(281f) Mapping the General 1-D Population Balance Solution Space

The general 1-D population balance model in particle size contains nucleation, accretional growth, collisional growth and breakage terms. When there is nucleation, there can never be similarity solutions or stationary states. In the absence of nucleation, there are 8 possible combinations of the other 3 mechanisms. Under the presumption of power-law rate kernels and self-similar fragment distributions in breakage, the attractors for these 8 combinations at long times are either stationary states or similarity solutions. This paper presents the development of a unified scaling for the population balance which allows identification of the following for each of the cases:

• A scaled time variable from which the characteristic time for the system can be extracted
• Reduced equations for evolution of the scaled number mean particle volume
• Scaled mean particle size trajectories that depend only on kernel order
• Expressions for the scaled moments of the size distributions for the long-time attractor of the system (either stationary state or similarity solution)