## Filtration Theory

The basis of this theory is the capture of particles by a single fiber. The single-fiber efficiency %iber is defined as the ratio of the number of particles striking the fiber to the number of particles that would strike the fiber if streamlines were not diverted around the fiber. If a fiber of diameter df collects all particles contained in a layer of thickness y, then the single-fiber efficiency is y/df (see Figure 5.16.9).

The general approach involves finding the velocity field around an isolated fiber, calculating the total collection efficiency of the isolated fiber due to the mechanisms of particle deposition, expressing the influence of neighboring fibers (interference effects) by means of empirical corrections, and finally obtaining the overall efficiency of a filter composed of many fibers. The following equation relates the overall efficiency of a filter composed of many fibers in a bed E to the single-fiber efficiency:

~4%beroE

wdf(1

where:

a = the solidity or packing density of the filter L = the filter thickness df = the fiber diameter

Note than even if %ber = 1, the total filter efficiency can be low if a is low or the filter thickness is small. The derivation of this equation assumes that particles are well-mixed in every plane perpendicular to the gas flow direction, no particles are reentrained into the gas stream, all fibers are perpendicular to the gas flow direction, and the gas has a uniform velocity.

FIG. 5.16.9 Single-fiber collection efficiency.
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