(281c) Solution Space Mapping for Power-Law Aggregation Rate Kernels

Using the scaling presented in an earlier paper at this meeting titled “Mapping the General 1-D Population Balance Solution Space”, the aggregation problem with power-law rate kernels is examined from the point of view of the Pulvermacher-Ruckenstein criterion for similarity solution existence. In this form one can map the solution space into two axes, one for kernel order and one for its internal structure. In this space, maps of approximate solution parameters in the form of modified-gamma distributions or the log-normal distribution can be identified in the existence region using a moment model. Davies, et al. studied and mapped gelation behavior in the non-existence region so that their results can be superimposed on the similarity solution map to generate complete mapping of the aggregation solution space.