A one-dimensional population balance governing the particle size distribution in a system where particles change their sizes due to both coagulation and individual growth is studied for the possibility of a similarity solution. It is found that when a dimensionless parameter γ is a constant, then the population balance can be transformed into an ordinary integrodifferential equation. Conditions under which the latter equation may have a self-preserving solution are established. Examples related to aerosol dynamics in the continuum regime, the free-molecule regime and the intermediate regime are discussed in detail.
Journal of colloid and interface science 50(3), pp.508-518