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

Fingerprint

Dissolution
Liquids
Pressure control
Bubbles (in fluids)
Equations of state
Entropy
Mass transfer
Gases
Mathematical models
Fluids

Keywords

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

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

Cite this

Bothe, D., & Soga, K. (2016). Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent. In Recent Developments of Mathematical Fluid Mechanics (Vol. none, pp. 111-134). Springer Verlag. https://doi.org/10.1007/978-3-0348-0939-9_7

Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent. / Bothe, Dieter; Soga, Kohei.

Recent Developments of Mathematical Fluid Mechanics. Vol. none Springer Verlag, 2016. p. 111-134.

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

Bothe, D & Soga, K 2016, Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent. in Recent Developments of Mathematical Fluid Mechanics. vol. none, Springer Verlag, pp. 111-134, International Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata’s 60th Birthday, 2013, Nara, Japan, 13/3/5. https://doi.org/10.1007/978-3-0348-0939-9_7
Bothe D, Soga K. Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent. In Recent Developments of Mathematical Fluid Mechanics. Vol. none. Springer Verlag. 2016. p. 111-134 https://doi.org/10.1007/978-3-0348-0939-9_7
Bothe, Dieter ; Soga, Kohei. / Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent. Recent Developments of Mathematical Fluid Mechanics. Vol. none Springer Verlag, 2016. pp. 111-134
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