Solid dissolution in a fluid solvent is characterized by the interplay of surface area-dependent diffusion and physical fragmentation

Muhammad H. Zaman,Andrew J. Acevedo,R. J. Seager,Fabian Spill

doi:10.1038/s41598-018-25821-x

Abstract

The processes of dissolution and fragmentation have high relevance in pharmaceutical research, medicine, digestive physiology, and engineering design. Experimentally, dissolution and fragmentation are observed to occur simultaneously, yet little is known about the relative importance of each of these processes and their impact on the dissolution process as a whole. Thus, in order to better explain these phenomena and the manner in which they interact, we have developed a novel mathematical model of dissolution, based on partial differential equations, taking into consideration the two constituent processes of surface area-dependent diffusive mass removal and physical fragmentation of the solid particles, and the basic physical laws governing these processes. With this model, we have been able to quantify the effects of the interplay between these two processes and determine the optimal conditions for rapid solid dissolution in liquid solvents. We were able to reproduce experimentally observed phenomena and simulate dissolution under a wide range of experimentally occurring conditions to give new perspectives into the kinetics of this common, yet complex process. Finally, we demonstrated the utility of this model to aid in experiment and device design as an optimisation tool.

Highlights

Dissolution, by definition, is the process wherein the mixture of two phases results in a new, homogeneous phase– that is, the solution[1,2]
Nernst and Brunner developed a model which built upon its predecessors by explicitly describing dissolution as the diffusion of solute molecules across a boundary layer of unstirred solvent surrounding each dissolving particle, noting that the rate of diffusion is inversely proportional to the width of this unstirred boundary layer, and that the width is affected by the flow properties of the fluid around it[10,11]
We will use our modelling framework to demonstrate the influence of both diffusive mass removal and particle fragmentation on the overall dissolution process

Summary

Introduction

Dissolution, by definition, is the process wherein the mixture of two phases results in a new, homogeneous phase– that is, the solution[1,2]. The word dissolution commonly describes a specific class of these processes wherein a solid is dissolved in a liquid, with the solid forming the minor component of the mixture, known as the solute, and the liquid forming the major component, or the solvent[2,4] In this specific class of dissolution processes, the liquid solvent interacts with any exposed surface area on the solute structure. The early mathematical foundations of dissolution are based on the work of Noyes and Whitney Their eponymous model was among the first to describe dissolution as a diffusive process, proportional to the difference between the saturation concentration of the solute in the solvent, or the solubility, and the bulk concentration of the solute in the solvent[7]. For a more in-depth review of the historical progression of dissolution modelling, this matter has been discussed extensively by Siepmann and Dokoumetzidis[13,14]

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