Analysis of compressible bubbly flows. Part I : construction of a microscopic model

Matthieu Hillairet (1) , Hélène Mathis (2) , Nicolas Seguin (3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Two-phase flows; compressible Navier-Stokes equations; Cauchy theory

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Hillairet, Hélène Mathis, Nicolas Seguin. Analysis of compressible bubbly flows. Part I : construction of a microscopic model. 2022. ⟨hal-03621294⟩