### 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 language | English |
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Title of host publication | Recent Developments of Mathematical Fluid Mechanics |

Publisher | Springer Verlag |

Pages | 111-134 |

Number of pages | 24 |

Volume | none |

ISBN (Print) | 9783034809382 |

DOIs | |

Publication status | Published - 2016 |

Event | International Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata’s 60th Birthday, 2013 - Nara, Japan Duration: 2013 Mar 5 → 2013 Mar 9 |

### Other

Other | International Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata’s 60th Birthday, 2013 |
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Country | Japan |

City | Nara |

Period | 13/3/5 → 13/3/9 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent

AU - Bothe, Dieter

AU - Soga, Kohei

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Entropy principle

KW - Incompressible limit

KW - Mass transfer

KW - Two-phase fluid system

UR - http://www.scopus.com/inward/record.url?scp=84964297977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964297977&partnerID=8YFLogxK

U2 - 10.1007/978-3-0348-0939-9_7

DO - 10.1007/978-3-0348-0939-9_7

M3 - Conference contribution

AN - SCOPUS:84964297977

SN - 9783034809382

VL - none

SP - 111

EP - 134

BT - Recent Developments of Mathematical Fluid Mechanics

PB - Springer Verlag

ER -