Numerical Phase-Field Model Validation for Dissolution of Minerals
Source abstract
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.
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Research context
OpenAlex topics: Solidification and crystal growth phenomena · Aluminum Alloy Microstructure Properties · Advanced Mathematical Modeling in Engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Institute of Construction and Building Materials, TU Darmstadt, Franziska Braun-Straße 3, 64287 Darmstadt, Germany
CONICET and LMNI-FIUBA, Universidad de Buenos Aires, Buenos Aires C1127AAR, Argentina
References (100+)
Show source-provided references
1. Wollastonite: Incongruent dissolution and leached layer formation10.1016/S0016-7037(00)00475-0 ↗
2. The incongruent dissolution of scorodite—Solubility, kinetics and mechanism10.1016/j.hydromet.2007.03.003 ↗
3. Reinhardt, H.W., Jonkers, H.M., Van Tittelboom, K., Snoeck, D., De Belie, N., De Muynck, W., Verstraete, W., Wang, J., and Mechtcherine, V. (2013). Recovery against Environmental Action, Springer.10.1007/978-94-007-6624-2_3 ↗
4. Autogenous healing of engineered cementitious composites under wet-dry cycles10.1016/j.cemconres.2009.01.013 ↗
5. A Review of Self-Healing Concrete for Damage Management of Structures10.1002/admi.201800074 ↗
6. Diffusion-limited phase transformations: A comparison and critical evaluation of the mathematical approximations10.1063/1.1658474 ↗
7. Monte Carlo simulations of surface morphologies during mineral dissolution10.1016/0021-9797(89)90232-4 ↗
8. Analytical solution of a mathematical model for rock salt dissolution in still water10.1007/s12517-018-4122-1 ↗
9. Theoretical Analysis of Drug Dissolution: I. Solubility and Intrinsic Dissolution Rate10.1016/j.xphs.2015.12.006 ↗
10. Mathematical modeling of drug dissolution10.1016/j.ijpharm.2013.04.044 ↗
11. Comparison and Analysis of Theoretical Models for Diffusion-Controlled Dissolution10.1021/mp2002818 ↗
12. Diffusion-limited dissolution of spherical particles: A critical evaluation and applications of approximate solutions10.1002/aic.15676 ↗
13. Modeling and comparison of dissolution profiles of diltiazem modified-release formulations10.14227/DT160209P41 ↗
14. General solution for diffusion-controlled dissolution of spherical particles. 2. Evaluation of experimental data10.1002/jps.10039 ↗
15. Mathematical and numerical modelling of limestone dissolution
16. Analytical Model for the Alite (C 3 S) Dissolution Topography10.1111/jace.13647 ↗
17. Quantitative phase field modeling of diffusion-controlled precipitate growth and dissolution in Ti–Al–V10.1016/j.scriptamat.2003.10.032 ↗
18. Domain formation and elastic long-range interaction in ferroelectric perovskites10.1103/PhysRevB.50.5838 ↗
19. Computer simulations of two-dimensional and three-dimensional ideal grain growth10.1103/PhysRevE.74.061605 ↗
20. Phase field microelasticity theory and modeling of multiple dislocation dynamics10.1063/1.1366370 ↗
21. Wen, Y.-H., Chen, L.-Q., and Hawk, J.A. (2012). Phase-field modeling of corrosion kinetics under dual-oxidants. Model. Simul. Mater. Sci. Eng., 20.10.1088/0965-0393/20/3/035013 ↗
22. Vector-valued phase field model for crystallization and grain boundary formation10.1016/S0167-2789(98)00026-8 ↗
23. Phase-Field Models for Microstructure Evolution10.1146/annurev.matsci.32.112001.132041 ↗
24. Phase-field simulation of solidification10.1146/annurev.matsci.32.101901.155803 ↗
25. Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics10.1103/PhysRevE.53.R3017 ↗
26. Phase-Field model for microstructure evolution at the mesoscopic scale10.1146/annurev-matsci-071312-121703 ↗
27. Thermodynamically-consistent phase-field models for solidification10.1016/0167-2789(93)90189-8 ↗
28. An introduction to phase-field modeling of microstructure evolution10.1016/j.calphad.2007.11.003 ↗
