Dose calculations for diameter distributions of aerosol particles

In case the aerosol particle diameter is a distribution rather than a deterministic value, the dose metric calculations change as follows.

It is assumed here that particle diameter distributions P_M(δ) are mass (or equivalently: volume) distributions, i.e. P_M(δ)dδ gives the fraction of the total mass (volume) of the particles with diameter between δ and δ+dδ.

The relation between the normalized diameter distribution P_M(δ) and the actual (non-normalized) diameter distribution P(δ) is given by

Pδ=Map ×PM(δ)

When considering a distribution of the diameter of the aerosol particle, the dose metric calculations of the ‘surface area aerosol particle’ and ‘number of aerosol particles’ change to:

Surface area aerosol particles:  

 Sap=P(δap)ρap×vapπδap2dδap=6×Mapρap1δapPM,apdδap

Number of aerosol particles

 Nap=P(δap)ρap×vapdδap=6×Mapρap×π1δap3PM,apdδap