Mechanisms of Particle Deposition - Aerosols: Measurement, Dosimetry, and Health Effects - page 50

TABLE 3.1
Dynamic Shape Factors for Common Particle Shapes
and Types

Type of Particle Dynamic Shape Factor, Π Reference

Particles of regular shape
Sphere 1.00 12

Cube 1.08 12

Cylinder (vertical axis) 1.01 12

Cylinder (horizontal axis) 1.14 12

Cube octahedron 1.03 2

Octahedron 1.06 2

Tetrahedron 1.17 2

Other particles
Bituminous coal

1.05-1.11 12

Sand 1.57 12

Talc 1.88-2.04 12

Quartz (0.65-1.85 μm) 1.84 2

Quartz (>4 μm) 1.23 2

The correction factor χ can also be used to modify d ae for shape irregularity 7 :

ρ
χ

p

(3.9)

d = d

ae g

The terminal settling velocity, corrected for shape, is given by

2

= ρ

d g

p p

V (3.10)

TS

18

μχ

Moss, 8 Stober, 9,10 and Leith 11 have investigated the effects of shape on the aerodynamic properties of
particles. Table 3.1 provides dynamic shape factors for common particle shapes and types.

3.2.4.2 Correction for Slip
Stokes's Law assumes that the luid velocity at the particle surface is zero. This no-slip assumption
is not valid for small particles; thus, the Cunningham slip correction factor, C c , should be applied
when particles smaller than 10 μm are being considered. C c may be expressed as

⎡
⎢

A
Kn

⎤
⎥

⎛
⎜

⎞
⎟

3

C

c = +

1 Kn A + A exp − (3.11)

1 2

where
Kn is the dimensionless Knudsen number (deined in the following)
A 1 , A 2 , and A 3 are constants derived from experimental measurements

While the values of these constants vary in the literature, 1,13-15 the most commonly accepted values,
as determined by Davies, 13 are A 1 = 1.257, A 2 = 0.4, and A 3 = 1.1.