  This paper presents a detailed analysis of the three-dimensional stability
properties of an annular liquid film coating a cylindrical fibre in the
presence of van der Waals (vdW) interactions, whose influence depends on the
wettability of the solid by the liquid. Under wetting conditions, vdW
interactions can stabilise a uniform annular film when its thickness is smaller
than a critical value that depends only on the fibre radius, the Hamaker
constant, and the surface tension coefficient. In contrast, under non-wetting
conditions, both surface tension and vdW forces contribute to destabilise the
interface, and non-axisymmetric modes may become dominant depending on the
thickness of the film and the relative strength of the surface tension and vdW
forces. We perform temporal stability analyses of both the Stokes and
lubrication equations of motion, allowing us to reveal the dominant azimuthal
mode, as well as the optimal axial wavenumber and the corresponding temporal
growth rate, as a function of the relevant governing parameters.
