Abstract
The atmosphere interacts with the Earth’s surface. Thus, air pollutants may be transferred toward surfaces and emitted (or reemitted) from surfaces toward the atmosphere. Atmospheric deposition processes are important because (1) they impact the atmospheric lifetime of air pollutants and (2) they may lead to the contamination of other environmental media. Processes of emission and reemission may contribute significantly to the atmospheric budget of some pollutants and it is, therefore, essential to take those into account. This chapter describes the mechanisms that lead to atmospheric deposition of pollutants, either via dry processes (dry deposition) or via precipitation scavenging (wet deposition). Emissions of particles by the wind (aeolian emissions), waves, and on-road traffic are also described.
The atmosphere interacts with the Earth’s surface. Thus, air pollutants may be transferred toward surfaces and emitted (or reemitted) from surfaces toward the atmosphere. Atmospheric deposition processes are important because (1) they impact the atmospheric lifetime of air pollutants and (2) they may lead to the contamination of other environmental media. Processes of emission and reemission may contribute significantly to the atmospheric budget of some pollutants and it is, therefore, essential to take those into account. This chapter describes the mechanisms that lead to atmospheric deposition of pollutants, either via dry processes (dry deposition) or via precipitation scavenging (wet deposition). Emissions of particles by the wind (aeolian emissions), waves, and on-road traffic are also described.
11.1 Dry Deposition
Atmospheric pollutants may deposit on buildings, vegetation, soil, and surface waters via ”dry” processes, i.e., processes that do not depend on precipitation. The fundamental processes that lead to dry deposition are sedimentation, impacts by inertia or interception, and diffusion (Wesely and Hicks, 2000). The first cases pertain only to particles, whereas diffusion concerns both particles and gases. The concept of dry deposition velocity was first proposed by Gregory (1945). Although sedimentation was the only process mentioned explicitly in his analysis, he noted that atmospheric conditions (turbulence intensity) and the surface roughness affected the dry deposition process.
11.1.1 Sedimentation and Fall Velocity
Sedimentation corresponds to the effect of the Earth’s gravity on particles. All particles, regardless of their size, undergo sedimentation. However, only coarse particles (i.e., those particles with a diameter greater than about 2.5 μm) have a sedimentation velocity that is large enough for this process to become commensurate with the process of impact by inertia. Thus, for particles with a diameter of a few tens of microns, sedimentation is the dominant process. For example, a spherical particle with a diameter of 10 μm and a density of 1 g cm−3 has a sedimentation velocity of about 0.3 cm s−1. This sedimentation velocity corresponds to the terminal fall velocity of the particle, which results from an equilibrium between the gravitational force and the frictional force. The frictional force is due to interactions between the particle and the surrounding air. The equilibrium between these two forces is represented mathematically by Stokes’ law.
When the Reynolds number is very small (Re ≪ 1), the force, FoSt, exerted by the fluid (here the air) on a moving particle or droplet may be written as follows:
(11.1) where μv,a is the dynamic viscosity of the air (kg m−1 s−1), dp is the diameter of the particle (or droplet) (m), vs is the particle sedimentation velocity (m s−1), and cc is the Cunningham correction factor, which is a function of the particle size. The Cunningham factor is a correction that applies to fine and ultrafine particles (it is equal to 1.01 for a particle with a diameter dp = 10 μm, 1.16 for dp = 1 μm, 2.8 for dp = 0.1 μm, and 22 for dp = 0.01 μm). This formula applies to ultrafine and fine particles and to some coarse particles, because for particles with a diameter less than 10 μm, Re < 2.5 × 10−3.
When the Reynolds number is greater (Re ≫ 1), the following expression applies:
(11.2) where cd is the drag factor (or drag coefficient), ρa is the air density, and the other terms are the same as in the previous formula. The drag coefficient is a function of Re and, therefore, depends on the particle size since: Re = ρa dp vs /μv,a. This formula applies to very large particles and droplets (dp > 50 μm), for example raindrops and some dust particles.
