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

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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.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P. R. China

    Zhi-liang Wang  (王志亮) & Zhe-wei Zhou  (周哲玮)

  2. Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, 13699, USA

    Zhi-liang Wang  (王志亮) & S. P. Lin  (林松飘)

Authors
  1. Zhi-liang Wang  (王志亮)
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  2. S. P. Lin  (林松飘)
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  3. Zhe-wei Zhou  (周哲玮)
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Corresponding author

Correspondence to Zhi-liang Wang  (王志亮).

Additional information

Contributed by Zhe-wei ZHOU

Project supported by the National Natural Science Foundation of China (Nos. 10702038 and 10772107), the National Science Foundation of USA (No. CTS-0138057), and the Shanghai Leading Academic Discipline Project (No. Y0103)

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Wang, Zl., Lin, S.P. & Zhou, Zw. Spatio-temporal instability of two-layer liquid film at small Reynolds numbers. Appl. Math. Mech.-Engl. Ed. 31, 1–12 (2010). https://doi.org/10.1007/s10483-010-0101-x

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  • DOI: https://doi.org/10.1007/s10483-010-0101-x

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