AGGREGATION AND GELATION .1. ANALYTICAL SOLUTIONS FOR CST AND BATCH OPERATION

This work is part of a study of model discrimination for aggregation p rocesses characterised by continuous particle size distributions. Crit eria are sought for the acceptance or rejection of proposed functional forms of the aggregation kernel, of a more fundamental nature than th e goodness of fit which they might afford to a perhaps narrow range of experimental data. New analytical results for well-mixed, continuousl y operated vessels are contrasted with those for batch operation. It i s shown that some forms of kernel result in solutions to the populatio n balance that exhibit the mathematical equivalent of a phase-transiti on phenomenon, manifested as divergence of the sixth moment of the par ticle size distributions, of a type referred to in the literature as g elation. Kernels that predict this ''mathematical gelation'' for one m ode of operation, e.g. continuous, need not do so for another mode, e. g. batch. It is moreover shown that, for a kernel that predicts mathem atical gelation for both these modes of operation, the gelation points correspond to different values of the index of aggregation for the tw o modes. In addition, the gelation points are dependent on the shape o f the feed or charge PSD. We propose that gelling kernels-those capabl e of predicting gelation-be rejected a priori as unsuitable for modell ing systems that do not exhibit physical gelation, since whatever thei r powers for interpolation of experimental data, they are unsafe for e xtrapolation from one mode of operation to another, from smaller to la rger values of the index of aggregation, or from one feed to another.