Analytic solution of the aerosol rigorous general dynamic equation without coagulation in multidimension

We present the analytic solution to the problem of multicomponent aerosol evolution due to condensation and/or evaporation of its components, sources, and deposition mechanisms. We use the rigorous formulation, which utilizes a particle number distribution depending on time and on the amount of each component, being that the particle size is a derived variable. This allows us to analyze the aerosol without the usual assumption of internal mixing. We solve the hyperbolic equation obtained through the method of characteristic curves. When all components condense, the obtained solution is always valid. When some of the components evaporate, the problem is more complex and its solution (which is not provided here) has to incorporate nonlinear phenomena such as shock and rarefaction waves, which are difficult to handle. The analytic solutions can be used to validate the numerical methods that could be developed in the future for more complex cases. We have analyzed a bicomponent case, and we have shown that in the aerosol evolution following condensation, nearly vertical "walls" appear in the particle size distribution.