W ) ϭt u0 W (33) where (31) where g is the extinction coefficient Introduction of the value of Ϫ0.02 for C* gives the well known Koschmieder equation, Lv ϭ 3.912/g The operating principle of an impactor is illustrated in Figure The particle trajectory which may or may not collide with the impaction surface can be calculated from solving the equation of motion of a particle in the impactor flow field Marple’s results obtained for round jets are illustrated in Figure (Marple and Liu, 1974), where the collection efficiency at the impaction surface is expressed in terms of the Stokes number, Stk, defined as, tϭ Cc ϭ ϩ 2.514 rp D p Cc (34) 18m Dp ⎞ ⎛ l l ϩ 0.80 exp ⎜Ϫ0.55 ⎟ Dp Dp l⎠ ⎝ (35) AEROSOLS 25 TABLE Methods of aerosol particle size analysis Quantity to be measured Method or instrument Media Detection Approx size range Concentration Principle gas vacuum gas number number – Ͼ0.5 mm Ͼ0.001 Ͼ0.01 liquid gas – Ͼ0.1 liquid gas number number Ͼ0.3 Ͼ1 low low Stokes equation liquid liquid liquid gas mass mass area mass number mass Ͼ1 Ͼ1 Ͼ0.05 Ͼ0.05–1 high high high high–low Stokes equation Stokes equation Stokes equation Stokes equation gas mass number Ͼ0.5 high–low relaxation time gas number Ͼ0.05 high–low in low pressure gas mass number 0.002–0.5 high–low Brownian motion liquid gas number number (current) 0.02–1 0.005–0.1 high high–low gas number (current) 0.002–0.5 high–low light scattering differential type (DMA) gas liquid number >0.1 low Mie theory light diffraction gas liquid number high–low length absorbed gas microscope electron microscope adsorption method, BET area permeability volume motion in fluid permeability method electric resist gravitational Coulter Counter (individual) ultramicroscope (differential conc.) (cumulative conc.) (differential conc.) spiral centrifuge, conifuge impactor, acceleration method impactor, aerosol beam method diffusion battery and CNC photon correlation integral type (EAA) settling velocity centrifugal settling velocity inertial collection inertial motion diffusion loss Brownian motion BET KozenyCarman’s equation electric mobility © 2006 by Taylor & Francis Group, LLC AEROSOL PHOTOMULTIPLIER INCIDENT BEAM θ PARTICLE DIAMETER LIGHT TRAP PULSE VOLTAGE PULSE VOLTAGE SENSING VOLUME FREQUENCY rp is the particle density, m the viscosity and l is the mean free path of the gas The remaining quantities are defined in Figure The value of the Stokes number at the 50 percent collection efficiency for a given impactor geometry and operating condition can be found from the figure, and it follows that the cut-off size, the size at 50 percent collection efficiency, is determined If impactors having different cut-off sizes are appropriately connected in series, the resulting device is called a cascade impactor, and the size distribution of aerosol particles can be obtained by weighing the collected particles on each impactor stage In order to obtain an accurate particle size distribution from a cascade impactor, the following must be taken into account: 1) data reduction considering cross sensitivity between the neighboring stages, 2) rebounding on the impaction surfaces, and 3) particle deposition inside the device Various types of impactors include those using multiple jets or rectangular jets for high flow rate, those operating under low pressure (Hering et al., 1979) or having microjets for particles smaller than about 0.3 mm and those having a virtual impaction surface, from which aerosols are sampled, for sampling the classified aerosol particles (Masuda et al., 1979) PARTICLE NUMBER intensity of scattered light TIME FIGURE Measurement of aerosol particle size by an optical method (Other Inertial Methods) Other inertial methods exist for particles larger than 0.5 mm, which include the particle acceleration method, multi-cyclone (Smith et al., 1979), and pulsation method (Mazumder et al., 1979) Figure illustrates the particle acceleration method where the velocity difference between 26 AEROSOLS PHOTOMULTIPLIER W LARGE PARTICLE NOZZLE CHAMBER PRESSURE GAUGE T AEROSOL SMALL PARTICLE PUMP BEAM SPLITTER CLEAN AIR S STREAMLINE OF