Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 336

This is called “below-cloud scavenging.” The rate of increase in concentration in the
droplet is given by the mass transfer to the drop (Seinfeld and Pandis, 2006):

D P
6

d [A] aq
d t

= π D P K mt [A] g , π

d [A] aq
d t

6
D P K mt [A] g ,
where we assume that the pollutant is irreversibly absorbed into the drop and the
pollutant is nonreactive. For a falling drop at its terminal velocity, U T , we can write
d [A] aq
d t

=

d [A] aq
d z

= U T

since U T = d z/ d t . Thus,

d [A] aq
d z =

6
D P

K mt
U T

[A] g .

If we assume that [A] g is constant (homogeneous atmosphere), we can obtain the
following equation upon integration:

K mt
U T [A] g z .
The mass scavenged ( W) by a droplet of volume π D P / 6 will be given by ([A] aq -[A] aq )
times the droplet volume

6
D P

[A] aq = [A] aq +

W = π D P K mt
U T

[A] g z .

If the rainfall intensity is R I (mm/h), the number of drops falling per unit area per hour
will be

N d m 2 / h

K mt [A] g
U T D P z .
Hence, the rate of removal of the pollutant by rain (fog) drops from below-cloud volume
of V is given by

= 0.006 R I

− V d [A] g

d t = N d WA c .

Noting that V/A c = z ,wehave

d [A] g

d t = 0.006 R I K mt

−

U T D P [A] g ,

which upon integration gives

[A] g = [A] g e −λ t ,

where λ = 0.006 (R I K mt /U T D P ) iscalledthe scavengingratio .Theamountofpollutant
scavenged from the atmosphere by rain or fog depends on the drop diameter D P . Note
that λ is inversely proportional to D P ; the smaller the drop diameter, the better the
scavenging efficiency. Small drops also have low U T and hence have a large residence
time in the atmosphere, which increases the mass transfer to the drop.