<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.</p></abstract>

The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.

Dynamics of a bubble rising in gravitational field

CNR-INSEAN, Marine Technology Research Institute, Italy

Department of Industrial and Information Engineering, Second University of Naples, Italy

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Dynamics of a bubble rising in gravitational field"}

The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is...

Dynamics of a bubble rising in gravitational field

Published Online: May 20, 2016

Page range: 48 - 67

Received: Nov 11, 2014

Accepted: Jun 22, 2015

DOI: https://doi.org/10.1515/caim-2016-0018

Keywords
cavitation, bubble dynamics, Rayleigh-Plesset equation

© 2016 Enrico De Bernardis et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Dynamics of a bubble rising in gravitational field

Published Online: May 20, 2016

Page range: 48 - 67

Received: Nov 11, 2014

Accepted: Jun 22, 2015

DOI: https://doi.org/10.1515/caim-2016-0018

Keywordscavitation, bubble dynamics, Rayleigh-Plesset equation

© 2016 Enrico De Bernardis et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
cavitation, bubble dynamics, Rayleigh-Plesset equation