A puristic analysis of population balance—II.

Abstract This paper in sequel to an earlier paper by the authors [1] establishes that the population balance equation for any particulate system is only one of an infinite sequence of equations in product densities associated with the description of point processes. The population balance equation yields only information about mean quantities and a rigorous description of the system requires the calculation of fluctuations about mean values; such fluctuations can be calculated from considering the higher order product density equations. In establishing these results, the rather restrictive assumption that no more than a single particle can be identified of a given state made in the earlier paper [1] has been relaxed so that a broader generalization has been obtained. It is to be noted that such a generalization is more essential for a realistic analysis of particulate systems than for the sake of mere completeness. It is shown that the population balance equation derived by number balance is not always correct in the sense that the rates at which existing particles disappear and new particles appear as normally written are valid only under suitable (but not universally applicable) assumptions which are naturally brought to light by the framework presented herein.