Biomedical Engineering Reference
In-Depth Information
3.3.2.1
Particle-Particle Agglomeration
Agglomeration is the process whereby individual particles collide to produce larger
particles and is continuously occurring once an aerosol has been formed. Coagulation
refers to the process of agglomeration in which the combined particles merge
together by the process of coalescence immediately on contact and is confined to
liquid droplets [
51
]. Thermal coagulation or agglomeration is the result of the ran-
dom motion of particles caused by transfer of energy by collisions with adjacent gas
molecules (Brownian diffusion) and is most evident with only the finest particles
< ca. 1
m
d
ae
produced from OIPs [
15
]. As well as thermal agglomeration/coagula-
tion, particles may come together as the result of relative motion caused by kine-
matic processes, such as the result of differing settling velocities due to gravity.
Whenever a flow velocity gradient exists, gradient or shear agglomeration/coagula-
tion will occur, as in turbulent flow [
51
].
The classical theory for agglomeration was developed initially for monodisperse
aerosols, based on Smoluchowski theory, and the reader is referred to the textbook
by Hinds [
51
], for a full description of the processes involved, including exact solu-
tion of equations that enable time-dependent changes to particle number concentra-
tion and associated size distribution to be calculated.
In this chapter, it is necessary to focus on understanding time-dependent changes
in OIP aerosol APSD that might be detected by the CI method; however, such aero-
sols are as a general rule polydisperse. An explicit mathematical solution, similar to
that for monodisperse systems, describing the agglomeration process does not at
present exist. It is therefore necessary to make some assumptions about the proper-
ties of the aerosol, the most common being that it is unimodal and lognormally
distributed. Under such circumstances, Lee and Chen have described the process for
agglomeration of an aerosol having a count median diameter (CMD) and geometric
standard deviation (
μ
σ
g
) by the relationship [
52
]:
(
)
2
k
T
abs
249
.
l
+
2
2
2
ln
s
05
. n
s
25
.
ln
s
K
=
1
+
e
e
+
e
(3.1)
g
g
g
3
h
CMD
in which
k
is the Boltzmann constant,
λ
is the mean free path length of gas (air)
molecules supporting an aerosol,
T
is the absolute temperature (degrees Kelvin),
η
is the gas (air) density, and
K
is the average agglomeration coefficient for the sys-
tem. It should be noted that a simpler relationship exists for monodisperse aerosols,
in which the coagulation coefficient becomes
K
mono
, and:
N
NK
0
(3.2)
Nt
()
=
1
+
T
0
mono
where
N
0
is the initial number concentration (density) of the aerosol and
N
(
t
)
describes the time-dependent decrease due to agglomeration. Using this equation,
if the aerosol number concentration is close to 10
13
particles/m
3
(high in relation
to the likely scenario in association with an OIP [
53
]) with CMD of 0.2
μ
m
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