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 67

3.3.2.4 Molecular Diffusion (Brownian Motion)

Particle motion in relation to the motion of the supporting gas molecules (i.e.,
molecular diffusion or Brownian diffusion) becomes important at sizes <1-2

μ m

[ 53 ]. D d , the diffusion coefficient, is given by the expression:

kTC
d

c

D = 3 ph (3.14)

d

p

Finlay has compared the random particle motion as the result of Brownian diffu-
sion with the downward-directed motion due to gravitational sedimentation in
accordance with the relationship:

( )

18 h

r

Dt
gd Ct

2
2

p
p

d

diff

= (3.15)

sed ppc

in which p diff is the root mean square displacement of a particle of diameter and d p ,
due to molecular diffusion in time t . p sed is the distance travelled by the same particle
in the same time interval.
Molecular diffusion can be considered negligible if p diff / p sed < 0.1 [ 53 ] and is
therefore, in general, less important than either sedimentation or inertial behavior,
except within the highest generations of the HRT in which the dimensions of the
airways are finest or in cases where a breath-hold of several seconds takes place at
the end of inhalation to extend the residence time of the particles in these airways
and the alveolar sacs [ 53 ]. In this context, Landahl has reported that the influence of
molecular diffusion becomes important in terms of deposition in the HRT only for
particles m [ 63 ], significantly finer than the range of interest in connection

with currently marketed OIPs. Its impact on CI-measured APSDs of OIP aerosols is
also likely to be minimal, given the short residence times between the inhaler and
size-fractionating apparatus, even when a VHC is present in the context of MDI
testing.

≤ 0.1 μ

3.3.2.5 Electrostatic Charge

Electrostatic charge-based particle motion is a significant and somewhat unpredict-
able contributor to APSD changes with almost all OIPs, except perhaps nebulizing
systems. The likelihood that MDI-produced aerosols will carry significant intrinsic
charge has already been discussed in connection with aerosol formation. This sec-
tion is concerned with how electrostatic charging can affect the particle transport
process from the inhaler. In contrast with the previous physical mechanisms, there
are no analytical expressions that can reliably be used to describe the motion of