ON THE SOLUTION OF POPULATION BALANCE-EQUATIONS BY DISCRETTIZATION .1. A FIXED PIVOT TECHNIQUE

A new framework for the discretization of continuous population balanc e equations (PBEs) is presented in this work. It proposes that the dis crete equations for aggregation or breakage processes be internally co nsistent with regard to the desired moments of the distribution. Based on this framework, a numerical technique has been developed. It consi ders particle populations in discrete and contiguous size ranges to be concentrated at representative volumes. Particulate events leading to the formation of particle sizes other than the representative sizes a re incorporated in the set of discrete equations such that properties corresponding to two moments of interest are exactly preserved. The te chnique presented here is applicable to binary or multiple breakage, a ggregation, simultaneous breakage and aggregation, and can be adapted to predict the desired properties of an evolving size distribution mor e precisely. Existing approaches employ successively fine grids to imp rove the accuracy of the numerical results. However, a simple analysis of the aggregation process shows that significant errors are introduc ed due to steeply varying number densities across a size range. Theref ore, a new strategy involving selective refinement of a relatively coa rse grid while keeping the number of sections to a minimum, is demonst rated for one particular case. Furthermore, it has been found that the technique is quite general and yields excellent predictions in all ca ses. This technique is particularly useful for solving a large class o f problems involving discrete-continuous PBEs such as polymerization-d epolymerization, aerosol dynamics, etc.