The efficienty of air filters is usually expressed in terms of Collection Efficiency (when used in sampling), or Penetration (when used in air-cleaning equipment).
are the particle counts entering and leaving the filter.
In terms of the particle mass, the collection efficiency can also be expressed as
are the particle mass concentration entering and leaving the filter.
Single Fiber Efficiency
In order to effectively study the complex process of air filtration, it is beneficial to look at the particle collection by a single fiber. In this analysis, the fiber is placed with its axis perpendicular to the air flow, and various depostition mechanis
ms are investigated. Classically, the single fiber is considered to be isolated, i.e., without the existence of other fibers; whereas modern single fiber theory takes into account the neighboring fibers.
Let us first look at the Reynolds Number
which characterizes the flow around the fiber:
is the gas density,
the single fiber diameter,
the velocity of air inside the filter, and
the kinematic viscosity.
The analysis shows that under most circumstances the flow around the fiber will be laminar.
The single fiber efficiency, defined as the capability of a fiber to remove particles from an aerosol stream, is
i.e., it is the ratio of the particles that are collected by the single fiber in one second to the number of particles that would have passed through an imaginary outline of the fiber in one second.
Thus, the overall efficiency
is a function of
. The following relationship can be obtained: