General solution for diffusion‐controlled dissolution of spherical particles. 1. Theory

Abstract

Three classical particle dissolution rate expressions are commonly used to interpret particle dissolution rate phenomena. Our analysis shows that an assumption used in the derivation of the traditional cube-root law may not be accurate under all conditions for diffusion-controlled particle dissolution. Mathematical analysis shows that the three classical particle dissolution rate expressions are approximate solutions to a general diffusion layer model. The cube-root law is most appropriate when particle size is much larger than the diffusion layer thickness, the two-thirds-root expression applies when the particle size is much smaller than the diffusion layer thickness. The square-root expression is intermediate between these two models. A general solution to the diffusion layer model for monodispersed spherical particles dissolution was derived for sink and nonsink conditions. Constant diffusion layer thickness was assumed in the derivation. Simulated dissolution data showed that the ratio between particle size and diffusion layer thickness (a0/h) is an important factor in controlling the shape of particle dissolution profiles. A new semiempirical general particle dissolution equation is also discussed which encompasses the three classical particle dissolution expressions. The success of the general equation in explaining limitations of traditional particle dissolution expressions demonstrates the usefulness of the general diffusion layer model.

The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder

“…Numerous models have been proposed for rehydration/dissolution kinetics [6], including empirical/semi-empirical (Weibull function [16]) as well as mechanistically realistic ones (e.g. diffusion [24], swelling [3] and erosion/degradation [22]). …”

Development of a Novel Simplified PBPK Absorption Model to Explain the Higher Relative Bioavailability of the OROS® Formulation of Oxybutynin

“…Particularly for OXY, the dissolution rate was predicted by using a modification of the model proposed by Wang and Flanagan for spherical particles dissolving over time (53,63,64) as shown in Eq. 19,…”

“…The time-varying radius for the dissolving spherical particles was calculated using Eq. 20 (63,64,67). When the particle radius reached a critical value of 10 −9 cm, the dissolution was assumed complete and the dissolution rate was assumed to be zero.…”

Understanding the Effect of API Properties on Bioavailability Through Absorption Modeling

“…Equations 1 and 2 can be further modified to account for gastrointestinal transit of the particles which was the initial derivation by Dressman and Fleisher, changes in the effective boundary layer thickness over time (9), cylindrical geometry instead of spherical (17), or for the nonlinear concentration gradient across the diffusion layer of spherical particles as proposed by Wang and Flanagan model (18). Currently available commercial software packages apply the above discussed principles to simulate in vivo dissolution of drug compounds.…”