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Applied Mathematics and Mechanics

, Volume 31, Issue 1, pp 1–12 | Cite as

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

  • Zhi-liang Wang (王志亮)Email author
  • S. P. Lin (林松飘)
  • Zhe-wei Zhou (周哲玮)
Article

Abstract

The onset of instability with respect to the spatio-temporally growing disturbance 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 

Chinese Library Classification

O357 

2000 Mathematics Subject Classification

80A20 

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Copyright information

© Shanghai University and Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Zhi-liang Wang (王志亮)
    • 1
    • 2
    Email author
  • S. P. Lin (林松飘)
    • 2
  • Zhe-wei Zhou (周哲玮)
    • 1
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP. R. China
  2. 2.Department of Mechanical and Aeronautical EngineeringClarkson UniversityPotsdamUSA

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