Diffusion-Controlled Quasi-Stationary Mass Transfer for an Isolated Spherical Particle in an Unbounded Medium

TL;DR

This paper develops a comprehensive mathematical framework for diffusion-controlled mass transfer around a spherical particle, providing exact solutions and practical formulas for particle radius evolution in dissolution and precipitation processes.

Contribution

It introduces a unified formulation with exact analytical solutions and semi-empirical formulas for quasi-stationary mass transfer around isolated spherical particles.

Findings

Exact analytical solutions covering all parameters

Explicit formulas for particle radius over time

Applicable to dissolution and precipitation scenarios

Abstract

A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the diffusion-controlled quasi-stationary process, a mathematically complete set of the exact analytical solutions is obtained in implicit forms to cover the entire parameter range. Furthermore, accurate explicit formulas for the particle radius as a function of time are also constructed semi-empirically for convenience in engineering practice. Both dissolution of a particle in a solvent and growth of it by precipitation in a supersaturated environment are considered in the present work.