On the solution of population balance equations for multisize aerosol cloud undergoing simultaneous evaporation and coalescence

Time evolution of multisize aerosol cloud undergoing simultaneous evaporation and coalescence processes is analyzed. New closed-form analytical solutions of the discrete population balance equations are obtained and the relative contributions of evaporation and coalescence are determined. The instability of governing equations is revealed under enhanced coalescence rate, indicating the formation of a large droplet via an unstable rapid growth process. This process may be suppressed by the enhanced evaporation rate. The domain of operating conditions under which the unstable or stable modes of droplet size evolution may be realized is determined via a general stability analysis.