Difficulties inherent to the use of analytic solution of the condensation-evaporation equation for multicomponent aerosols

We present the analytic solution to the problem of multicomponent aerosol e volution due to condensation and/or evaporation of its components. We pose the general equation that governs the evolution of the particle size distri butions of each species, and then solve it through the method of characteri stic curves. The obtained solution is of interest because it permits an app roximate analysis of cases of practical importance without numerical method s. Furthermore, the analytic solutions can be used to validate the numerica l methods which, up to now, are only compared with mono-component cases. Wh en all components condense, the obtained solution is valid for all time val ues. When some of the components evaporate the problem is more complex, due to the fact that no component exists in a negative amount. This suggests t he formation of shock waves (high peaks in particle size distribution) and rare-faction waves, which are difficult to handle. Finally, we apply the me thod to several interesting cases. (C) 1999 Elsevier Science Ltd. All right s reserved.