The acceleration of a particle (or droplet) moving in the atmosphere is governed by gravity, the buoyant force due to displacement of the fluid (Archimedes’ principle), and the air resistance:
(11.3) The mass of the particle or droplet (mp) is about 1,000 times greater than that of the displaced air (mair) and the corresponding buoyant force (mair g) may, therefore, be neglected. The particle or droplet reaches its terminal fall velocity (dvs/dt = 0) when the friction due to the air resistance compensates gravity:
Thus, the terminal sedimentation velocity (vsf) may be calculated for the two regimes defined in Equations 11.1 and 11.2 for Stokes’ law. If Re ≪ 1 (particles and fog droplets):
(11.5) The particle mass may be expressed as a function of its diameter and density:
(11.6) Then, the terminal fall velocity of the particle as a function of its diameter and density is as follows:
(11.7) For an atmospheric particle or fog droplet, the final fall velocity is proportional to the square of its diameter (however, the Cunningham correction modifies this simple relationship); therefore, it decreases as its diameter decreases.
If Re ≫ 1 (large dust particles and raindrops):
(11.8) where νv,a is the kinematic viscosity of the air. Therefore, the terminal fall velocity must be calculated by iteration since it depends on the drag coefficient, which depends via the Reynolds number on the fall velocity. Expressing the mass of a particle or drop as a function of its density and diameter:
(11.9) Thus, the terminal fall velocity is proportional to the square root of the particle diameter (with a correction due to the drag coefficient). For raindrops, the simplified Kessler formula may be used (Kessler, 1969):
(11.10) where vsf is the raindrop fall velocity (m s−1) and dr is the raindrop diameter (m). The difference between these two equations is <10 % for a raindrop of 1 mm: 4.5 m s−1 with Equation 11.9 and 4.1 m s−1 with Equation 11.10. These formulas tend to overestimate the terminal fall velocity of drops greater than 2.5 mm. More detailed parameterizations are available that better represent the fall velocity of raindrops over a wide range of sizes (see the review by Duhanyan and Roustan, 2011). Note that raindrops rarely have diameters greater than 6 mm, because they tend to break into several smaller drops when they get bigger.
11.1.2 Interception and Inertia
Deposition by interception and inertia concerns atmospheric particles that may interact with surfaces via these processes and then deposit. When the air flow must go around an obstacle, particles present in the air may get into contact with the obstacle either because of their size or mass. The size of a particle is much greater than that of an air molecule and the particle may, therefore, interact with the obstacle because of its size. This interception process is roughly proportional to the cross-section of the particle, i.e., (π dp2). On the other hand, the mass of a particle leads to inertia when the air flow changes direction to go around an obstacle. This inertia is roughly proportional to the particle mass, i.e., proportional to its volume, (π dp3/ 6). Therefore, these two processes are negligible for ultrafine particles and are only relevant for fine particles (0.1 μm < dp < 2.5 μm) and coarse particles (dp > 2.5 μm).
These processes of impact by inertia and interception are also essential for technologies of particulate matter emission control (see Chapter 2). For example, cyclones use inertia and baghouses use interception and inertia to capture particles. Also, atmospheric particles with a diameter greater than a few microns (μm) are captured efficiently by these processes in the nose and upper airways and, therefore, are not transported deeply into the lungs, unlike fine and ultrafine particles (see Chapter 12).
11.1.3 Diffusion
The diffusion of a gas molecule or particle in the atmosphere toward a surface may be considered to include several steps (Wesely, 1989). For all pollutants (gases and particles), two successive steps bring the pollutant in contact with the surface: (1) turbulent mass transfer in the atmosphere toward the surface and (2) diffusive mass transfer within a very thin layer (on the order of a millimeter) in direct contact with the surface. This latter layer is not affected by atmospheric turbulence and is, therefore, considered to be in a quasi-laminar regime. Mass transfer within that layer occurs by molecular diffusion for gases and via brownian diffusion for particles. In addition, the processes of impact by inertia and interception for particles take place within that layer. Typically, one considers that particles deposit on a surface once they get into contact with that surface (a bouncing coefficient may be used in some cases to account for the fact that some particles may bounce and, therefore, will not remain on the surface). For gases, a third step is included. It determines the deposition rate by absorption into the surface (for example, dissolution into a dew layer), adsorption onto the surface (for example, adsorption onto activated carbon) or chemical reaction at the surface (for example, an acid gas may react with an alkaline surface). A combination of absorption or adsorption followed by chemical reaction may also occur. For particles, inertia and interception processes are important in the case of deposition on surfaces with complex geometries, such as vegetation, for particles with a diameter between about 1 and 10 μm.
