Gravitydriven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder
Mayo, Lisa C., McCue, Scott W., & Moroney, Timothy J. (2013) Gravitydriven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 87(5), pp. 116.

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Abstract
A numerical study is presented to examine the fingering instability of a gravitydriven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully threedimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the twodimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.
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ID Code:  59839 

Item Type:  Journal Article 
Refereed:  Yes 
Keywords:  thin film flow, contact line instability, viscous fingering, pattern formation, drops, pearling, numerical simulation, ADI method, travelling wave, linear stability, rivulets 
DOI:  10.1103/PhysRevE.87.053018 
ISSN:  15393755 
Subjects:  Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207) Australian and New Zealand Standard Research Classification > PHYSICAL SCIENCES (020000) > CLASSICAL PHYSICS (020300) > Fluid Physics (020303) 
Divisions:  Current > Institutes > Institute for Future Environments Current > Schools > School of Mathematical Sciences Current > QUT Faculties and Divisions > Science & Engineering Faculty 
Copyright Owner:  Copyright 2013 American Physical Society 
Deposited On:  12 May 2013 23:27 
Last Modified:  01 Jun 2013 20:04 
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