{"title":"分形维数的泡沫排水方程:破碎与不稳定。","authors":"Rami Ahmad El-Nabulsi, Waranont Anukool","doi":"10.1140/epje/s10189-023-00368-6","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p><h3>Graphical abstract</h3>\n<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":790,"journal":{"name":"The European Physical Journal E","volume":"46 11","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epje/s10189-023-00368-6.pdf","citationCount":"2","resultStr":"{\"title\":\"Foam drainage equation in fractal dimensions: breaking and instabilities\",\"authors\":\"Rami Ahmad El-Nabulsi, Waranont Anukool\",\"doi\":\"10.1140/epje/s10189-023-00368-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p><h3>Graphical abstract</h3>\\n<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>\",\"PeriodicalId\":790,\"journal\":{\"name\":\"The European Physical Journal E\",\"volume\":\"46 11\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1140/epje/s10189-023-00368-6.pdf\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The European Physical Journal E\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epje/s10189-023-00368-6\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal E","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epje/s10189-023-00368-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
Foam drainage equation in fractal dimensions: breaking and instabilities
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.
期刊介绍：
EPJ E publishes papers describing advances in the understanding of physical aspects of Soft, Liquid and Living Systems.
Soft matter is a generic term for a large group of condensed, often heterogeneous systems -- often also called complex fluids -- that display a large response to weak external perturbations and that possess properties governed by slow internal dynamics.
Flowing matter refers to all systems that can actually flow, from simple to multiphase liquids, from foams to granular matter.
Living matter concerns the new physics that emerges from novel insights into the properties and behaviours of living systems. Furthermore, it aims at developing new concepts and quantitative approaches for the study of biological phenomena. Approaches from soft matter physics and statistical physics play a key role in this research.
The journal includes reports of experimental, computational and theoretical studies and appeals to the broad interdisciplinary communities including physics, chemistry, biology, mathematics and materials science.
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