Geoscience Reference
In-Depth Information
For a given particle, the relative importance of each of these physical pro-
cesses depends on how close the particle approaches the surface. Generally two
atmospheric layers are distinguished to describe dry deposition processes: a first
layer close to the surface, with a thickness on the order of centimeters, where
Brownian diffusion and gravitational settling are the main deposition processes,
and a second layer, above the previous one, called the constant flux layer, where
turbulent processes and gravitational settling are dominant (e.g., Slinn and Slinn
1980 ;Giorgi 1986 , 1988 ).
Conceptually, diffusive (turbulent and Brownian) and gravitational processes
are considered to act in parallel while the two layers operate in series. On a
practical point of view, the derivation of such a formulation requires to neglect
the influence of gravity in transport. Thus, the steady-state gravitational settling
velocity of particles (also called terminal velocity, V s ) is added a posteriori to the
calculated deposition rate from diffusive processes. The dry deposition of a particle
with a given aerodynamic diameter is then considered as a set of associated pseudo
resistances (Wesely 1989 ): one is the aerodynamic resistance, R a (s m 1 ), operating
in the constant flux layer, and the other, the quasi-laminar resistance, R b (s m 1 ),
operating in the layer closest to the surface. The dry deposition velocity of the
system is the inverse of the total equivalent resistance:
R a R b V s / 1
V d D
V s C
.R a C
R b C
(8.2)
Gravitational Settling Velocity
V s can be expressed according to the modified Stokes law:
D p p gC c
18 air
V s D
(8.3)
with D p the particle diameter (if particles are assumed spherical, the geometric
diameter equals the aerodynamic diameter), p the particle density (generally taken
as 2.6 g m 3
for dust particles), air the dynamic viscosity of air (1.789 10 5
Pa s
at 288 K, 1013.25 hPa), and g the gravitational acceleration (9.81 m s 2 ).
For small particles (i.e., with sizes comparable to that of the mean free path of
the molecules), the drag force onto settling particles must be corrected (reduced)
since the considered fluid becomes more a discontinuous medium than a “dense”
continuum. This is the purpose of the Cunningham (slip) correction factor, C c .
This correction factor, which can affect the deposition velocity for mineral particles
smaller than about 1 m in diameter by almost 10 %, is expressed as (Seinfeld and
Pandis 1998 )
1:257
0:4 exp
1:1D p
2
2
D p
C c D
1
C
C
(8.4)
with , the mean free path of gas molecules in air (6.6 10 6 cm).
 
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