Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent

Dieter Bothe, Kohei Soga

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We derive mathematical models of the elementary process of dissolution/growth of bubbles in a liquid under pressure control. The modeling starts with a fully compressible version, both for the liquid and the gas phase so that the entropy principle can be easily evaluated. This yields a full PDE system for a compressible two-phase fluid with mass transfer of the gaseous species. Then the passage to an incompressible solvent in the liquid phase is discussed, where a carefully chosen equation of state for the liquid mixture pressure allows for a limit in which the solvent density is constant. We finally provide a simplification of the PDE system in case of a dilute solution.

Original languageEnglish
Title of host publicationRecent Developments of Mathematical Fluid Mechanics
EditorsYoshikazu Giga, Hideo Kozono, Masao Yamazaki, Hisashi Okamoto, Herbert Amann
PublisherSpringer Verlag
Pages111-134
Number of pages24
ISBN (Print)9783034809382
DOIs
Publication statusPublished - 2016
EventInternational Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata’s 60th Birthday, 2013 - Nara, Japan
Duration: 2013 Mar 52013 Mar 9

Publication series

NameAdvances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday
Volumenone

Other

OtherInternational Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata’s 60th Birthday, 2013
CountryJapan
CityNara
Period13/3/513/3/9

Keywords

  • Entropy principle
  • Incompressible limit
  • Mass transfer
  • Two-phase fluid system

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

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