Page 129 - Advanced Mine Ventilation

110 Advanced Mine Ventilation

Table 8.3 Aerodynamic Shape Factors (ASFs)

Author Material Instrument ASF
Timbrell [6] Ground glass Elutriator 1.49
Timbrell [6] Coal Elutriator 1.35
Sawyer and Walton [8] South Wales coal Conifuge 1.35
Sawyer and Walton [8] Lancashire coal Conifuge 1.31
Sawyer and Walton [8] Cumberland coal Conifuge 1.35
Sawyer andWalton [8] China clay Conifuge 1.61
Sawyer and Walton [8] Quartz Conifuge 1.67
Thakur [1] Bituminous coal Elutriator 1.42 (1.34e1.48) a

a
ASF ¼ 1.34 for Stoke’s diameter of 3.98 mm.
ASF ¼ 1.37 for Stoke’s diameter of 2.77 mm; ASF ¼ 1.38 for Stoke’s diameter of 1.97 mm; ASF ¼ 1.48 for Stoke’s
diameter of 1.48 mm.

8.3 NonSettling Fraction of Respirable Dust

Thakur [1] postulated that a small portion of respirable dust (under 1 mm of unit den-
sity) may not settle by gravity or be affected by water sprays. As the particle size goes
down, its settling velocity reduces but its random movement owing to Brownian mo-
tion increases. The nonsettling dust size upper limit is defined as the size for which
settling velocity equals Brownian displacement [1].
Settling velocity for a particle was already derived in article 8.1. Brownian motion
of particle suspended in air is given by Einstein [9] in Eq. (8.12).

2
X ¼ 2 Dt (8.12)
B
2
where X is the mean square displacement with respect to any coordinate axis in time,
B
t. D is the diffusion coefficient of the particle.
Einstein defined,
D ¼ KTB (8.13)

where K is the Boltzmann constant; T, absolute temp in Kelvin; B, particle mobility
defined in Eq. (8.10).
Fuchs [2] expanded Eq. (8.13) further and concluded:

1
4D 2

X ¼ Average displacement=s ¼ (8.14)
p