Numerical Phase-Field Model Validation for Dissolution of Minerals

Abstract

Modelling of a mineral dissolution front propagation is of interest in a wide range of scientific and engineering fields. The dissolution of minerals often involves complex physico-chemical processes at the solid–liquid interface (at nano-scale), which at the micro-to-meso-scale can be simplified to the problem of continuously moving boundaries. In this work, we studied the diffusion-controlled congruent dissolution of minerals from a meso-scale phase transition perspective. The dynamic evolution of the solid–liquid interface, during the dissolution process, is numerically simulated by employing the Finite Element Method (FEM) and using the phase–field (PF) approach, the latter implemented in the open-source Multiphysics Object Oriented Simulation Environment (MOOSE). The parameterization of the PF numerical approach is discussed in detail and validated against the experimental results for a congruent dissolution case of NaCl (taken from literature) as well as on analytical models for simple geometries. In addition, the effect of the shape of a dissolving mineral particle was analysed, thus demonstrating that the PF approach is suitable for simulating the mesoscopic morphological evolution of arbitrary geometries. Finally, the comparison of the PF method with experimental results demonstrated the importance of the dissolution rate mechanisms, which can be controlled by the interface reaction rate or by the diffusive transport mechanism.

Phase field modelling of crystal growth of NaCl in two dimensions

“…Both S and L are physical parameters that can be determined experimentally 34 or computationally. 29,35 The surface energy S (ref. 35) depends on the direction of the Miller planes.…”

“…22-24. It has to a much lesser extent been employed in relation to the precipitation and dissolution processes involved in crystallization that is controlled by a discontinuous solute concentration at the solid-liquid interface, [25][26][27][28] and PF modelling of the crystallization of real systems with direct quantitative comparison to experimental data is rare. [29][30][31] According to reaction diffusion theory ionic crystals develop a diffuse interface of several tens of micrometres in solution 32,33 and the PF model is in principle well suited to provide quantitative results on microscopic and macroscopic scales for such systems. The model is appealing because it can provide information about properties such as the crystal growth rate and the growth mode.…”

A phase-field approach for portlandite carbonation and application to self-healing cementitious materials

“…30%. Based on the relationship between the diffusion coefficient, the open porosity and the pore morphology [68,69], D sou is set to be 5 orders of magnitude smaller than in its solution. As this is a crack scale model, it operates both with ion diffusivity in pore (crack) solution and effective diffusivity through porous matrix.…”

Modeling of Particle Dissolution Behavior Using a Geometrical Phase-Field Approach

“…In the literature, references with different focuses on the dissolution process can be found. It ranges from intrinsic dissolution experiments of single crystal dissolution , to analytical equations for predicting dissolution process − and numerical models. − Nevertheless, the basis of these experiments, calculations, and models is the dissolution behavior of each single substance used for these formulations. However, previous work has shown that the dissolution behavior of drugs is not limited only by diffusion and convection.…”