Title

Fingering Instability Down The Outside Of A Vertical Cylinder

Abstract

We present an experimental and numerical study examining the dynamics of a gravity-driven contact line of a thin viscous film traveling down the outside of a vertical cylinder of radius R. Experiments on cylinders with radii ranging between 0.159 and 3.81 cm show that the contact line is unstable to a fingering pattern for two fluids with differing viscosities, surface tensions, and wetting properties. The dynamics of the contact line is studied and results are compared to previous studies of inclined plane experiments in order to understand the influence substrate curvature plays on the fingering pattern. A lubrication model is derived for the film height in the limit that ε=H/Rγ1, where H is the upstream film thickness, and in terms of a Bond number ρgR3/(γH), and the linear stability of the contact line is analyzed using traveling wave solutions. Curvature controls the capillary ridge height of the traveling wave and the range of unstable wavelength when ε=O(10-1), whereas the shape and stability of the contact line converge to the behavior one observes on a vertical plane when ε≤O(10-2). The most unstable wave mode, cutoff wave mode for neutral stability, and maximum growth rate scale as Bo0.45 where Bo=ρgR2/γ≥1.3, and the contact line is unstable to fingering when Bo≥0.56. Using the experimental data to extrapolate outside the range of validity of the thin film model, we estimate the contact line is stable when Bo<0.56. Agreement is excellent between the model and the experimental data for the wave number (i.e., number of fingers) and wavelength of the fingering pattern that forms along the contact line. © 2011 American Institute of Physics.

Publication Date

1-1-2011

Publication Title

Physics of Fluids

Volume

23

Issue

9

Number of Pages

-

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1063/1.3633530

Socpus ID

80053432041 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/80053432041

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