This series of processes represents the overall dry deposition phenomenon by diffusion and it may be seen as a series of resistances to mass transfer, by analogy with an electrical circuit.
Aerodynamic Resistance
The first step is associated with an aerodynamic resistance and pertains to the turbulent mass transfer of the pollutant (gas molecule or particle) in the atmosphere toward a layer near the surface. Therefore, it is governed by the vertical transport processes, i.e., vertical atmospheric dispersion. This transfer resistance is large when the atmosphere is stable. It is small when the atmosphere is unstable; then, turbulence readily brings pollutants into contact with the surface via vertical mixing.
The vertical mass flux, Fd, due to this turbulent process may be calculated using a first-order closure of atmospheric turbulence. A K type turbulence representation is generally used (the negative sign is used here because the flux corresponds to a sink for the atmospheric compartment):
(11.11) The vertical dispersion coefficient may be expressed as follows (see Chapter 6):
where κ is the von Kármán constant (κ = 0.4) and u* is the friction velocity. This expression is valid for a neutral atmosphere. If the atmosphere is stable or unstable, the vertical profile of the concentrations in the surface layer differs and this equation must be modified using the parameter ΦH(z). The corresponding parameter ΦM(z) for momentum is sometimes used; however, mass transfer is better associated with heat transfer (both are scalars) than with momentum transfer (a vector). Therefore, the temperature profile seems more appropriate for mass transfer than the vertical profile of the horizontal wind speed (see Chapter 4):
(11.13) 
(11.14) Integrating between the reference height (located within the surface layer), zr, which corresponds to the height of the reference concentration, C, and the bottom of this turbulent layer (taken to be by definition the roughness length, z0):
(11.15) Thus:
(11.16) For a neutral atmosphere (ΦH(z) = 1):
(11.17) The vertical flux may be expressed as a function of the aerodynamic resistance, ra:
(11.18) Thus, ra may be written as a function of the variables that govern the turbulent mass transfer:
(11.19) In the case of a neutral atmosphere, ΦH(z) = 1, therefore:
(11.20) In the case of stable or unstable atmospheres, the solution is more complicated, because one must integrate using the profile of ΦH(z). The profile given in Equation (4.68) is used for a stable atmosphere and the integration leads to the following solution for ra:
(11.21) where LMO is the Monin-Obukhov length (see Chapter 4). The profile given in Equation (4.69) is used for an unstable atmosphere and the integration leads to the following solution:
(11.22) These formulations imply several assumptions and they apply in theory only within the surface layer, i.e., the layer where the vertical fluxes for momentum, heat, and mass are constant with height. This surface layer ranges from the surface up to a height that varies between a few tens of meters to about 100 m (~10 % of the planetary boundary layer, see Chapter 4).
Resistance Due to Diffusion and Impact Processes
The second step corresponds to a resistance by diffusion in a very thin layer in contact with the surface. This layer (with a thickness on the order of 1 mm) is characterized by a quasi-laminar flow. Therefore, resistance is mostly due to diffusion and is a function of the molecular diffusion coefficient for gases and brownian diffusion coefficient for particles. Molecular diffusion coefficients depend on the physico-chemical properties of the molecule; however, they vary within a rather limited range of values. For example, the diffusion coefficient of carbon monoxide (CO) in the air is 0.12 cm2 s−1, that of ozone (O3) is 0.14 cm2 s−1, and that of nitrogen dioxide (NO2) is also 0.14 cm2 s−1.
