| Issue |
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2835 - 2863 | |
| DOI | https://doi.org/10.1051/m2an/2023045 | |
| Published online | 19 September 2023 | |
Analysis of compressible bubbly flows. Part I: construction of a microscopic model
1
Institut Montpelliérain Alexander Grothendieck, Univ Montpellier, CNRS, Montpellier, France
2
INRIA & Institut Montpelliérain Alexander Grothendieck, Univ Montpellier, CNRS, Montpellier, France
* Corresponding author: matthieu.hillairet@umontpellier.fr
Received:
15
September
2022
Accepted:
16
May
2023
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.
Mathematics Subject Classification: 76T05 / 76T10 / 35Q30
Key words: Two-phase flows / compressible Navier–Stokes equations / Cauchy theory
© The authors. Published by EDP Sciences, SMAI 2023
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