Aerosol formation from heat and mass transfer in vapour–gas mixtures

Abstract

Heat and mass transfer equations and their coupling to the equation for the aerosol size distribution are examined for mixtures in which pressure changes are slow. Equilibrium between an aerosol and its surrounding vapour is shown to be generally fast so that vapour supersaturations are small. Diffusion and conduction control evaporation and condensation on aerosols so that the sign of the aerosol growth term can be determined by the ratio of their relative rates, given by the Lewis number, Le ; for example where Le < 1, as for water vapour–air mixtures, aerosols may evaporate as the mixture is cooled. A ‘condensation number’, Cn ( T ), representing the ratio of the rate of heat transport to that of latent heat by vapour diffusion, and which is a strong function of temperature, is introduced to describe the other main controlling physical effect in aerosol formation. Where Cn ≪ 1, as for high-temperature water vapour–air mixtures, the proportion of vapour that can condense as an aerosol is very small. For a fixed total heat transport rate, the maximum aerosol formation rate occurs near Cn ( T ) = 1, which is at T ≈ 4°C for water vapour–air mixtures at 1 atm pressure (101 325 Pa). Specific results in terms of Cn and Le are obtained for the proportion of vapour condensing as an aerosol during the cooling and heating of a mixture in a well-mixed cavity. The assumption of allowing no supersaturations, the validity of which is examined, is shown to lead to maximum aerosol formation. For water vapour–air mixtures predictions are made as to temperature regions in which aerosols will evaporate or not form in cooling processes. The results are also qualitatively applied to some atmospheric effects as well as to water aerosols formed in the containment of a pressurized water reactor following a possible accident. In this context the present conclusion that the whereabouts of vapour condensation is controlled by heat and mass transfer contrasts with previous assumptions that the controlling factor is relative surface areas.