Dust Deposition - Mineral Dust: A Key Player in the Earth System - page 183

dust particles to act more efficiently as cloud condensation nuclei (Fan et al. 2004 ).
In-cloud processes, especially for dust particles, remain poorly understood and their
representation in models is very crude (see Chap. 12 ) . In models, dust particles
are represented either as purely hydrophobic aerosols, and no in-cloud scavenging
is considered (Genthon 1992 ; Tegen and Fung 1994 ) or in-cloud scavenging is
considered and the scavenging efficiency of dust is assumed to be that of sulfate
aerosols (Chin et al. 2000 ; Zender et al. 2003 ; Grini et al. 2005 ).
The below-cloud scavenging size dependency is better understood (Dana and
Hales 1976 ; Slinn 1984 ; Garcia Nieto et al. 1994 ). Following Seinfeld and Pandis
( 1998 ), the removal of particles by washout can be computed as

C i .t C 1/ D C i .t/ ƒ i C i .t/ t (8.10)

where i refers to a given particle diameter D p and C i is the mass or number
concentration of particles, t the time step, and ƒ i the scavenging coefficient (s 1 ).
The scavenging coefficient is linked to the collision efficiency by

ƒ i D .3=2/ E i .D d / .p 0 =D d / (8.11)

with E the collision efficiency; p 0 the rainfall intensity, i.e., the amount of rain that
falls over time (cm s 1 ); and D d , the droplet diameter (cm).
E is the key parameter since it represents the capacity of falling droplets to catch
aerosols. It is computed as the ratio between the number of collisions between
droplets and particles and the number of particles in the column swept by a falling
droplet. Collision efficiency equal to 1 means that all particles of an air column
swept by one droplet are removed by this droplet. Thus, E is the sum of the
collision efficiencies due to Brownian diffusion, interception, and inertial impaction
as explained in the following.

Brownian Diffusion

The collision efficiency due to Brownian diffusion results from the thermal motion
of particles and thus is primarily important for submicron particles. Slinn ( 1984 )
proposes the following expression to describe the collision efficiency due to
Brownian diffusion:

Re d Sc h 1

1 = 2 Sc 1 = 2 i 4 1 = 2 Sc 1 = 3

E B D C 0:4Re d C 0:16Re d (8.12)

In this expression Re d and Sc refer to different objects: Re d is the Reynolds
number of the droplet while Sc is the Schmidt number of the aerosol.