Recovery curves: how long until the air clears

After a source event ends, every pollutant decays toward its background level, but the shape of the decay differs by physics. The shape is also a clue: an indoor event such as cooking clears once the source stops, while smoke getting in from outside keeps coming back until the outdoor air improves, even when the peak PM_2.5 looks similar.

The core math is first-order decay: concentration falls exponentially with time, at a rate set by the air changes per hour (ACH), where one air change replaces the room's volume once. Two contributions add together: passive air exchange (typically 0.2–0.5 ACH in a well-sealed home, more with windows open) plus filtration from any purifier. A purifier adds its CADR in cfm × 60 ÷ the room volume in cubic feet: a 300-CADR purifier in a 1,500 ft³ room adds about 12 ACH.

The half-life of a contaminant is about 0.693 ÷ total ACH, in hours. At 4 ACH (a typical HEPA purifier in a moderately sized room), the half-life is about 10 minutes, with a 95% reduction in about 45 minutes. At 8 to 10 ACH (a well-sized HEPA in a small bedroom), the half-life drops to 4 or 5 minutes. Terrestream can estimate each room's own air-change rate from how CO₂ falls after people leave; it needs several clean decays, usually over a few days, before it relies on one, and it uses the estimate to flag rooms that clear slowly rather than displaying the number.

PM and CO₂ both decay roughly exponentially when the source stops and ventilation stays steady. Coarse PM₁₀ often drops faster at first as the heaviest particles settle, then follows a slower tail. VOCs are two-stage: walls, fabric, and carpet absorb VOCs quickly during a pulse and release them slowly over hours to days, so after a ten-minute cooking event the VOC index usually falls most of the way back within half an hour but can stay a little above its starting point for hours.

Humidity decays slowly compared with gases because hygroscopic materials such as wood, paper, and fabric absorb and release water. A shower spike falls faster than it built while the bathroom fan runs, but the room takes longer to dry below its starting humidity than a gas calculation would predict.

Three caveats. First, the math assumes well-mixed air; closed doors, dead zones, and poor mixing slow real-world clearance. Second, settled particles (PM₁₀, dander) get stirred back up by movement, so a room may clear and then spike again when someone walks in. Third, sources can continue (a still-warm pan, off-gassing furniture), and decay only starts when the source stops. Rated CADR comes from standard laboratory tests; real rooms often clear more slowly. See HEPA and CADR.