Biomedical Engineering Reference
In-Depth Information
(a conservative estimate of the size effect) with GSD close to 2.0 (typical of the
dispersity of OIP aerosols), after a 2 s delay,
N
2s
is only reduced to 9.98 × 10
12
par-
ticles/m
3
, and CMD has increased by less than 10%. Agglomeration is therefore
unlikely to result in significant changes to the overall APSD of typical OIP aerosols,
during the short transit time from creation to size fractionation, except perhaps in
the immediate time interval after atomization takes place from MDI products, where
aerosol number densities are at their highest.
3.3.2.2
Particle Inertia
The influence of inertia on particle motion is a significant factor in the development
of the APSD both during inhalation by the patient [
54
] and during the transit of the
aerosol to the measurement equipment in laboratory testing [
55
]. At its simplest, the
effect of inertia can be related to how the motion of an individual gas-borne particle
takes place relative to the suspending gas [usually air, oxygen, oxygen-enriched air,
or occasionally a helium-oxygen (Heliox) mixture]. Finlay [
53
] has shown that the
particle Stokes number (
St
) describes the influence of inertial force on particle
motion in accordance with:
t
U
D
d
d
v
′
g
U
t
·
0
=
gv
− ′
rel
(3.3)
′
t
0
in which
U
0
is the mean velocity of the gas flow;
D
is a characteristic size related to
that of the particle, typically the diameter of the airway through which it is moving
as it passes through the HRT; and the differential term represents particle accelera-
tion.
·
is the non-dimensionalized gravitational term (
g
/
g
) and
v
rel
is the particle
velocity relative to that of the surrounding gas.
t
is the particle relaxation time,
which is particle size-dependent, through the relationship:
2
r
dC
pp c
t
=
(3.4)
18
h
where
r
p
is the particle density,
h
is the gas (air) viscosity, and
C
c
is the Cunningham
slip correction factor (close to unity for particles >2
μ
m
d
p
).
Both particle velocity (
v
′
) and time (
t
′
) are in nondimensional forms where:
v
v
′=
U
0
(3.5)
and
t
D
U
′
t
=
(3.6)
0
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