Dissolution kinetics of crystals in suspension and its application to l-aspartic acid crystals

doi:10.1016/S1385-8947(01)00259-5

Chemical Engineering Journal

Volume 88, Issues 1–3, 28 September 2002, Pages 53-58

https://doi.org/10.1016/S1385-8947(01)00259-5 Get rights and content

Abstract

The kinetics of the dissolution of l-aspartic acid crystals under the gentle and vigorous agitation was investigated. A dissolution rate equation was derived by assuming two steps: the disintegration of molecules from the surface of crystals and the mass transfer of disintegrated molecules into the bulk solution. An intrinsic expression of the relationship between the solute concentration of the bulk solution and the dissolution time was also derived. The dissolution process of monodisperse and polydisperse crystals of l-aspartic acid was well estimated, and the change of crystal size distribution of polydisperse crystals during dissolution was simulated with good accuracy.

Introduction

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. The importance of dissolution kinetics is not, however, confined to the pharmaceutical industry but the dissolution kinetics also has important implications in industrial crystallization processes. For example, the dissolution of fine crystals is effective for the production of large crystals with narrow size distribution [1], [2]. Moreover, the solvent-mediated transformation of crystal polymorphs involves the process of dissolution of metastable crystals [3].

Many efforts have been made to describe the crystal dissolution behavior. Noyes and Whitney [4] expressed the dissolution rate by assuming that the process is diffusion controlled and involves no chemical reaction. Their equation simply expresses that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration. Dressman and Fleisher [5] developed an expression based on the Noyes–Whitney equation, where the dissolution rate was expressed as a function of the remaining surface area of the crystal and the concentration gradient across the boundary layer. Hintz and Johnson [6] and Lu et al. [7] used the same dissolution rate expression, assuming a mass transfer controlled process, to simulate the dissolution of drugs in polydisperse powder form. These latter studies were made to deal with the oral absorption of drugs.

In industrial crystallization, not only mass transfer but also surface reaction (disintegration of crystals) must be taken into account in order to understand the dissolution process because industrial crystallization is not always carried out under gentle agitation. However, there are only few reports dealing with the effect of the surface reaction rate on the dissolution rate (see e.g. [8]).

In this paper, we examine the dissolution kinetics of crystals in suspension by taking into account the effects of the surface reaction and mass transfer. An analytical equation describing the relationship between the solute concentration and the dissolution time was obtained. Based on our analytical equation, the dissolution rate constant of l-aspartic acid crystals was determined. Furthermore, the change of CSD of polydisperse l-aspartic crystals during dissolution process was simulated in success.

Section snippets

Kinetics of crystal dissolution

We assume a consecutive process for crystal dissolution as presented in Fig. 1. First, crystals are disintegrated at the crystal surface, and then the solute diffuses from the surface to the bulk solution. This is the reverse process of crystal growth. Assuming that the disintegration rate r_d and the diffusion rate r_dif are proportional to a, being the surface area of the remaining crystals per unit volume of solution, and the difference of concentration as a driving force, we obtain two

Solubility of l-aspartic acid

l-Aspartic acid used was of reagent grade and purchased from Wako Pure Chemical Industries, Japan. The concentration of l-aspartic acid was determined from UV absorption at 210 nm. The solubility of l-aspartic acid in water was determined by dissolving crystals in water over the temperature range from 5 to 60 °C.

Dissolution of monodisperse crystals of l-aspartic acid

l-Aspartic acid crystals were precipitated from an aqueous supersaturated solution using a jacketed glass batch crystallizer with a working volume of 200 ml at 20 °C. The crystals were

Dissolution of monodisperse crystals and estimation of dissolution rate constant k

The changes in the bulk concentration C_b at 30 °C are presented in Fig. 2 as a function of time for monodisperse crystals of l-aspartic acid with L of 200 μm with the agitation rate as parameter. The dissolution rate increased with an increase in agitation rate up to 500 rpm, but not when the agitation was in excess of 500 rpm. The dissolution model presented in Fig. 1 can explain this result; namely, for agitation rates less than 500 rpm the dissolution rate is strongly affected by a mass transfer

Conclusions

We have presented here an investigation of dissolution kinetics that can be used for analyzing the dissolution of crystals suspended under agitation. The dissolution rate equation (Eq. (13)) was derived by taking into account the disintegration of molecules at the surface of the crystal and mass transfer. Furthermore, an intrinsic expression of the change in C_b during dissolution was derived (Eq. (16)). When l-aspartic acid crystals of a given size were dissolved under agitation, the

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