Biomedical Engineering Reference
In-Depth Information
While studying the drug release, a first task is to understand whether aerosols settle down
or not. For this purpose, one could carry out an experiment by suspending the particles
(10-mm size) in air at 20
°
C (density 1.2 kg/m
3
, 1.8
×
10
-4
g/cm.s) inside a 30-cm-tall mea-
suring jar. If the density of the particle is 1.01 g/cm
3
, how long will it take for the particle
to settle from the top of the measuring jar?
Solution: In this case there is no fluid flow. Thus, (4.17) becomes
∑∑
∑
F
mV
mV
0
=
−
=
y
in
in
out
out
For objects in fluids, there
are
three forces acting on the particle:
(a) Gravity,
F
g
g g
(acting downward)
==
ρ
p
Fm
g g
(acting upward)
(b) Buoyant force,
=
=
ρ
b
fluid displaced
f
1
2
(c) Hydrodynamic drag,
CV A
(acting upward opposing settling)
2
F
=
ρ
D
D
f
1
∑
2
F
C
V A
Vg
Vg
0
=
ρ
+
ρ
−
ρ
=
y
D
f
f
p
2
Rearranging,
(
ρρ
−
)
(
ρρ
−
)
2
Vg
4
3
g
p
f
p
f
(E4.1)
V
D
=
=
p
AC
C
ρ
ρ
D
f
D
f
Assuming a
N
RE
<
0.1, using (4.14),
24
μ
24
p
C
=
=
D
N
D V
ρ
Re
f
p
Substituting into (E4.1),
2
(
ρρ
μ
−
)
Dg
1
p
f
p
V
0.3 cm/s
=
=
18
f
To confirm whether the
N
RE
assumption is true, calculate the
N
RE
.
ρ
Dv
0.001* 0.001* 0.3
f
p
N
0.0017
=
=
=
Re
0.00018
μ
f
Hence, the assumption is valid. Furthermore, the time taken for settling is
t
=
L/V
=
30/0.3
=
100 seconds.
