Foam structures have been attracting many scientists for a long time. However, the physics behind these structures is very complicated, and complete modeling has not yet been achieved. In this paper, a phase-field modeling of the rearrangement process of foam structures was proposed, and simulations were conducted to show its effectiveness. Adjacent foam cells were assumed to interact with each other through the pressure difference, and four different conditions were introduced. When the cells had identical inner pressures at the initial state, they were stabilized, keeping the initial volume. In contrast, a volumetric change occurred when the amount of the substance in the initial cells was provided. Other models to regenerate small-cell distribution were also proposed, and the foam structures observed in real liquid foam were successfully reproduced.
References
[1]
Liu. P.S. and Chen, G.F. (2014) Porous Materials: Processing and Applications. Tsinghua University Press.
[2]
Gibson, L.J. and Ashby, M.F. (1988) Cellular Solids: Structure and Properties. Cambridge University Press.
[3]
Ashby, M., Evans, A., Fleck, N., Gibson, L., Hutchinson, J., Wadley, H., et al. (2001) Metal Foams: A Design Guide. Applied Mechanics Reviews, 54, B105-B106. https://doi.org/10.1115/1.1421119
[4]
Kulshreshtha, A. and Dhakad, S.K. (2020) Preparation of Metal Foam by Different Methods: A Review. Materials Today: Proceedings, 26, 1784-1790. https://doi.org/10.1016/j.matpr.2020.02.375
[5]
Aste, T. and Weaire, D. (2008) The Pursuit of Perfect Packing. Taylor & Francis.
[6]
Saye, R.I. and Sethian, J.A. (2013) Multiscale Modeling of Membrane Rearrangement, Drainage, and Rupture in Evolving Foams. Science, 340, 720-724. https://doi.org/10.1126/science.1230623
[7]
Bae, J., Lee, K., Seo, S., Park, J.G., Zhou, Q. and Kim, T. (2019) Controlled Open-Cell Two-Dimensional Liquid Foam Generation for Micro-and Nanoscale Patterning of Materials. Nature Communications, 10, Article No. 3209. https://doi.org/10.1038/s41467-019-11281-y
[8]
Guidolin, C., Mac Intyre, J., Rio, E., Puisto, A. and Salonen, A. (2023) Viscoelastic Coarsening of Quasi-2D Foam. Nature Communications, 14, Article No. 1125. https://doi.org/10.1038/s41467-023-36763-y
[9]
Weaire, D. and Phelan, R. (1994) A Counter-Example to Kelvin’s Conjecture on Minimal Surfaces. Philosophical Magazine Letters, 69, 107-110. https://doi.org/10.1080/09500839408241577
[10]
Weaire, D. and Hutzler, S. (2000) The Physics of Foams. Oxford University Press.
[11]
Uehara, T. and Suzuki, H. (2012) Numerical Simulation of Homogeneous Polycrystalline Grain Formation Using Multi-Phase-Field Model. Applied Mechanics and Materials, 197, 628-632. https://doi.org/10.4028/www.scientific.net/amm.197.628
[12]
Uehara, T. (2014) Numerical Simulation of Foam Structure Formation and Destruction Process Using Phase-Field Model. Advanced Materials Research, 1042, 65-69. https://doi.org/10.4028/www.scientific.net/amr.1042.65
[13]
Uehara, T. (2015) Phase-field Modeling for the Three-Dimensional Space-Filling Structure of Metal Foam Materials. Open Journal of Modelling and Simulation, 3, 120-125. https://doi.org/10.4236/ojmsi.2015.33013
[14]
Steinbach, I., Pezzolla, F., Nestler, B., Seeßelberg, M., Prieler, R., Schmitz, G.J., et al. (1996) A Phase Field Concept for Multiphase Systems. Physica D: Nonlinear Phenomena, 94, 135-147. https://doi.org/10.1016/0167-2789(95)00298-7
[15]
Steinbach, I. and Pezzolla, F. (1999) A Generalized Field Method for Multiphase Transformations Using Interface Fields. Physica D: Nonlinear Phenomena, 134, 385-393. https://doi.org/10.1016/s0167-2789(99)00129-3
[16]
Uehara, T. (2021) Simulation of Polyhedral Crystal Growth Based on the Estimated Surface Energy of Crystallographic Planes. Materials Sciences and Applications, 12, 519-533. https://doi.org/10.4236/msa.2021.1211034
