Mean field theory for condensation on aerosols and application to multi-component organic vapours

The timescale is calculated for a particle to equilibrate by vapour condensation from a surrounding volume equal to the volume per particle in an aerosol, and is compared to the timescale to transport vapour by diffusion to neighbouring particle volumes. For practically all aerosols, the diffusive timescale is much smaller, showing that vapour diffusion, and, in the same way heat conduction, ensure that the vapour concentration and temperature in the vapour–gas mixture assume mean field values with which the whole of the aerosol equilibrates. Recent claims that individual particles equilibrate with the mixture are refuted. The concept is applied to obtain equations for the condensation of organic vapours whose equilibrium with condensate is governed by absorption partitioning coefficients together with a Kelvin term at small sizes. These dynamic equations, which contain vapour production and condensational loss terms, have steady-state solutions when these terms are changing slowly with time. Such solutions are obtained for non-volatile and semi-volatile constituents, their difference being defined to be that the equilibrium concentration is small compared to the actual concentration in the non-volatile case. For semi-volatile material, the concentration will generally be maintained at a value close to equilibrium over plane surfaces, so that it cannot contribute to nucleation and growth at small sizes. As for water condensation in the atmosphere, particles need to reach a certain size to be activated for growth by condensation of semi-volatile organics.