The resistance to diffusion in the quasi-laminar layer, rb, is defined as follows:
(11.23) where u* is the friction velocity (u*2=−u‘w‘¯
) and Sc is the Schmidt number, which characterizes the relative importance of advection and diffusion (it corresponds to the Prandtl number, which is used in heat transfer):
(11.24) where νv,a is the kinematic viscosity of the air (m2 s−1; the kinematic viscosity is related to the dynamic viscosity via the fluid density: νv,a = μv,a / ρa) and Dm is the molecular diffusion coefficient of the gaseous pollutant in the air (m2 s−1).
For a particle, mass transfer within the quasi-laminar layer depends on brownian diffusion. However, inertia and interception processes also take place within that layer and they are, therefore, treated jointly with diffusion. The following empirical formula may be used (Zhang et al., 2001):
(11.25) where EB, EIM, and EIN are collection efficiencies of brownian diffusion, impact by inertia, and interception, respectively, and fp is a correction factor representing the fraction of particles that stick to the surface after contact:
(11.26) where Sc is defined as in Equation 11.24 for gaseous molecules, but using the brownian diffusion coefficient, Dp, instead of the molecular diffusion coefficient, St is the Stokes number, dp is the particle diameter, df is a characteristic dimension of the surface (vegetation leaf, filter …), and α and β are empirical parameters that depend on the surface type. Zhang et al. (2001) proposed some values for these parameters depending on surface type: α ranges between 0.6 and 100, β = 2, and df ranges between 2 and 10 mm. Here, the brownian diffusion term, EB, has been modified to be consistent with (1) the formulation of the molecular diffusion for gaseous pollutants and (2) the experimental data of Möller and Schumann (1970). The Stokes number is a characteristic of both the particle and the flow; the smaller the particle, the smaller St. It is defined differently for vegetation-covered surfaces and smooth surfaces:
(11.27) where vs is the particle sedimentation velocity, u* is the friction velocity, df is the characteristic length of the surface, and νv,a is the kinematic viscosity of the air.
The brownian diffusion coefficient of a particle decreases with increasing particle size, whereas the mass transfer velocities for inertia, interception, and sedimentation increase with increasing particle size. As a result, ultrafine particles (i.e., those with a diameter less than 0.1 μm) and coarse particles (i.e., those with a diameter greater than 2.5 μm) have lower resistances than fine particles (i.e., those with a diameter less than 2.5 μm but greater than 0.1 μm), because ultrafine particles are rapidly deposited via brownian diffusion and coarse particles are deposited effectively via sedimentation, inertia, and interception. Figure 11.1 shows the contributions of these different deposition processes as a function of particle diameter. Conditions used in this figure correspond to deposition over grassland under neutral atmospheric conditions with a friction velocity of 0.5 m s−1, a roughness length of 0.01 m, a particle density of 1.5 g cm−3, and a characteristic length of 2 mm for grass. Under these conditions, dry deposition via interception is negligible compared to the other processes. The aerodynamic resistance limit is indicated. Note that sedimentation is not affected by the aerodynamic resistance, whereas all other processes are. Therefore, the process of deposition via inertia, which is commensurate with sedimentation up to a particle diameter of about 10 μm, becomes capped for larger particles.
Figure 11.1. Dry deposition velocities of particles as a function of diameter (u* = 0.5 m s−1, z0 = 0.01 m, ρp = 1.5 g cm−3, df = 2 mm).
Surface Resistance
For gaseous pollutants, a third resistance is taken into account. It corresponds to the transfer of the molecule from the air to the surface and, accordingly, it is called the surface resistance, rc. It may be a complicated formula, for example, in the case of deposition of gaseous pollutants on vegetation. For particles, this surface resistance is incorporated implicitly into the diffusion resistance via the correction factor, fp.
Total Resistance
The total resistance to atmospheric deposition is simply the sum of these two or three resistances. It is expressed in s m−1. The deposition velocity is the inverse of the resistance and it is expressed in m s−1. The vertical mass flux is constant in the surface layer and for gaseous pollutants the following relationships may be written (for particles, the last equation is not taken into account):
(11.28) where the subscript of Δ represents the atmospheric layer of interest for the corresponding resistance. The total resistance is obtained from the overall concentration difference:
(11.29) Thus, for the overall concentration difference: