Fundamentals of Particle Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 148

Fig. 6.7 Predictions of
various models for drag
coefficient for a spherical
particle

Equation (6.14) is an empirical fit to the data and is quite useful for analysis of aerosol
motion.
For higher Re p in the range of 10 3 <Re p < 2.5 10 5 , the drag coefficient is roughly ×

constant (C D = 0.4). This regime is referred to as the Newton regime. However

this regime is typically not applicable for airborne particulates, where the particle
diameters are in the order of nanometer and micrometer, leading to low Re p numbers.
Predictions of various models for drag coefficient with the trend of the experimental
data are shown in Fig. 6.7 .
For a particle moving near a wall, the drag force varies with the distance of the
particle from the surface. Brenner (1961) analysed the drag acting on a particle
moving toward a wall under the creeping flow condition. To the first order, the drag
coefficient is given as

1

24
Re p

d
2 h

C D =

+

(6.15)

where h is the distance of the particle centre from the wall.
For a particle moving parallel to the wall, the Stokes drag force needs to be
modified. For large distances from the wall, the following equation was suggested
by Faxen (1923):

1

5 − 1 d

2 h

d
2 h

3 d

2 h

4 d

2 h

24
Re p

9
16

1
8

45
256

1
16

C D = − + − − (6.16)

6.4.2 Cunningham Correction Factor

When a particle becomes so small that its size becomes comparable to the mean
free path of the molecules of the surrounding gas, the flow field can no longer be