by Robert P. Donovan

I continue to marvel at the fact that one of the most important defining components in a stateoftheart cleanroom is nothing more than a collection of randomly oriented fibers packaged as HEPA and ULPA filters for removing aerosol particles from the air circulating through the cleanroom.
The mechanisms of particle removal from the airflow by these filters depend on just physical interactions between the fibers and the aerosol particles—nothing fancy or seemingly high tech needed to obtain what I characterize as remarkable performance.
The particle capture efficiency of a fibrous filter depends on the following physical properties: fiber diameter, airflow velocity through the filter, filter thickness (measured in the direction of air flow) and packing density (the fraction of the filter volume occupied by the fibers, typically on the order of 0.1 for cleanroom filters and always less than 1 for any filter).
Electrical charge can aid particle capture or, as is most often true in liquid systems, degrade particle capture by introducing a repulsive force between the fiber and the particle. These electrical forces are less commonplace in air filtration, often require special manufacturing procedures to achieve and will not be discussed further.
With the elimination of electrical forces, four mechanisms of particle capture in a fibrous filter remain: interception, inertial impaction, diffusion and gravitational settling.
Gravitational settling of aerosol particles of concern in a cleanroom filter is minor. Indeed one definition of an aerosol particle is an airborne particle whose settling velocity in still air is less than 0.01 cm/s. By this definition, unit density spheres must be less than about 2 microns in diameter to even qualify as aerosol particles. The particles of highest interest in today's cleanrooms, however, are even much smaller—0.10.5 micrometer in diameter with settling velocities one to two or more orders of magnitude lower.
These velocities are negligible compared with the typical convective airflow velocity through a cleanroom, say 50 cm/s. Thus, regardless of whether the gravitational field is oriented perpendicular or parallel to the airflow through the filter, particle capture attributable to gravitational settling is also expected to be negligible.
For similar reasons, inertial impaction at the particle size of concern in cleanrooms is also expected to be minor. The rule of thumb for predicting when inertial impaction represents a significant capture mechanism between an aerosol particle and an obstruction is a dimensionless Stokes number (Stk) greater than unity (see CleanRooms November 2000, p. 10, and December 2000, p. 8) where the Stokes number is given by:
Stk = S/C = τV/C = ρ_{p}d_{p}^{2} V/18ηd_{f}
df represents the fiber diameter, the obstruction dimension perpendicular to the air flow; V, the upstream air velocity; dp, the particle diameter.
A 1micron fiber and a V of 50 cm/s yield a Stk value of 0.5 for a 0.5micron particle. As can be seen from Equation (1), the Stokes number becomes even smaller for smaller particles. Thus we also eliminate inertial impaction as a significant particle capture mechanism in cleanroom fibrous filters, leaving only interception and diffusion.
Interception is the mechanism whereby particles entrained in a streamline contact a fiber in passing through the filter—the particle radius exceeds the clearance distance between the fiber surface and the streamline in which it is entrained. The efficiency of particle capture by this mechanism depends on the ratio of particle diameter to fiber diameter:
R = d_{p}/d_{f}
and increases with increasing values of R. Thus, smaller diameter fibers are more efficient in collecting particles by interception, perhaps a counterintuitive conclusion. What happens is that the distance between the fiber surface and the streamlines decreases with decreasing fiber diameter, allowing smaller particles in the streamline to be captured by this mechanism.
Capture by interception at constant fiber diameter decreases with decreasing particle diameter. Air flow velocity does not effect particle capture by interception but packing density does, the larger values of packing density increasing the capture efficiency, an easily visualized conclusion the more fibers per unit volume, the more particle capture.
The other remaining particle capture mechanism, diffusion, arises from the Brownian motion of particles caused by collisions with air molecules. This mechanism is important only for small particles and depends on the dimensionless ratio Pe, called the Peclet number:
Pe = d_{f}V/D
where D is the particle diffusion coefficient.
Particle capture by diffusion increases with decreasing values of Pe. Smaller particles have higher values of D, decreasing Pe. On the other hand, increasing V increases Pe and, hence, decreases particle capture of a given diameter particle by diffusion.
At atmospheric pressure these two simple mechanisms produce the amazing results that make fibrous filters so useful in cleanrooms. However, fibrous filters are not perfect; next month's column discusses some of the lessdesirable traits of cleanroom fibrous filters.
Robert P. Donovan is a process engineer assigned to the Sandia National Laboratories as a contract employee by L & M Technologies Inc., Albuquerque, NM. His Sandia project work is developing technology for recycling spent rinse waters from semiconductor wet benches.
References
 Hinds, W. C., Aerosol Technology: Properties, Behavior and Measurement of Airborne Particles, Chap 9. Filtration, John Wiley & Sons, 1982.