Linear Instability of Ultra-Thin Liquid Films Flowing Down a Cylindrical Fibre

ZHAO Lu-hai-bo; HU Guo-hui; ZHOU Zhe-wei

doi:10.3879/j.issn.1000-0887.2011.02.001

Volume 32 Issue 2

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ZHAO Lu-hai-bo, HU Guo-hui, ZHOU Zhe-wei. Linear Instability of Ultra-Thin Liquid Films Flowing Down a Cylindrical Fibre[J]. Applied Mathematics and Mechanics, 2011, 32(2): 127-134. doi: 10.3879/j.issn.1000-0887.2011.02.001

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Linear Instability of Ultra-Thin Liquid Films Flowing Down a Cylindrical Fibre

doi: 10.3879/j.issn.1000-0887.2011.02.001

Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

Received Date: 2010-10-06
Rev Recd Date: 2010-12-07
Publish Date: 2011-02-15

Abstract

Abstract

The stability characteristics of an ultra-thin layer of viscous liquid flowing down a cylindrical fibre were investigated by linear theory. The film with a thickness less than 100 nm was driven by an external force,and under the influence of van der Waals forces. Results show that when the relative film thickness decreases,the curvature of the fibre depresses the development of the linear perturbations,whereas the van der Waals forces promote instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from absolute to convective instability,which demonstrates that the van der Waals forces have the role of enlarging the absolutely unstable region. Furthermore,the surface tension is benefitial for the development of the absolute instability,whereas the external force plays an opposite effect.
- cylindrical fibre,
- ultra-thin films,
- van der Waals force,
- stability

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References(20)

References

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