29. Provatas, N., and Elder, K. (2011). Phase-Field Methods in Materials Science and Engineering, John Wiley & Sons.10.1002/9783527631520 ↗
30. Phase-field model for isothermal phase transitions in binary alloys10.1103/PhysRevA.45.7424 ↗
31. A phase field model for isothermal solidification of multicomponent alloys10.1016/S1359-6454(01)00184-7 ↗
32. Phase-field model of dendritic growth10.1016/S0022-0248(01)01891-7 ↗
33. Quantitative phase-field model of alloy solidification10.1103/PhysRevE.70.061604 ↗
34. Multicomponent alloy solidification: Phase-field modeling and simulations10.1103/PhysRevE.71.041609 ↗
35. Computation of multiphase systems with phase field models10.1016/S0021-9991(03)00280-8 ↗
36. A reaction model for cement solidification: Evolving the C–S–H packing density at the micrometer-scale10.1016/j.jmps.2018.05.010 ↗
37. Phase-field model with finite interface dissipation10.1016/j.actamat.2012.01.035 ↗
38. Phase field model with a variable chemical potential10.1017/S0308210500001980 ↗
39. Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics10.1021/ar300145c ↗
40. A phase-field model coupled with large elasto-plastic deformation: Application to lithiated silicon electrodes10.1149/2.0171411jes ↗
41. Multi-phase-field modeling of localized corrosion involving galvanic pitting and mechano-electrochemical coupling10.1016/j.corsci.2020.108900 ↗
42. A continuum phase field model for fracture10.1016/j.engfracmech.2010.08.009 ↗
43. Thermodynamically consistent algorithms for a finite-deformation phase-field approach to fracture10.1002/nme.4709 ↗
44. A phase-field modeling approach of hydraulic fracture in saturated porous media10.1016/j.mechrescom.2016.07.002 ↗
45. Free energy of a nonuniform system. I. Interfacial free energy10.1063/1.1744102 ↗
46. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening10.1016/0001-6160(79)90196-2 ↗
47. Phase-field model for solidification of a eutectic alloy10.1098/rspa.1996.0026 ↗
48. Phase-field model for binary alloys10.1103/PhysRevE.60.7186 ↗
49. A phase field concept for multiphase systems10.1016/0167-2789(95)00298-7 ↗
50. Selection of doublet cellular patterns in directional solidification through spatially periodic perturbations10.1103/PhysRevE.58.7492 ↗
51. Phase-field Model for Solidification of Ternary Alloys10.2355/isijinternational.40.870 ↗
52. Interfacial compositions of solid and liquid in a phase-field model with finite interface thickness for isothermal solidification in binary alloys10.1103/PhysRevE.58.3316 ↗
53. The multiphase-field model with an integrated concept for modelling solute diffusion10.1016/S0167-2789(97)00226-1 ↗
54. Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application10.1103/PhysRevE.73.066122 ↗
55. Phase-field model of solute trapping during solidification10.1103/PhysRevE.47.1893 ↗
56. Phase–field model for solidification of Fe–C alloys10.1016/S1468-6996(99)00004-2 ↗
57. Modeling melt convection in phase-field simulations of solidification10.1006/jcph.1999.6323 ↗
58. Phase-field model for multicomponent alloy solidification10.1016/j.jcrysgro.2004.10.002 ↗
59. Phase field method10.1179/174328409X453190 ↗
60. Phase-field modeling of solute precipitation and dissolution10.1063/1.2948949 ↗
61. Phase field modeling of V2O5 hot corrosion kinetics in thermal barrier coatings10.1016/j.commatsci.2014.12.004 ↗
62. Coupling of multicomponent thermodynamic databases to a phase field model: Application to solidification and solid state transformations of superalloys10.1016/S1359-6462(00)00355-9 ↗
63. A phase-field model for the solidification of multicomponent and multiphase alloys10.1016/j.jcrysgro.2005.02.005 ↗
64. Phase-field model of pitting corro-sion kinetics in metallic materials10.1038/s41524-018-0089-4 ↗
65. A phase field model for simulating the pitting corrosion10.1016/j.corsci.2016.04.001 ↗
66. A phase field model for simulating the stress corrosion cracking initiated from pits10.1016/j.corsci.2017.06.006 ↗
