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Foam drainage equation in fractal dimensions: breaking and instabilities

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Abstract

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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Acknowledgements

The authors would like to thank the anonymous referees for useful comments and valuable suggestions.

Funding

The authors would like to thank Chiang Mai University for funding this research.

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Authors and Affiliations

  1. Faculty of Engineering, Center of Excellence in Quantum Technology, Chiang Mai University, Chiang Mai, 50200, Thailand

    Rami Ahmad El-Nabulsi & Waranont Anukool

  2. Quantum-Atom Optics Laboratory and Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Rami Ahmad El-Nabulsi & Waranont Anukool

  3. Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Waranont Anukool

  4. Institute of Hydrobiology, Biology Centre of the Czech Academy of Sciences, České Budějovice, Czech Republic

    Rami Ahmad El-Nabulsi

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  1. Rami Ahmad El-Nabulsi
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RAE-N contributed to the conceptualization, formal analysis, investigation, and methodology; WA contributed to the sources and investigation.

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Correspondence to Rami Ahmad El-Nabulsi.

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El-Nabulsi, R.A., Anukool, W. Foam drainage equation in fractal dimensions: breaking and instabilities. Eur. Phys. J. E 46, 110 (2023). https://doi.org/10.1140/epje/s10189-023-00368-6

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