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Applied Mathematics and Mechanics

, Volume 37, Issue 12, pp 1607–1614 | Cite as

Effect of surface tension and viscosity on bubble growth of single mode Rayleigh-Taylor instability

  • Mingjun LiEmail author
  • Qiaofeng Zhu
  • Guibo Li
Article

Abstract

Based on the Zufiria theoretical model, a new model regarding the asymptotic bubble velocity for the Rayleigh-Taylor (RT) instability is presented by use of the complex velocity potential proposed by Sohn. The proposed model is an extension of the ordinary Zufiria model and can deal with non-ideal fluids. With the control variable method, the effect of the viscosity and surface tension on the bubble growth rate of the RT instability is studied. The result is consistent with Cao’s result if we only consider the viscous effect and with Xia’s result if we only consider the surface tension effect. The asymptotic bubble velocity predicted by the Zufiria model is smaller than that predicted by the Layzer model, and the result from the Zufiria model is much closer to White’s experimental data.

Key words

viscosity surface tension Rayleigh-Taylor (RT) instability Zufiria model 

Nomenclature

A

Atwood number

Bo

Bond number

F

complex velocity potential

Fr

Froude number

g

gravity acceleration

k

wave number

R

curvature radius of bubble

Re

Reynolds number

Q

source strength

U

asymptotic bubble velocity

η

amplitude of bubble

θ

stream function

λ

wave length

µ

dynamic viscosity coefficient

υ

kinetic viscosity coefficient

ρ

fluid density

σ

surface tension

φ

velocity potential

Chinese Library Classification

O351 O359 O361 

2010 Mathematics Subject Classification

76T10 76E17 76W05 

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References

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematics and System ScienceShenyang Normal UniversityShenyangChina
  2. 2.School of Mathematics and Computational ScienceXiangtan UniversityHunan ProvinceChina

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