A variationally consistent and asymptotically convergent phase-field model for solute precipitation and dissolution
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909693394288640 |
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| author | Lamperti, Andrea De Lorenzis, Laura |
| author_facet | Lamperti, Andrea De Lorenzis, Laura |
| contents | We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the solute ion concentration and the phase-field variable, are derived in a variationally consistent way starting from a free energy functional of Modica-Mortola type. The phase-field variable is assumed to follow the non-conservative Allen-Cahn evolution law, whereas the solute ion concentration obeys the conservative Cahn-Hilliard equation. We also assess the convergence of the new model to the corresponding sharp-interface model via the method of matched asymptotic expansions, and derive a novel expression of the reaction rate of the sharp-interface model. Through a finite element discretization, we present several numerical examples in two and three dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A variationally consistent and asymptotically convergent phase-field model for solute precipitation and dissolution Lamperti, Andrea De Lorenzis, Laura Computational Physics We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the solute ion concentration and the phase-field variable, are derived in a variationally consistent way starting from a free energy functional of Modica-Mortola type. The phase-field variable is assumed to follow the non-conservative Allen-Cahn evolution law, whereas the solute ion concentration obeys the conservative Cahn-Hilliard equation. We also assess the convergence of the new model to the corresponding sharp-interface model via the method of matched asymptotic expansions, and derive a novel expression of the reaction rate of the sharp-interface model. Through a finite element discretization, we present several numerical examples in two and three dimensions. |
| title | A variationally consistent and asymptotically convergent phase-field model for solute precipitation and dissolution |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2507.13270 |