Improved Solution Methods For An Inverse Problem Related To A Population Balance Model In Chemical Engineering

In this paper, a population balance equation, originating from applications in chemical engineering, is considered and novel solution techniques for a related inverse problem are presented. This problem consists in the determination of the breakage rate and the daughter drop distribution of an evolving drop size distribution from time-dependent measurements under the assumption of self-similarity. We analyze two established solution methods for this ill-posed problem and improve the two procedures by adapting suitable data fitting and inversion algorithms to the specific situation. In addition, we introduce a novel technique that, compared to the former, does not require certain a priori information. The improved stability properties of the resulting algorithms are substantiated with numerical examples.