  It is known that an axisymmetric viscous film flowing down the outside of a
thin vertical fiber becomes unstable to interfacial perturbations. We present
an experimental study using fluids with different densities, surface tensions
and viscosities to investigate the growth and dynamics of these interfacial
perturbations and to test the assumptions made by previous authors. We find the
initial perturbation growth is exponential followed by a slower phase as the
amplitude and wavelength saturate in size. Measurements of the perturbation
growth for experiments conducted at low and moderate Reynolds numbers are
compared to theoretical predictions developed from linear stability theory.
Excellent agreement is found between predictions from a long-wave Stokes flow
model (Craster & Matar, J. Fluid Mech. 553, 85 (2006)) and data, while fair
agreement is found between predictions from a moderate Reynolds number model
(Sisoev et al., Chem. Eng. Sci. 61, 7279 (2006)) and data. Furthermore, we find
that a known transition in the longer-time perturbation dynamics from unsteady
to steady behavior at a critical flow rate, Qc, is correlated to a transition
in the rate at which perturbations naturally form along the fiber. For Q < Qc
(steady case), the rate of perturbation formation is constant. As a result the
position along the fiber where perturbations form is nearly fixed, and the
spacing between consecutive perturbations remains constant as they travel 2 m
down the fiber. For Q > Qc (unsteady case), the rate of perturbation formation
is modulated. As a result the position along the fiber where perturbations form
oscillates irregularly, and the initial speed and spacing between perturbations
varies resulting in the coalescence of neighboring perturbations further down
the fiber.