67. A quantitative phase-field model of gas bubble evolution in UO210.1016/j.commatsci.2020.109867 ↗
68. New phase field model for simulating galvanic and pitting corrosion processes10.1016/j.electacta.2017.12.086 ↗
69. Phase-field simulation of solidification in multicomponent alloys coupled with ther-modynamic and diffusion mobility databases10.1016/j.actamat.2006.01.029 ↗
70. Phase-field model for solidification of ternary alloys coupled with thermodynamic database10.1016/S1359-6462(02)00557-2 ↗
71. Phase field simulation of equiaxed solidification in technical alloys10.1016/j.actamat.2006.02.008 ↗
72. Definitions of terms relating to phase transitions of the solid state
73. An experimental study of incongruent dissolution of CaCO3 under analogue glacial conditions10.3189/172756505781829223 ↗
74. Dissolution rates of NaCl and KCl in aqueous solution10.1016/0022-0248(81)90377-8 ↗
75. Rutile solubility in H2O, H2O—SiO2, and H2O—NaAlSi3O8 fluids at 0.7–2.0 GPa and 700–1000 C: Implications for mobility of nominally insoluble elements10.1016/j.chemgeo.2008.07.001 ↗
76. Incongruent dissolution and surface area of kaolinite10.1016/0016-7037(92)90383-T ↗
77. Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary10.1016/j.corsci.2006.03.019 ↗
78. Phase-field simulation of multi-phase interactions in Fe-C peritectic solidification10.1016/j.commatsci.2019.109220 ↗
79. Phase-field modeling of eutectic solidification10.1016/j.jcrysgro.2003.08.078 ↗
80. Analysis of diffusion-controlled dissolution from polydisperse collec-tions of drug particles with an assessed mathematical model10.1002/jps.24472 ↗
81. Crystal defects and dissolution10.1016/0378-5173(81)90007-7 ↗
82. The dissolution rate of CA(OH)2 in aqueous solutions10.1080/00986449808912726 ↗
83. The Dissolution of MgO and Mg(OH)2 in Aqueous Solutions10.1149/1.2412273 ↗
84. Modelling the kinetics of calcium hydroxide dissolution in water10.1002/(SICI)1521-401X(199902)27:2<72::AID-AHEH72>3.0.CO;2-H ↗
85. The kinetics of dissolution of slaked lime10.1016/0304-386X(93)90061-H ↗
86. Molecular Dynamics Simulation of NaCl Dissolution10.1021/jp512358s ↗
87. Dissolution dynamics of NaCl nanocrystal in liquid water10.1103/PhysRevE.72.012602 ↗
88. Dissolution of in monocrystalline sodium chloride10.1103/PhysRevB.21.5012 ↗
89. Dissolution process of sodium chloride crystal in water10.1351/pac198860081321 ↗
90. Kinetics of dissolution and recrystallization of sodium chloride at controlled relative humidity10.14356/kona.2011019 ↗
91. Manipulating single microdroplets of NaCl solutions: Solvent dissolution, microcrystallization, and crystal morphology10.1021/acs.langmuir.7b03977 ↗
92. Dissolution of NaCl nanocrystals: An ab initio molecular dynamics study10.1039/C4CP00635F ↗
93. A molecular dynamics study of hydration and dissolution of NaCl nanocrystal in liquid water10.1088/0953-8984/18/45/005 ↗
94. Dissolution of an NaCl crystal with the (111) and (-1-1-1) faces10.1351/pac198961020179 ↗
95. Dissolution of NaCl crystals in artificial saliva and water by video-microscopy10.1016/j.foodres.2015.01.020 ↗
96. The crystal-fluid interfacial free energy and nucleation rate of NaCl from different simulation methods10.1063/1.4921185 ↗
97. Plewa, T., Linde, T., and Weirs, V.G. (2005). Adaptive Mesh Refinement-Theory and Applications, Springer.10.1007/b138538 ↗
98. The effect of particle size and shape on the surface specific dissolution rate of microsized practically in-soluble drugs10.1016/0378-5173(95)00033-F ↗
99. The non-oxidative dissolution of galena nanocrystals: Insights into mineral dissolution rates as a function of grain size, shape, and aggregation state10.1016/j.gca.2008.10.010 ↗
100. Dissolution rates of finely divided drug powders I. Effect of a distribution of particle sizes in a diffu-sion-controlled process10.1002/jps.2600520114 ↗