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412 13 Nanoaerosol

where the subscript p and f stand for particle and filter surface, respectively. A
−19 −21
typical Hamaker constant is in the order of (10 –10 ) J. The values for some
materials are listed in Table 13.2.
Example 13.2: Specific adhesion energy
Estimate the specific adhesion energy between a NaCl particle and a glass fiber
Solution
For salt particles and a glass fiber filter, H p ¼ 7 10 20 J, H f ¼ 8:5 10 20 J; then
the Hamaker constant is

p
1=2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 20 20
H ¼ H p H f ¼ 7 8:5 10 J ¼ 7:71 10 J
The specific adhesion energy is

H 7:71 10 20 J 2
Dc ¼ ¼ ¼ 0:0128 J m
12pZ 2 9 2 2
ð
e 12p 0:4 10 Þ m
where Z e ¼ 0:4 nm.

By considering the effect of surface adhesion energy and contact pressure inside
the contact area, the contact radius between bodies and the adhesion energy are
respectively given by the following two equations, ignoring the external force:

8
1=3
R
>
a ¼ ð 6DcpR Þ ð JKR ModelÞ
>
Y
>
<
ð13:37Þ
1=3
> R
>
a ¼ ð 2DcpR Þ ð DMT ModelÞ
>
:
Y
where R ¼ the characteristic radius of two bodies. In this case, they are considered

as the nanoaerosol particle and the filter fiber. And it is defined as
1 1 1
¼ þ ð13:38Þ
2R d p d f
*
Y is the composite Young’s modulus of bodies with the mechanical constant of K P
and K f
4 1

Y ¼ ð13:39Þ
3p K p þ K f
Mechanical constants are also listed in Table 13.2.
Example 13.3: Nanoaerosol adhesion efficiency
Calculate the adhesion efficiency using the DMT model with the following