Particle Dilution
Purge Multiplier
Model concentration decay parameters to calculate the absolute recovery timeframe required to clear spikes after internal boundary disruptions.
The Mathematics of Airborne Contamination Purge & Logarithmic Concentration Decay
When an accidental breach or particle filtration failure occurs inside a cleanroom envelope, restoring standard operating limits is not instantaneous. Particulate concentration cleanup behaves like a classic chemical dilution profile governed by non-linear logarithmic decay calculus. The mathematical relationship states that the time required to flush the envelope depends directly on the natural log ($\ln$) of the ratio between the peak initial contamination ($C_i$) and the target certified baseline specification ($C_t$). This decay curve is driven by the room’s operational Air Changes Per Hour (ACH) adjusted by the Ventilation Mixing Factor ($E_v$). In a perfect laminar flow system ($E_v = 1.0$), air moves like a solid piston, wiping contaminants away cleanly. In conventional non-directional layouts, stagnant zones and dead corners reduce mixing efficiency, which stretches out the necessary cleanup time. Restarting production before this dilution cycle finishes risks trapping hidden micro-contamination inside process lines.
Frequently Asked Questions
A: Air distribution layout directly determines the mixing factor ($E_v$). If supply registers and exhaust louvers are positioned too close to each other on the ceiling, the air can “short-circuit,” bypassing the rest of the room. This leaves stagnant pockets near the floor where particles can settle. To achieve a high mixing factor ($E_v \ge 0.7$) in turbulent spaces, supply air must enter from the ceiling and exit through low wall-return grilles distributed evenly around the room’s perimeter.
A: Yes. Temporarily scaling up supply fan volumes boosts the room’s temporary ACH value, which steepens the dilution curve and cuts down the required purge time. However, this adjustment must be managed carefully. Ramping up velocity too quickly can over-pressurize the space, causing joint leaks or creating structural turbulence that lifts heavy settled particles off the floor and re-entrains them into the air stream.