{"title":"Analysis of compressible bubbly flows. Part I: Construction of a microscopic model.","authors":"M. Hillairet, H. Mathis, N. Seguin","doi":"10.1051/m2an/2023045","DOIUrl":null,"url":null,"abstract":"In this note, we introduce a microscopic model for the motion of gas bubbles in a viscous\nfluid. By interpreting a bubble as a compressible fluid with infinite shear viscosity, we\nderive a pde/ode system coupling the density/velocity/pressure in the surrounding\nfluid with the linear/angular velocities and radii of the bubbles. We provide a 1D analogue of the system and\nconstruct an existence theory for this simplified system in a natural regularity framework. The\nsecond part of the paper is a preparatory work for the derivation of an averaged or macroscopic\nmodel.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/m2an/2023045","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
Abstract
In this note, we introduce a microscopic model for the motion of gas bubbles in a viscous
fluid. By interpreting a bubble as a compressible fluid with infinite shear viscosity, we
derive a pde/ode system coupling the density/velocity/pressure in the surrounding
fluid with the linear/angular velocities and radii of the bubbles. We provide a 1D analogue of the system and
construct an existence theory for this simplified system in a natural regularity framework. The
second part of the paper is a preparatory work for the derivation of an averaged or macroscopic
model.
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