P. Grassia, C. Torres-Ulloa, Jacobo Hernández-Montelongo
{"title":"A cluster of\n N\n -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures","authors":"P. Grassia, C. Torres-Ulloa, Jacobo Hernández-Montelongo","doi":"10.1098/rspa.2023.0722","DOIUrl":null,"url":null,"abstract":"\n A cluster of\n \n \n N\n \n \n bubbles (with\n \n \n N\n \n \n odd) arranged in a channel in a zigzag staircase configuration is modelled. A limiting case is considered in which the staircase is set into motion by the application of a high driving pressure. In this limit, foam films between bubbles are predicted to become asymptotically flat. Angles at which these flat films are oriented and also bubble pressures are then determined. For\n \n \n N\n \n \n bubbles, the film orientations and bubble pressures differ from predictions for a staircase in the limit of an infinite number of bubbles. Differences are significant towards the downstream end of a staircase, but decay moving upstream. However, the decay is gradual. Hence, a very large\n \n \n N\n \n \n is needed for a finite staircase to align its film orientations towards its upstream end with the orientations in an infinite staircase.\n","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.1098/rspa.2023.0722","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
A cluster of
N
bubbles (with
N
odd) arranged in a channel in a zigzag staircase configuration is modelled. A limiting case is considered in which the staircase is set into motion by the application of a high driving pressure. In this limit, foam films between bubbles are predicted to become asymptotically flat. Angles at which these flat films are oriented and also bubble pressures are then determined. For
N
bubbles, the film orientations and bubble pressures differ from predictions for a staircase in the limit of an infinite number of bubbles. Differences are significant towards the downstream end of a staircase, but decay moving upstream. However, the decay is gradual. Hence, a very large
N
is needed for a finite staircase to align its film orientations towards its upstream end with the orientations in an infinite staircase.
模拟了 N 个气泡群（N 为奇数）在通道中呈之字形阶梯状排列的情况。考虑了一种极限情况，即通过施加高驱动压力使阶梯运动。在这种情况下，预测气泡之间的泡沫薄膜会逐渐变平。然后确定这些平膜的定向角度和气泡压力。对于 N 个气泡，薄膜方向和气泡压力与无限多个气泡极限下的阶梯预测不同。在阶梯的下游端，差异很大，但在上游则逐渐减小。然而，这种衰减是渐进的。因此，有限阶梯需要非常大的 N 才能使其上游端的薄膜方向与无限阶梯的方向一致。
期刊介绍：
Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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