Condensational Growth of Polydisperse Aerosol for the Entire Particle Size Range

The condensation problem of polydisperse aerosols is investigated theoretically. The single particle growth rate suggested by Kulmala (1993) is approximated and simplified by neglecting the Kelvin effect and by adopting the harmonic mean method for the transition correction, which is a good approximation of the representative flux-matching theories. An analytical solution to the particle size distribution change by condensation is derived in an explicit form using the modified growth rate. This study represents the first analytical solution to the condensation problem of polydisperse aerosols for the entire particle size range. The derived solution is compared with results of the previous study of Kulmala (1993) and is shown to be reasonably accurate, except for very small particles for which the Kelvin effect cannot be neglected.