Environmental Engineering Reference
In-Depth Information
3.7.1.3.1 Laminar Conditions
Under laminar plug low conditions, deposition by diffusion may be described by
101
K
P D
(
)
=
4
−
K
(3.29)
π
where
DL
V d
a
K
=
(3.30)
2
a a
and the diffusion coeficient,
D
is given by
C kT
d
c
D
=
3πμ
(3.31)
g
Under parabolic laminar low conditions, deposition by diffusion,
P
(
D
), can be calculated from the
expression derived by Ingham:
104
49 9
K
2 / 3
−
3 66
.
K
−
22 3
.
K
−
57
K
−
.
P D
(
)
= −
1
0.819
e
+
0.0976
e
+
0.0325
e
+
0.0509
e
(3.32)
The formulations given earlier have two major limitations: they are only valid for smooth-walled
tubes and they ignore entrance effects. Regarding application to airways, the limitations may be
quite serious because airways have natural surface features (e.g., cartilaginous rings).
121
In addition,
due to the serially branching quality of the respiratory network, velocity proiles may be developing
after each airway bifurcation. To address these issues, studies analyzed entrance effects in smooth-
walled and rough-walled tubes.
117,118,122
They determined that the deposition of ultraine (∼0.01 μm)
particles would be underestimated by ∼35% if airway surface structures were ignored.
3.7.1.3.2 Turbulent Conditions
Particle deposition by diffusion under turbulent conditions can be calculated as
21,101
⎡
⎢
ν
1/ 4
3/ 4
7/8
⎤
⎥
8
L
D
Re
a
P D
(
)
= −
1 exp
−
(3.33)
57
V
2
d
a a
which in air at STP reduces to
⎡
⎢
3/ 4
Re
2
7/8
⎤
⎥
0.088
L D
V d
a
P D
(
)
= −
1 exp
−
(3.34)
a a
3.7.2
s
econdary
d
ePosition
M
ecHanisMs
3.7.2.1 Interception
Deposition by interception occurs when a particle contacts an airway surface while passing it a
distance less than or equal to its radius, without deviating from the low streamline (Figure 3.5B).
Interception is an important deposition mechanism for ibers because as length increases, the
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