Bubble expansion rates in viscous compressible liquid

Kou Yamada,Hiroyuki Emori,Kiyoshi Nakazawa

doi:10.1186/bf03351991

Kou Yamada, Hiroyuki Emori + Show 1 more

Open Access

https://doi.org/10.1186/bf03351991

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Abstract

Abstract A new equation has been derived for radial expansion of a bubble in viscous liquid, taking into account the compressibility of liquid. This model is important in understanding the time-evolution of the bubble growth in a cavitating flow. We solved the equation of motion of viscous liquid and obtained the velocity field and the pressure distribution in liquid. It is found that the expansion rate of a bubble in viscous compressible liquid is governed by the friction force due to viscosity as well as the surface tension, the inertial force, and the gas pressure. Further, the bubble expansion rate is brought by the same expression to that in an incompressible liquid only in the case that the liquid is in a hydrostatic state before the bubble grows.

Highlights

Bubble dynamics is an important problem in many fields of science and technology
It is found that the expansion rate of a bubble in viscous compressible liquid is governed by the friction force due to viscosity as well as the surface tension, the inertial force, and the gas pressure
The bubble expansion rate is brought by the same expression to that in an incompressible liquid only in the case that the liquid is in a hydrostatic state before the bubble grows

Summary

Bubble expansion rates in viscous compressible liquid

A new equation has been derived for radial expansion of a bubble in viscous liquid, taking into account the compressibility of liquid. This model is important in understanding the time-evolution of the bubble growth in a cavitating flow. It is found that the expansion rate of a bubble in viscous compressible liquid is governed by the friction force due to viscosity as well as the surface tension, the inertial force, and the gas pressure. The bubble expansion rate is brought by the same expression to that in an incompressible liquid only in the case that the liquid is in a hydrostatic state before the bubble grows

Introduction

Conclusion

We introduce two positive functions of time t defined as