Available phase-field models for precipitation and dissolution [1, 2] are not variationally consistent, i.e. their governing equations are not derived starting from a free-energy functional, and do not incorporate nucleation. On the other hand, they fulfill the requirement that, as the regularization parameter tends to zero, convergence to an appropriate sharp-interface model is achieved. In this work, we develop a variational phase-field framework to model precipitation and dissolution. Our model features a closed-form expression of the free-energy functional, starting from which the non-linear coupled evolution equations of phase indicator and total ion concentration are obtained. The non-conserved phase indicator is assumed to be equal to the local solid volume fraction, and its evolution is governed by the Allen-Cahn equation. On the other hand, the conserved total ion concentration obeys the Cahn-Hilliard evolution law. In addition to being variationally consistent, our set of equations is also proved to converge to the appropriate sharp-interface model by applying the method of matched asymptotic expansions [3]. The variational nature of our proposed model, beside offering a clearer physical interpretation and computational advantages, is also useful to incorporate nucleation of new precipitates, for which we propose a first possible approach.
References:
[1] T. Van Noorden, C. Eck, Phase field approximation of a kinetic movingboundary problem modelling dissolution and precipitation, Interfaces and Free Boundaries 13 (1) (2011) 29–55.
[2] C. Bringedal, L. Von Wolff, I. S. Pop, Phase field modeling of precipitation and dissolution processes in porous media: Upscaling and numerical experiments, Multiscale Modeling & Simulation 18 (2) (2020) 1076–1112.
[3] M. H. Holmes, Introduction to perturbation methods, Vol. 20, Springer Science & Business Media, 2012.
| Subject : | : | oral |
| Topics | : | 5-1 - Computational microstructures |
| PDF version | : |  PDF version |
