Mathematical Modelling of Phase Transitions in Porous Media
| advisor: | prof. Dr. Ing. Michal Beneš |
| e-mail: | show e-mail |
| type: | phd thesis |
| branch of study: | MI_MM |
| key words: | phase transitions; porous media; phase-field method; structural changes; |
| link: | http://geraldine.fjfi.cvut.cz/~benes/ |
| description: | The Ph.D. project addresses the mathematical aspects of the interaction between air, water, and ice at the interfaces of partially frozen, variably saturated soils. This interaction affects water infiltration, pollutant transport, landscape transformation, damage, and gas release to the atmosphere on a global scale [1]. The dynamics of such phase interfaces within pore structures is a challenging mathematical problem in which the bulk conservation laws for key physical quantities, such as mass, momentum, and energy, are coupled across moving phase interfaces [2, 3]. Phase interfaces can be understood as hypersurfaces described geometrically, which evolve dynamically due to driving forces arising from governing partial differential equations (PDEs) [4, 5]. The difference in the specific volumes of water and ice causes the pores to expand or shrink, displacing grains and allowing water to flow between them. This impacts the surrounding water flow. Transport through the interface film between ice and grains contributes to additional structural changes [6]. This project involves the mathematical analysis of underlying PDEs using variational methods and the numerical solution of PDEs using finite-element and finite-volume methods. These computational studies are motivated by experimental reality. It addresses the formulation and analytical aspects of systems of nonlinear PDEs, including the Cahn-Hilliard theory of phase transitions [7, 8], as well as the structural dynamics generated by phase transitions due to differences in specific volume. It also involves solving such systems of PDEs using advanced numerical methods and computational modeling of scenarios observed in nature or in an experimental environment. The results will be published in relevant, high-impact international journals and presented at international scientific conferences worldwide. This topic is related to ongoing research supported by projects from the Czech Science Foundation, PICTUS at the CTU in Prague, and collaborations with the Faculty of Civil Engineering at the CTU in Prague, the Colorado School of Mines, the USACE ERDC in Vicksburg, and Kanazawa University in Japan. |
| references: | [1] C. Olid, V. Rodellas, G. Rocher-Ros et al.: Groundwater discharge as a driver of methane emissions from Arctic lakes. Nat Commun 13, 3667, 2022, DOI: 10.1038/s41467-022-31219-1. [2] A. Žák, M. Beneš, and T.H. Illangasekare, A.C. Trautz: Mathematical Model of Freezing in a Porous Medium at Micro-Scale. Commun. Comput. Phys. 24 (2), 2018, pp. 557--575. doi: 10.4208/cicp.OA-2017-0082. [3] A. Žák, M. Beneš, and T.H. Illangasekare: Pore-scale model of freezing inception in a porous medium, Comput. Methods Appl. Mech. Engrg., Volume 414, 1 September 2023, 116166, DOI: 10.1016/j.cma.2023.116166. [4] M. E. Gurtin, E. Fried, L. Anand: The Mechanics and Thermodynamics of Continua. Cambridge: Cambridge University Press, (2010). [5] M. E. Gurtin: Thermomechanics of Evolving Phase Boundaries in the Plane, Clarendon Press, Oxford Mathematical Monographs, 1993. [6] A.H. Sweidan, K. Niggemann, Y. Heider, M. Ziegler, B. Markert: Experimental study and numerical modeling of the thermo-hydro-mechanical processes in soil freezing with different frost penetration directions, Acta Geotech. 17 (2022) 231–255, DOI: 10.1007/s11440-021-01191-z. [7] J. W. Cahn, J. E.Hilliard: Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958), 258–267, DOI: 10.1063/1.1744102. [8] P. Strachota, A. Wodecki, M. Beneš: Focusing the latent heat release in 3D phase field simulations of dendritic crystal growth. Modelling Simul. Mater. Sci. Eng. 29 065009 (2021). https://doi.org/10.1088/1361-651X/ac0f55. |
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