Analysis of spherical crystal dissolution in the solution

Abstract

Dissolution has attracted considerable attention since the dissolution is a common phenomenon in nature, and is of fundamental interest to reveal the morphology evolutions and microstructures of materials in materials science and pharmaceutical industry. A lot of research has been made in the field of crystal dissolution. And the solid-liquid interfacial energy is recognized as playing a key role in a wide range of material phenomena.The goal of the present study is to present analytical results for the dissolution of spherical crystal with the consideration of surface tension. In this review, we introduce the recent progress of spherical particle dissolution through similar studies. In our paper, a mathematical model is proposed to describe the dissolution process of a spherical crystal with moving boundary. The effect of surface tension through the Gibbs-Thomson condition is included in the mathematical model. And the dissolution of the spherical crystal is considered from the perspective of the concentration change of the solution. An asymptotic solution of the concentration and morphology for a spherical crystal in the dissolution is obtained by using the matched asymptotic expansion method. The results show that the surface tension has great effects on the concentration and interface shape of spherical crystal dissolution. As the surface tension parameter increases, the radius of the crystal decreases, the velocity of the spherical dissolution and the concentration of the solution increase. We have the conclusion that surface tension accelerates the dissolution process of the spherical crystal. And the larger the surface tension parameter, the faster the dissolution rate is and the shorter the dissolution time. The particle radius decreases with time going by, and the dissolution velocity increases with time increasing until the dissolution is completed. The concentration of the dissolution and interface shape of the spherical crystal can be calculated with the results obtained in this paper. It is shown that our analytical results accord well with the results obtained from the numerical results of Vermolen et al. [Vermolen F J, Vuik C, Zwaag S V D 2003 Mater. Sci. Eng. A 347 265].