Biomedical Engineering Reference
In-Depth Information
Table 3.1
Sedimentation
velocity (
v
t
) at selected sizes
for spherical, unit density
particles
v
t
(mm/s)
Uncorrected for
C
c
d
p
(
μ
m)
Corrected for
C
c
0.1
0.00030
0.00086
0.5
0.0076
0.0100
1.0
0.0302
0.0348
2.0
0.121
0.134
5.0
0.749
0.782
10.0
3.014
3.060
For a spherical particle where
V
p
pd
3
, (3.11) becomes:
=
/
6
p
mg
=
r
p
dg
3
(3.12)
When the force on the particle equals the drag force, the particle will travel at a
constant settling velocity,
v
t
, given by:
r
gd
2
18
pp
v
t
=
(3.13)
h
Values of
v
t
for unit density particles (cgs system) can be tabulated as a function
of
d
p
in the size range of interest for OIP inhaled aerosols being size fractionated by
cascade impactor (Table
3.1
). The numerator of (3.13) is multiplied by the
Cunningham slip correction factor (
C
c
) for particles <0.5
m; the correction for air
at ambient pressure and temperature increases the settling velocity by 34 % when
d
p
is 0.5
μ
m [
53
].
The velocity acquired through gravitational sedimentation is relatively unim-
portant in relation to typical sampling velocities involved with cascade impaction
measurements, which approach 17 mm/s at the entry to the 19 mm internal diameter
USP/Ph. Eur. induction port, when a typical flow rate of 28.3 L/min is used to sam-
ple the aerosol via an ACI. However, if the aerosol is collected by a VHC in connec-
tion with MDI testing with this type of add-on device, the test protocol is likely to
be modified to include a delay interval of several seconds between MDI actuation
and the onset of sampling in order to mimic how the device might be used by a
patient [
60
]. The loss of aerosol due to gravitational sedimentation with elapsed
time may become observable, but only after very long intervals greater than 10 s, as
long as the confounding influence of electrostatic charge is eliminated [
61
]. In the
testing of these devices recommended by a Canadian standard, the delay interval is
kept to 2 s, as this is more typical of the elapsed time that might occur if a patient
exhales instead of inhaling when actuating their inhaler [
62
]. Under these circum-
stances, the influence of gravity on both mass concentration and APSD can be
treated as of minor consequence.
μ
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