Diffusion‐limited dissolution of spherical particles: A critical evaluation and applications of approximate solutions

Abstract

The analytical and numerical description of the effective dissolution kinetics of spherical particles into a solvent is often difficult in chemical and metallurgical engineering. The crucial first step is to identify the dissolution mechanisms, and subsequently, relevant kinetics parameters can be calculated. In this article, three frequently used approximations, i.e., the invariant‐field (IF) (Laplace), reverse‐growth (RG), and invariant‐size (IS) (stationary‐interface) approximations, are systematically discussed and compared with numerical simulation results. The relative errors of the dissolution curves and total dissolution time of the three approximations to the numerical simulations are calculated. The results reveal the appropriate application ranges of the approximations for given precision levels. With further experimental validation, this research provides a methodology to properly assess dissolution kinetics and adequately estimate effective diffusion coefficients and activation energy under the experimental uncertainties. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2926–2934, 2017

Quantitative Study on Dissolution Behavior of Nd2O3in Fluoride Melts

“…It can be seen that the k values in the systems are always small, and the dissolution in such systems is governed by the concentration profile in a steady state, which is the same in one system and determined by C I , C M , and C P . 20 This also suggests that the influence of the transition period before steady state is negligible. When a small disturbance occurs, the influence of the interruption before the establishment of a new stable concentration field is considered to be insignificant.…”

“…19 Approximate solutions are alternatives for solving related problems. To select an appropriate approximation, 20 the supersaturation index k is a crucial physicochemical parameter, expressing the supersaturation ratio, defined as 19 where C M is the far-field concentration of the solute in the solution in mol/L, C P is the composition of the particle in mol/L, which is taken as a constant in this study, and C I is the equilibrium concentration of the solute at the interface in mol/L.…”

“…20 In the IF approximation, the relationship between particle radius and time is described by 19 The theoretical dissolution curves of interface reaction (IR) control (eq 1) and of diffusion control (eq 7) are shown in Figure 4. Comparing the experimental data with theoretical curves can reveal the rate-limiting step(s) of the dissolution.…”

Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

“…Thus, if an exact analytical solution of the dissolving spherical particle could be found, perhaps solving Equation (1) instead of the standard Fick's second law could be an option. According to Aaron et al [6] and Guo et al [7], the reversed-growth approximation is not the best method to calculate the dissolution rates. However, one can acknowledge from the comparison made in [6] between the dissolution rates calculated by the recommended method (invariant size-approximation) and the reversed-growth approximation, that the dissolution times calculated by both methods are close one to each other, especially in the limit of small supersaturation.…”

“…For the modelling of dissolution, mathematical treatments are curiously not well developed since, according to Aaron et al [6], there is no exact solution available for spherical precipitates. This statement was written in 1970 but has been recently acknowledged by Guo et al [7]. The available dissolution models, therefore, have been based, up to now, on one of the frequently used approximate solutions.…”