(An) analytical approach to the population balance equation for radioactive aerosols

Abstract

An analytical approach to the population balance equation for radioactive aerosols is performed based on the general governing equation involving the effect of radioactivity. The analytical and numerical studies covering the quantitative analysis of the interaction among the various physical processes are carried out to elucidate the general properties of radioactive aerosol size distribution under the simultaneous influence of coagulation, condensation and removal. New analytical solutions have been obtained based on the dimensionless-form governing equation focusing on the volume-proportional removal process for the mathematically tractable cases. The physical meanings of the derived solutions was closely examined through graphical representations. The volume-proportional removal process was mainly focused and it was known that the major physical process to reduce the radioactivity should be the gravitational settling of particles. Also, it was examined that the definitions of the total airborne radioactivity might be slightly different. While total radioactivity defined conventionally could be underestimated compared with that of this work, the effect of removal process was believed to reduce the difference as time passes.