AGGREGATION AND GELATION .3. NUMERICAL CLASSIFICATION OF KERNELS AND CASE-STUDIES OF AGGREGATION AND GROWTH

This paper extends a method that significantly reduces the number of k ernels that one might consider as candidates for modelling systems whe re aggregation and growth may occur simultaneously. Gelling kernels an d their values of I-agg(rel) in both continuous and batch operation ar e identified using a simple numerical technique-a discretised populati on balance. Extensive testing of this numerical technique against anal ytical results developed in Part I shows that the onset of mathematica l gelation and hence the value of I-agg(rel) may be determined with hi gh accuracy. Well-known and commonly used kernels are identified as ge lling kernels. For example, the Thompson, gravitational settling and i nertia kernels are gelling kernels in both modes of operation. Here, f or approximately mono-disperse feed or charge PSDs, the onset of mathe matical gelation occurs almost instantly, i.e. I-agg(rel) approximate to 0. The shear kernel displays sum-kernel-like behaviour in that it i s a non-gelling kernel in batch operation but a gelling kernel in cont inuous operation. In the latter case, with a mono-disperse feed PSD, I -agg(rel) = 0.585. The value of I-agg(gel) for the shear kernel decrea ses as the CVnu of the feed PSD is increased. By contrast, for station ary kernels the value of I-agg(gel) increases as the CVnu of the feed PSD is increased. For the kernels studied it is shown numerically that a size-independent growth rate has no bearing on whether a kernel is a gelling kernel. Examples, taken from the literature for those cases where aggregation and growth occur simultaneously, are discussed in or der to show how this work aids model discrimination.