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174 6 Separation of Particles from a Gas

could be mathematically described precisely. However, the random orientations of
the filter media, especially the fibers within a filter, make it nearly impossible to
achieve accurate mathematical solution. Instead, simplified filtration models are
introduced as follows.

6.5.1 Single Fiber Filtration Efficiency

The simplest model consists of an isolated cylinder (simulating a single fiber) or a hole
(for single pore) or a sphere (simulating a granule) in an otherwise undisturbed flow of
fluid (gas or liquid). This may be justified for perfectly designed filters with exces-
sively high porosity. Although the model based on isolated filter medium has been
quite useful in illustrating the relative importance of different transport mechanisms, it
is challenging to relate the rate of particle deposition on an isolated medium to the
collection efficiency of a real filter that is filled with random fibers or granules.
A better approach, although still quite far from being realistic, is the model based
on Kuwabara [18] cell model of forces experienced by randomly distributed parallel
circular cylinders or spheres in a viscous flow at small Reynolds number. This cell
model has been used by several researchers as a starting point for their filtration
models, especially for fibrous filter models. Unlike the isolated cylinder or sphere
models, these newer models address the influence of the surrounding filter media.
However, the Kuwabara model and its modified versions still have limitations
because they cannot be justified. Kirsh and Fuchs [17] developed a 3D model to
represent a real filter more closely than earlier models; this model is too compli-
cated to be solved easily. Therefore, we will not discuss it.
Yeh and Liu [38, 39] developed a model of flow over a staggered array of
cylinders (Fig. 6.11) to investigate Kuwabara’s model with slip effect taken into
consideration. With this they quantified the effects of inertial impaction, diffusion,
and interception. These models were also experimentally validated [38, 39]. And,

Fig. 6.11 Staggered array
filter model
d f

h
U 0
2h