Biomedical Engineering Reference
In-Depth Information
Fig. 9.11
Comparison of
computer simulations of He
and Ahmadi (1998) for
deposition of spherical
particles in duct flows with
experimental data collected
by Papvergos and Hedley
(1984), Papavergos and
Hedley (1984), and earlier
simulations of Li and Ahmadi
(1993) and McLaughlin
(1989), as well as model
predictions of Fan and
Ahmadi (1993) and Wood
(1981)
is quite high for very small particles due to the increase in the particle diffusivity
(Brownian motion). The deposition velocity then decreases as particle size increases
since the particle diffusivity decreases with particle diameter. The minimum par-
ticle deposition occurs for non-dimensional relaxation time of the order of 0.1-1
(0
.
5
m). The deposition velocity then increases for a larger relaxation
time despite the decrease in the particle diffusivity. This is due to the interaction
of these relatively large particles with turbulent eddies (Wood 1981). The inertia of
these relatively large particles affects their transport in turbulent eddies, and their
deposition rate increases. For particles with non-dimensional relaxation time larger
than 15-20, deposition velocity approaches a saturation level of about 0.14. This is
because of the very large inertia of the particles in this size range. Wood (1981) has
suggested a simple empirical equation for the non-dimensional deposition velocity:
μ
m
<
d
<
5
μ
10
−
4
τ
+
2
u
d
0
.
057
S
c
−
2
/
3
=
+
4
.
5
×
(9.3)
where
S
c
ν/D
is the Schmidt number. Fan and Ahmadi (1993) developed an
empirical equation for deposition of particles in vertical ducts that includes the effects
of surface roughness and gravity along the flow direction and is given as
=
⎧
⎨
⎩
⎡
⎤
1
/
(1
+
τ
+
2
L
1
+
)
τ
+
2
g
+
L
1
+
0
.
01085(1
0
.
64
k
r
2
d
+
2
1
+
+
⎣
⎦
1
2
τ
+
2
L
1
+
)
+
0
.
084
S
c
−
2
/
3
+
(
τ
+
2
g
+
L
1
)
/
(0
.
01085(1
τ
+
2
L
1
+
))
3
.
42
+
+
u
d
=
1
8
e
−
(
τ
+
−
10)
2
/
32
0
.
037
if u
d
×
+
<
0
.
14
τ
+
2
L
1
+
(1
1
−
+
(
g
+
/
0
.
037))
0
.
14
otherwise.
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