@inproceedings{216d25973ae84f0bb54f9892e0ff3892,

title = "Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent",

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.",

keywords = "Entropy principle, Incompressible limit, Mass transfer, Two-phase fluid system",

author = "Dieter Bothe and Kohei Soga",

note = "Funding Information: This work was supported by the DFG within scope of the IRTG 1529 {"}Mathematical Fluid Dynamics{"} and by the JSPS Japanese-German Graduate Externship. The authors gratefully acknowledge this support. Publisher Copyright: {\textcopyright} Springer Basel 2016.; International Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata{\textquoteright}s 60th Birthday, 2013 ; Conference date: 05-03-2013 Through 09-03-2013",

year = "2016",

doi = "10.1007/978-3-0348-0939-9_7",

language = "English",

isbn = "9783034809382",

series = "Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday",

publisher = "Springer Verlag",

pages = "111--134",

editor = "Yoshikazu Giga and Hideo Kozono and Masao Yamazaki and Hisashi Okamoto and Herbert Amann",

booktitle = "Recent Developments of Mathematical Fluid Mechanics",

}