https://doi.org/10.1140/epje/s10189-023-00368-6
Tips and Tricks -- Soft Matter
Foam drainage equation in fractal dimensions: breaking and instabilities
1
Faculty of Engineering, Center of Excellence in Quantum Technology, Chiang Mai University, 50200, Chiang Mai, Thailand
2
Quantum-Atom Optics Laboratory and Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, 50200, Chiang Mai, Thailand
3
Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, 50200, Chiang Mai, Thailand
4
Institute of Hydrobiology, Biology Centre of the Czech Academy of Sciences, České Budějovice, Czech Republic
Received:
22
August
2023
Accepted:
18
October
2023
Published online:
13
November
2023
This paper is concerned with the construction of a phenomenological model for drainage of a liquid in foam in fractal dimensions. Our model is based on the concepts of “product-like fractal measure” introduced to model dynamics in porous media and “complex fractional transform” which converts a fractal space on a small scale to a smooth space with a large scale. The solution of the fractal foam drainage equation has been approximated using the He’s homotopy perturbation method. Qualitative analysis shows that the behavior of the solitonic wave in fractal dimensions differ from the behavior in integer dimensions. This deformation generates instabilities in the foam dynamics, dispersion and spontaneous breaking of the solitonic wave.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
