Population balance modeling of the dissolution of polydisperse solids: Rate limiting regimes

Abstract

Significant errors can result in modeling dissolution processes if the polydispersity of the solid particles is ignored and the sample is treated as a collection of monodisperse spheres having the average size of the mixture. Population balance modeling provides an effective analytical means of predicting the effect of polydispersity on a wide variety of heterogeneous reaction systems including dissolution processes.

Simple dissolution-reaction model for enzymatic conversion of suspension of solid substrate

“…In modeling dissolution processes, significant errors may occur if the polydispersity of the solid particles is ignored and the sample is treated as a collection of monodisperse spheres having the average size of the mixture (LeBlanc and Fogler, 1987). For a particle size distribution of i size intervals with initial volume percentage x i,0 and (volume) average diameter d i,0 , the number of particles (n i ), and the initial concentration of solids (c S Ai,0 ) can be calculated from (1), (2), and (8), respectively, and A ‫ס‬ ∑ A,i in Equation (6).…”

General population balance model of dissolution of polydisperse particles

“…Errors of this origin can be eliminated through the use of the population balance method. This fact has been demonstrated by LeBlanc and Fogler (1987) for the special cases of rate-limiting regimes, namely, the regimes of mass-transfer control and surface-reaction control. No general analyses of the transition regime, however, have been reported until now, for the situations with either the surface-reaction control or the bulk-liquid reaction control as the kinetic asymptote.…”

“…The purpose of the present paper is to combine these two approaches in order to generate a population balance theory of a dissolution process which is valid not only for the rate-limiting regimes of mass-transfer control and bulk-liquid reaction control, but also for the general transition regime. In essence, it is a generalization of an analysis which, while being analogous to that of LeBlanc and Fogler (1987), describes the dissolution accompanied by a bulk-liquid reaction.To cope with the variety of influences of the different methods of particulate production on the size distribution, a number of distribution models and parameters have been analysed allowing also for the distribution shift with reaction. …”

“…Solids possessing wide distributions of particle sizes appear in most dissolution processes (e.g., crystallization: Randolph and Larson, 197 1) and shrinkage processes (e.g., combustion: Dickinson and Marshall, 1986). Models formulated in terms of the average particle size can lead to objectionably large errors in predicting the behavior of a realistic dissolution process (LeBlanc and Fogler, 1987). Errors of this origin can be eliminated through the use of the population balance method.…”

Fractal analysis in particle dissolution: a review

“…To some extent, the fractal dimension values of the undissolved particles obtained from the equations might be dependable, but one will doubt the result indicating the irregularity while or after dissolving. The PSD was combined with the shrinking core model by Gbor and Jia (2004) and LeBlanc and Fogler (1987), who proposed the population balance model and particle growth (decrease) rate during dissolution, which were then considered as an important influence factor on the dissolving kinetics in the latter research (Giona et al 2002, Haenchen et al 2007) but without fractal theory. Therefore, we recommend that the PSD should be performed on the surface and reactive fractal models.…”