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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 lessthan 100 nm is driven by an external force and under the influence of the van der Waalsforces. 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 unstableregion. Furthermore, the surface tension can cause the development of the absolute instability, where as the external force has an opposite effect.
The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fiber are investigated by a linear theory. The film with the thickness lessthan 100 nm is driven by an external force and under the influence of the van der Waalsforces. results show that, when the relative film thickness decreases, the curvature of the fiber depresses the development of the linear perturbations, but 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 show the absolute unstableability as the external force has an opposite effect.