Linear instability of ultra-thin liquid films flowing down cylindrical fibre |
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Authors: | Lu-hai-bo Zhao Guo-hui Hu Zhe-wei Zhou |
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Institution: | Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China |
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Abstract: | The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fibre are investigated
by a linear theory. The film with the thickness less than 100 nm is driven by an external force and under the influence of
the van der Waals forces. The 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 the 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 the absolute instability to the convective instability, indicating that the van der Waals
forces can enlarge the absolutely unstable region. Furthermore, the surface tension can cause the development of the absolute
instability, whereas the external force has an opposite effect. |
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Keywords: | cylindrical fibre ultra-thin film van der Waals force stability |
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