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

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
PublisherSpringer Verlag
Pages111-134
Number of pages24
Volumenone
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

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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