General population balance model of dissolution of polydisperse particles

Abstract

Dissolution of solid particles in liquids is commonly encountered in the chemical process industry. 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. 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. Even the simpler ratelimiting regime of bulk-liquid reaction control for a polydisperse system has apparently remained unanalysed so far. Recent work on the concept of kinetic invariance (Bhaskarwar, 1987) has led to some useful approximate analytical solutions describing the dissolution behaviour of small particles. 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. Model Development for the Transition Regime

Analysis of Diffusion-Controlled Dissolution from Polydisperse Collections of Drug Particles with an Assessed Mathematical Model

“…By balancing the time rate of change in the number of particles from radius R to written in terms of with the time rate of change of particle radius between R and , the differential equation for the time evolution of the particle distribution function can be derived: …”

“…The aim is to Q(R, t)predict, from which the change in volume of all particles, the number of molecules introduced into the bulk and the bulk concentration are determined as a function of time. By balancing the time rate of change in the number of particles from radius R to R + dR written in terms of Q(R, t) with the time rate of change of particle radius R(t) between R and R + dR, the differential equation for the time evolution of the particle distribution Q(R, t)function can be derived 20 :…”

Kinetic invariant model of dissolution with chemical reaction of large particles

“…The diffusion-reaction equations governing the fluid-solid reactions frequently are not amenable to analytical procedures that could lead to general solutions. The pseudosteady-state approximation is, therefore, commonly employed, especially for the gas-solid reactions (Bischoff, 1963;Luss, 1968;Sidorov et al, 1986;Bhaskarwar, 1988Bhaskarwar, , 1989. In general, the aforestated approximation may be valid for the gas-solid reacting systems, but not always for the liquid-solid s~ stems (e.g., ion exchange).…”

“…LeBlanc and Fogler (1987) described the rate-limiting regimes in the dissolution of polydisperse particulates. C nder certain circumstances, different possible controlling steps might be in a concurrent action (Bischoff, 1963;Sidorov et al, 1986;Bhaskarwar, 1988Bhaskarwar, , 1989. Nonisothermal fluid-solid reactions have also received the attention of some researchers (Carberry, 1976;Luss and Amundson, 1969).…”

“…It has been used recently for description of the kinetics of a complex multiphase process of organic synthesis (Sidorov et al, 1986). Approximate analytical and rigorous numerical solutions of a comparatively more logical kinetic invariant model are available now for the dissolution of very fine monodisperse (Bhaskarwar, 1988) and polydisperse (Bhaskarwar, 1989) solid particles under the conditions of negligible slip velocity between the particles and liquid phase. This article extends the kinetic invariance analysis to the more practical case of large, monodisperse solid particles with their significant characteristic slip velocities.…”