It's great to draw pictures, really helps thinking! It is true that the lines will curve exponentially, but maybe unnecessary to get into that detail on the sketch charts.

Could you add a line to both the charts showing the value of [pollutant concentration * ventilation rate] at each point in time? That's equal to the amount of pollution being removed, in kg/h, or whatever unit you're using.

If you double the concentration and halve the ventilation, you still get the same kg/h of pollution removed.

The area under that line equals the total mass of pollution that is been removed, say over a cycle. So long as that area is equal to the mass of pollution that is generated during a cycle, then you're at equilibrium.

You can optimise the ventilation rate (hence heat loss) by ventilating more at the times when pollution is most concentrated, so the [concentration * ventilation] product becomes greater. If you take this optimisation to its limit, and do maximum ventilation only when the pollutants are at maximum concentration, you end up with a purge ventilation cycle.

(Edit for posterity: by 'concentration' I mean the excess concentration indoors, compared to the background concentration in incoming ventilation air, which obvs already contains humidity, CO2 etc.)

That scenario could be achieved (hypothetically!) by covering the window opening with a sheet of something that allows humidity and pollutants to diffuse out, but stops cold air blowing in. (A permeable membrane).

Plasterboard or woodfibre board or breather membrane would be ok.

Now imagine how much faster the humidity would be cleared if you removed that sheet and just had the window opening - or try the smell experiment on the previous page!

Old houses are traditionally very vapour-open with lath/plaster ceilings and t&g pine floorboards, but even with those huge areas of permeable membranes, you still need airflow to properly ventilate them, usually deliberately as well as through air leakage.


BTW, even diffusion and MHRV have large energy losses in the form of the latent heat of the water vapour, this can be as much as the sensible heat of the warm air extract. One way to recover both the sensible and latent heats is to use an Exhaust Air Heat Pump EAHP for ventilation. Even on a warm day, the EAHP can cool the outgoing air enough to condense the outgoing water vapour and so recover the latent heat, often for use in DHW.