GAS MEAN GAS FLOW U0 SIGNAL PROCESSING He–Ne LASER FIGURE Measurement of aerosol particle size by laserdoppler velocimetry IMPACTION SURFACE COLLECTION EFFICIENCY (%) 100 AEROSOL 80 25000 3000 500 10 S/W= 60 0.25 0.5 40 5.0 OL S RO AIR AE EAN CL S/W=0.5, T/W=1 Re=3000, T/W=2 20 0.3 DISTRIBUTOR Re = 0.4 0.5 0.6 0.7 0.8 N O TI TA O R 0.9 CLEAN AIR PLASTIC FILM DISTRIBUTOR Stk FIGURE Principle of operation of an impactor Collection efficiency of one stage of an impactor as a function of Stokes number, Stk, Reynolds number, Re, and geometric ratios a particle and air at the outlet of a converging nozzle is detected (Wilson and Liu, 1980) Sedimentation Method By observing the terminal settling velocities of particles it is possible to infer their size This method is useful if a TV camera and He–Ne gas laser for illumination are used for the observation of particle movement A method of this type has been developed where a very shallow cell and a TV system are used (Yoshida et al., 1975) Centrifuging Method Particle size can be determined by collecting particles in a centrifugal flow field Several different types of centrifugal © 2006 by Taylor & Francis Group, LLC EXHAUST FIGURE 10 Spiral centrifuge for particle size measurements chambers, of conical, spiral and cylindrical shapes, have been developed for aerosol size measurement One such system is illustrated in Figure 10 (Stöber, 1976) Particle shape and chemical composition as a function of size can be analyzed in such devices Electrical Mobility Analyzers The velocity of a charged spherical particle in an electric field, ve, is given by Eq (20) The velocity of a particle having unit charge (np ϭ 1) in an electric field of V/cm is illustrated in Figure The principle of electrical mobility analyzers is based upon the relation expressed by Eq (20) Particles of different sizes are separated due to their different electrical mobilities AEROSOLS DC H.V AEROSOL AEROSOL UNIPOLAR IONS RADIOACTIVE SOURCE SCREEN BIPOLAR IONS a) Corona discharge (unipolar ions) b) Radioactive source (bipolar ions) DC H.V Qc AEROSOL CLEAN AIR Qa Qc AEROSOL CLEAN AIR Qa (a) Charging section for particles DC H.V r1 L L r2 UNCHARGED PARTICLE EXHAUST, Qc TO DETECTOR Qa + Qc TO DETECTOR a) Integration type b) Differential type (b) Main section AEROSOL AEROSOL FILTER CNC ELECTROMETER b) CNC or Electrometer a) Electrometer ELECTRICAL CURRENT or PARTICLE NUMBER ELECTRICAL CURRENT or PARTICLE NUMBER (c) Detection of charged particles APPLIED VOLTAGE a) Integration type APPLIED VOLTAGE b) Differential type (d) Response curve FIGURE 11 Two types of electrical mobility analyzers for determining aerosol size Charging, classification, detection and response are shown for both types of analyzers © 2006 by Taylor & Francis Group, LLC 27 28 AEROSOLS Two different types of electrical mobility analyzers shown in Figure 11 have been widely used (Whitby, 1976) On the left hand side in the figure is an integral type, which is commercially available (EAA: Electrical Aerosol Analyzer) That on the right hand side is a differential type, which is also commercially available (DMA: Differential Mobility Analyzer) The critical electrical mobility Bec at which a particle can reach the lower end of the center rod at a given operating condition is given, respectively, for the EAA and DMA as Bec ϭ Bec ϭ (Qa ϩ Qc ) ln ⎛ r1 ⎞ 2pLV ⎜r ⎟ ⎝ 2⎠ ⎛r ⎞ ⎛r ⎞ Q Qc ln ⎜ ⎟ , ⌬Be ϭ a ln ⎜ ⎟ pLV ⎝ r2 ⎠ 2pLV ⎝ r2 ⎠ (36) (37) Bec can be changed by changing the electric voltage applied to the center rod A set of data of the particle number concentration or current at every Bec can be converted into a size distribution by data reduction where the number distribution of elementary charges at a given particle size is taken into account Electrical mobility analyzers are advantageous for smaller particles because ve in Eq (20) increases with the decrease in particle size The differential mobility analyzer has been increasingly utilized as a sizing instrument and a monodisperse aerosol generator of particles smaller than mm diameter (Kousaka et al., 1985) Diffusion Batteries The diffusion