Dynamics of free surface perturbations along an annular viscous film
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It is known that the free surface of an axisymmetric viscous film flowing down the outside of a thin vertical fiber under the influence of gravity 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 that 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 and Matar, J. Fluid Mech. 553, 85 (2006)] and data, while fair to excellent agreement (depending on fiber size ) 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 Q(c) is correlated with a transition in the rate at which perturbations naturally form along the fiber. For Q < Q(c) (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 > Q(c) (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.