Fundamentals of Particle Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 153

Fig. 6.10 Representation of a
non-spherical particle such as
a fibre, using a cluster of
spheres

six spheres, respectively, k is 1.12, 1.32, and 1.57. For other combinations of spheres,
the values of shape factors can be found in the literature (Hidy 1984; Lerman 1979;
Tran-Cong et al. 2004).
The aerodynamic flight of a fibre can be described by the spherical drag coefficient
as described in Eq. (6.14); however the fibre has to be converted into an equivalent
aerodynamic diameter. This can be performed by applying the following correlations.
An equivalent aerodynamic diameter for a fibre is given as

d ve ρ
(1000

d ae = (6.30)

·

k )

where d ve is the volume equivalent diameter, ρ is the density of the fibre, and k
is the dynamic shape factor. The dynamic shape factor taking the length oriented
perpendicularly to the flow is given as

(8 / 3)( β 2 − 1)

k ⊥ =

3) / β 2

β 2 (6.31)

[(2 β 2 − − 1 ] ln ( β + − 1) + β

and for the length oriented parallel to the flow,

( 4 / 3)( β 2 1) β 1 / 3

−

k || =

1) / β 2 1 ] ln ( β + β 2

(6.32)

[(2 β 2 − − − 1) − β

where β is the aspect ratio and is defined as the ratio of the fibre length to the
diameter. For random orientation of the fibre, the shape factor is a combination of
the two orientations and is given as

1
k R =

2
3 k ⊥ +

1
3 k ||

(6.33)

If we consider carbon fibre (density of 1830 kg/m 3 ) and asbestos fibre (density of
300 kg/m 3 ), the range for its equivalent aerodynamic diameter for random orientation
of the fibre is given in Table 6.4
Therefore the asbestos fibre has a shorter relaxation time than does the carbon
fibre, and we expect that the asbestos is likely to penetrate the upper respiratory
airways and into the lungs while the carbon fibre will deposit onto the respiratory
walls earlier, especially where the passageways have sharp turns.