coefficient of a particle D is given by Eq (15) As shown in Figure 3, D increases with a decrease in particle size This suggests that the deposition loss of particles onto the surface of a tube through which the aerosol is flowing increases as the particle size decreases The penetration (ϭ1–fractional loss by deposition) hp for a laminar pipe flow is given as (Fuchs, 1964), h p ϭ 0.8191exp (Ϫ3.657β ) ϩ 0.00975exp (Ϫ22.3β ) ϩ 0.0325exp (Ϫ57β ) , b ϭ pDL Q Ն 0.0312 where L is the pipe length and Q is the flow rate A diffusion battery consists of a number of cylindrical tubes, rectangular ducts or a series of screens through which the gas stream containing the particles is caused to flow Measurement of the penetration of particles out the end of the tubes under a number of flow rates or at selected points along the distance from the battery inlet allows one to obtain the particle size distribution of a polydisperse aerosol The measurement of particle number concentrations to obtain penetration is usually carried out with a condensation nucleus counter (CNC), which detects particles with diameters down to about 0.003 mm REFERENCES Flagan, R.C., Seinfeld, J.H (1988) Fundamentals of Air Pollution Engineering Prentice Hall, Englewood Cliffs, NJ Fuchs, N.A (1964) The Mechanics of Aerosols Pergamon Press, New York, 204–205 Hering, S.V., Friedlander, S.K., Collins, J.J., Richards, L.W (1979) Design and Evaluation of a New Low-Pressure Impactor Environmental Science & Technology, 13, 184–188 Kousaka, Y., Okuyama, K., Adachi, M (1985) Determination of Particle Size Distribution of Ultra-Fine Aerosols Using a Differential Mobility Analyzer Aerosol Sci Technology, 4, 209–225 Lodge, J.P., Waggoner, A.P., Klodt, D.T., Grain, C.N (1981) Non-Health Effects of Particulate Matter Atmospheric Environment, 15, 431–482 Marple, V.A., Liu, B.Y.H (1974) Characteristics of Laminar Jet Impactors Environmental Science & Technology, 8, 648–654 Masuda, H., Hochrainer, D and Stöber, W (1979) An Improved Virtual Impactor for Particle Classification and Generation of Test Aerosols with Narrow Size Distributions J Aerosol Sci., 10, 275–287 Mazumder, M.K., Ware, R.E., Wilson, J.D., Renninger, R.G., Hiller, F.C., McLeod, P.C., Raible, R.W and Testerman, M.K (1979) SPART analyzer: Its application to aerodynamic size distribution measurement J Aerosol Sci., 10, 561–569 Seinfeld, J.H (1986) Atmospheric Chemistry and Physics of Air Pollution Wiley, New York Smith, W.B., Wilson, R.R and Harris, D.B (1979) A Five-Stage Cyclone System for In Situ Sampling Environ Sci Technology, 13, 1387–1392 Stöber, W (1976) Design, Performance and Application of Spiral Duct Aerosol Centrifuges, in “Fine Particles”, edited by Liu, B.Y.H., Academic Press, New York, 351–397 Van de Hulst, H.C (1957) Light Scattering by Small Particles Wiley, New York Whitby, K.T (1976) Electrical Measurement of Aerosols, in “Fine Particles” edited by Liu, B.Y.H., Academic Press, New York, 581–624 Wilson, J.C and Liu, B.Y.H (1980) Aerodynamic Particle Size Measurement by Laser-Doppler Velocimetry J Aersol Sci., 11, 139–150 Yoshida, T., Kousaka, Y., Okuyama, K (1975) A New Technique of Particle Size Analysis of Aerosols and Fine Powders Using an Ultramicroscope Ind Eng Chem Fund., 14, 47–51 (38) h p ϭ Ϫ 2.56 b2 ϩ 1.2 b ϩ 0.177 b4 / , b Ͻ 0.0312 (39) KIKUO OKUYAMA YASUO KOUSAKA JOHN H SEINFELD University of Osaka Prefecture and California Institute of Technology AGRICULTURAL CHEMICALS: see PESTICIDES © 2006 by Taylor & Francis Group, LLC ... The first term on the right-hand side represents the rate of formation of particles of volume v due to coagulation, and the second term that rate of loss of particles of volume v by coagulation... of operation of an impactor Collection efficiency of one stage of an impactor as a function of Stokes number, Stk, Reynolds number, Re, and geometric ratios a particle and air at the outlet of. .. Design and Evaluation of a New Low-Pressure Impactor Environmental Science & Technology, 13, 184–188 Kousaka, Y., Okuyama, K., Adachi, M (1985) Determination of Particle Size Distribution of Ultra-Fine