(356f) Mechanism Discrimination Based on Population Balance Models

When observing the evolution of particle populations, it may not be obvious which of the possible mechanisms are influencing the system trajectory. For 1-D populations in which particle size is the internal dimension, the mechanisms most likely at work are some combination of nucleation, accretional growth, collisional growth and breakage. If we do not consider nucleation, there are eight possible combinations of these mechanisms, some of which exhibit stationary states and others similarity solutions. In this paper, we class these eight combinations based on the direction of particle concentration change, the direction of mean particle size change, and the value of the scaled 2^nd moment of the population at either the stationary state or similarity solution. We find that when all three mechanisms reach similarity solutions when occurring in isolation, consideration of these three measures allows identification of the particular combination of mechanisms causing the observed behavior. For certain collisional growth rate kernels, a similarity solution is not reached. In these cases, there are two mechanism combinations that cannot be distinguished from each other this way, but one can still discriminate this pair from the other six possible combinations and those remaining combinations from each other.