Page 205 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

180 6 Separation of Particles from a Gas

diameter. Diffusion is the only important mechanism for particles below 0.2 µm,
but drops quickly with the increase of particle diameter. The total efficiency is at the
bottom for particles around 0.2 µm. This is because this group of particles is too
large for diffusion and too small for impaction or interception to be effective.

6.5.2 Overall Fibrous Filtration Efficiency

Eventually we need to quantify the overall efficiency of an actual filter. “Overall
filtration efficiency” is used here to avoid the confusion with the term “total effi-
ciency” that has been used above to describe the total efficiency of a single fiber,
Eq. (6.87). The overall filtration efficiency, η, can be derived from the total single
fiber efficiency, η sf , by the following simplified one-dimensional analysis.
As depicted in Fig. 6.13, analysis of overall filtration efficiency, consider a filter
with a bulk thickness of L along x-direction, which is also the face velocity
direction. The filter is filled with homogeneous fibers of diameter, d f , and the length
of the uniform single fiber is denoted as ds f . Within an elemental thickness of dx,
the solidity, a, from its definition is,

.
pd 2
f 4 ds f
a ¼ ð6:88Þ
A c dx
where A c is the bulk cross section area of the filter that is normal to the face
velocity. It can be determined by the air flow rate

Q
A c ¼ ð6:89Þ
U 1
where U 1 is the bulk face speed, or the air speed approaching the filter. It is less
than that approaching the fiber within the filter, U 0 , because of the existence of solid
fibers

Fig. 6.13 Analysis of overall L
filtration efficiency

C Nin
C Nx C Nx+dx C Nout
U∞

x x+dx x