Dynamics of Free Surface Perturbations Along an Annular Viscous Film

TL;DR

This study experimentally investigates the growth and dynamics of interfacial perturbations in an annular viscous film on a vertical fiber, validating theoretical models and revealing a flow rate-dependent transition in perturbation behavior.

Contribution

The paper provides experimental validation of linear stability theory predictions for viscous film perturbations and identifies a flow rate-induced transition in perturbation formation dynamics.

Findings

Excellent agreement with long-wave Stokes flow model predictions.

Fair agreement with moderate Reynolds number model.

Transition from steady to unsteady perturbation behavior at a critical flow rate.

Abstract

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.