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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (1): 1-12.doi: https://doi.org/10.1007/s10483-010-0101-x

• Articles •    下一篇

Spatio-temporal instability of two-layer liquid film at small Reynolds numbers

王志亮1,2 林松飘2 周哲玮1   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P. R. China;
    2. Department of Mechanical and Aeronautical Engineering, Clarkson University,Potsdam, NY 13699, USA
  • 收稿日期:2009-10-20 修回日期:2009-11-19 出版日期:2010-01-03 发布日期:2010-01-01

Spatio-temporal instability of two-layer liquid film at small Reynolds numbers

 WANG Zhi-Liang1,2, LIN Song-Piao2, ZHOU Zhe-Wei1   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P. R. China;
    2. Department of Mechanical and Aeronautical Engineering, Clarkson University,Potsdam, NY 13699, USA
  • Received:2009-10-20 Revised:2009-11-19 Online:2010-01-03 Published:2010-01-01

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3

摘要： The onset of instability with respect to the spatio-temporally growing dis-turbance in a viscosity-stratified two-layer liquid film flow is analyzed. The known results obtained from the temporal theory of instability show that the flow is unstable in the limit of zero Reynolds numbers. The present theory predicts the neutral stability in the same limit. The discrepancy is explained. Based on the mechanical energy equation, a new mechanism of instability is found. The new mechanism is associated with the convective nature of the disturbance that is not Galilei invariant.

关键词: flow instability, film coating, energy budget, low Reynolds number, Galilei invariant

Abstract: The onset of instability with respect to the spatio-temporally growing dis-turbance in a viscosity-stratified two-layer liquid film flow is analyzed. The known results obtained from the temporal theory of instability show that the flow is unstable in the limit of zero Reynolds numbers. The present theory predicts the neutral stability in the same limit. The discrepancy is explained. Based on the mechanical energy equation, a new mechanism of instability is found. The new mechanism is associated with the convective nature of the disturbance that is not Galilei invariant.

Key words: flow instability, film coating, energy budget, low Reynolds number, Galilei invariant

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