Biomedical Engineering Reference
In-Depth Information
Table 8.5
Shape of
agglomerate of spheres to
model a sample fibre particle
with diameter
d
and length
7d
Normalisation of the fibres can be performed through correlations from Stöber
(1972) for an equivalent aerodynamic diameter (
d
ae
) given as
d
ve
ρ
(1000
d
ae
=
(8.19)
·
κ
)
where
d
ve
is the volume equivalent diameter,
ρ
is the density of the fibre and
κ
is the
dynamic shape factor for a prolate spheroid. The dynamic shape factor taking the
length oriented perpendicular to the flow is given as
3
β
2
1
β
1
8
3
−
√
β
2
−
1
ln
β
1
κ
⊥
=
(8.20)
β
2
2
β
2
+
−
+
β
−
3
and also for the length oriented parallel to the flow is given as
3
β
2
1
β
1
4
3
−
κ
||
=
√
β
2
−
1
ln
β
1
(8.21)
β
2
2
β
2
+
−
−
β
−
1
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
κ
R
=
1
3
κ
||
+
2
3
κ
⊥
(8.22)
Taking the random orientation for the dynamic shape factor, the equivalent aerody-
namic diameter range for carbon fibre is 7.6-12.8
μ
m for, respectively, lengths of
10-300
m.
Submicron and nanoparticles
, which may be considered here as spherical, are
extremely small in size and therefore require additional forces to be included to
μ
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