Physical Causes of APSD Changes in Aerosols from OIPs and Their Impact on CI Measurements - Good Cascade Impactor Practices, AIM and EDA for Orally Inhaled Products - page 65

St is the coefficient before the differential term in (3.3), and:

tU
D

0

St = (3.7)

or more familiarly by substitution into (3.4):

2

UdC
D

r

0 pp c

St = (3.8)

18 h

Equation (3.8) [which is similar to (2.6) for the special case of a single-stage
impactor] can be used to calculate particle Stokes numbers in order to assess the
likelihood of inertial deposition to adjacent surfaces. From this equation, it can be
seen that the square root of St is directly proportional to the square root of [ r p d 2 ]
and therefore also to d ae (assuming a dynamic shape factor of unity). As a practical
guide, the probability of inertial deposition increases with larger particle size, since
as St approaches zero, (3.3) indicates that the particle motion will converge to be
identical with that of the supporting gas. Conversely, if St approaches unity or larger,
the likelihood of the particle following the streamlines of the local gas flow
decreases. In the round-nozzle CIs described in Chap. 2 , it was mentioned that a
value of St of 0.49 or greater is associated with inertial deposition [ 20 ], and similar

estimates for this parameter have been made in modeling particle deposition in both
models of the oropharynx and upper airways of the HRT [ 54 , 56 , 57 ] and with actual
airways in vivo [ 58 , 59 ].

√

3.3.2.3 Gravitational Sedimentation

Gravitational sedimentation is a potentially important external force affecting aero-
sol particle motion during transit from the inhaler to the patient or measurement
equipment. Under Stokesian conditions, which apply to the sampling of OIP-
generated aerosols, the drag force generated by passing through the support gas on
the particle under consideration ( F d ) is counterbalanced by the relative motion of the
particle with respect to the gas ( v particle − v gas ) in accordance with:

F =− 3 ph d ( v − v ) (3.9)

d p particle gas

from which the particle sedimentation velocity ( v t ) in a still gas is reduced to:

F =− 3 ph d v (3.10)

d p t

The force on the particle, with volume V p and density r p , due to gravity is:

mg = r p V g (3.11)