Abstract
Abstract
Highlights
The coating of liquid film on a fibre has given rise to considerable scientific interest because of its relevance to many industrial applications, for example, draining, coating of insulation on a wire, and the protection of tube walls (Quéré 1999)
We have investigated the dynamics of a coating flow driven by gravity over a fibre rotating about its axis
The evolution equation for the surface is derived in the framework of the long-wave theory with an assumption that the characteristic radius of fluid ring is much smaller than the capillary length scale
Summary
The coating of liquid film on a fibre has given rise to considerable scientific interest because of its relevance to many industrial applications, for example, draining, coating of insulation on a wire, and the protection of tube walls (Quéré 1999). Ruyer-Quil et al (2008) took into account inertia and streamwise viscous diffusion and formulated two coupled evolution equations for both the film thickness and volumetric flow rate This model is valid for moderate Reynolds numbers, both small and O(1) aspect ratios of h/a. We consider the problem of a gravity-driven coating flow outside a vertical rotating fibre. At high frequency of rotation, the most unstable mode is achieved by streamwise uniform and non-axisymmetric disturbance In this case, no asymptotic model can be obtained for thick films. The linear stability analysis of the three-dimensional (3-D) problem of the Navier–Stokes equations is performed to evaluate the contribution of Coriolis forces and to examine the most unstable mode for various rotation frequencies.
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