Apparent size-dependent growth in aggregating crystallizers

Abstract

Population balance equations for steady-state crystallizers with nucleation, growth, and aggregation were solved using a sectional method with modified shapes for the distribution functions within the sections that accounted for the particle dynamics. The system of number balances were generated using section shapes that were decaying exponentials with modified residence times and growth rates consistent with fluxes due to particle deposition, and solved with a modified Newton's method. The solutions obtained satisfied the number, volume, and sixth moment balances, and had minimal discontinuities at the section boundaries for five forms of the aggregation kernel (size-independent, linear, quadratic, cubic in size, and Brownian), with growth parameters that are easily derived with a high level of confidence. Each kernel had unique characteristics, and showed different kinds of size-dependent growth. Simulations were compared with a distribution obtained for the continuous crystallization of an alum salt, and showed that the linear kernel compared well. Incorporating aggregation provides a physically supportable alternative to fitting models of size-dependent growth (SGD) or growth rate dispersion (GRD).