ON THE SOLUTION OF POPULATION BALANCE-EQUATIONS BY DISCRETIZATION .2.A MOVING PIVOT TECHNIQUE

Discretized population balances of aggregating systems are known to co nsistently over-predict number densities for the largest particles. Th is over-prediction has been attributed recently by the authors (Kumar and Ramkrishna, 1996, Chem. Engng Sci. 51, 1311-1332) to steeply non-l inear gradients in the number density when a fixed pivotal particle si ze is used for each discrete interval. The present work formulates mac roscopic balances of populations with due regard to the evolving non-u niformity of the size distribution in each size interval as a result o f breakage and aggregation events. This is accomplished through a vary ing pivotal size for each interval adapting to the prevailing non-unif ormity of the number density in the interval. The technique applies to a general grid and preserves any two arbitrarily chosen properties of the population. Comparisons of the numerical and analytical results h ave been made for pure aggregation for the constant, sum and product k ernels. It is established that numerical predictions from macroscopic balances are significantly improved by an adapting pivot accounting fo r non-uniformities in the number density.