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Published in:
The Work of Yoshihiro Shibata Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Thermodynamically Consistent Modeling for Dissolution/Growth of Bubbles in an Incompressible Solvent

Authors : Dieter Bothe, Kohei Soga

Published in: Recent Developments of Mathematical Fluid Mechanics

Publisher: Springer Basel

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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.

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previous chapter On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case
next chapter On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary
Appendix
Available only for authorised users
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Metadata
Title
Thermodynamically Consistent Modeling for Dissolution/Growth of Bubbles in an Incompressible Solvent
Authors
Dieter Bothe
Kohei Soga
Copyright Year
2016
Publisher
Springer Basel
Book
Recent Developments of Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-0938-2

Electronic ISBN: 978-3-0348-0939-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-0348-0939-9_7

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