Hostname: page-component-54dcc4c588-nx7b4 Total loading time: 0 Render date: 2025-10-01T16:52:12.292Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrostatically controlled large-amplitude, non-axisymmetric waves in thin film flows down a cylinder

Published online by Cambridge University Press:  08 November 2013

A. W. Wray ,
D. T. Papageorgiou  and
O. K. Matar
A. W. Wray
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
D. T. Papageorgiou
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2BZ, UK
O. K. Matar*
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: o.matar@imperial.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine the dynamics of a thin film flowing under gravity down the exterior of a vertically aligned inner cylinder, with a co-aligned, concentric cylinder acting as an outer electrode; the space between the outer cylinder and the film is occupied by an inviscid gas. The stability of the interface is studied when it is subjected to an electric field, applied by imposing a potential difference between the two cylinders. Leaky-dielectric theory is used in conjunction with asymptotic reduction, in the large-conductivity limit, to derive a single, two-dimensional evolution equation for the interfacial location, which accounts for gravity, capillarity, and electrostatic effects. A linear stability analysis is carried out which shows that non-axisymmetric modes become more dominant with increasing electric field strength. Our fully two-dimensional numerical solutions of the evolution equation demonstrate qualitative agreement between the trends observed in the nonlinear regime and those predicted by linear theory. These numerical solutions also show that, depending on the electric field strength and the relative proximity of the outer electrode, the interface either remains spatially uniform, or exhibits either axisymmetric or, importantly, non-axisymmetric travelling waves. The effect of wave formation on the interfacial area is investigated in connection with the use of electric fields to control thin film flows to enhance heat and mass transfer rates.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , R2
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494.Google Scholar
Conroy, D. T., Matar, O. K., Craster, R. V. & Papageorgiou, D. T. 2011 Breakup of an electrified viscous thread with charged surfactants. Phys. Fluids 23 (2), 022103.Google Scholar
Craster, R. V. & Matar, O. K. 2005 Electrically induced pattern formation in thin leaky dielectric films. Phys. Fluids 17, 032104.Google Scholar
Craster, R. V. & Matar, O. K. 2006 On viscous beads flowing down a vertical fibre. J. Fluid Mech. 553, 85–106.Google Scholar
Darabi, J., Ohadi, M. M. & Dessiatoun, S. V. 2000a Augmentation of thin falling-film evaporation on horizontal tubes using an applied electric field. Trans. ASME: J. Heat Transfer 122 (2), 391–398.CrossRefGoogle Scholar
Darabi, J., Ohadi, M. M. & Desiatoun, S. V. 2000b Falling film and spray evaporation enhancement using an applied electric field. Trans. ASME: J. Heat Transfer 122 (4), 741–748.Google Scholar
Frenkel, A. L., Babchin, A. J., Levich, B. G., Shlang, T. & Sivashinsky, G. I. 1987 Annular flows can keep unstable films from breakup: nonlinear saturation of capillary instability. J. Colloid Interface Sci. 115 (1), 225–233.Google Scholar
Gañán-Calvo, A. M. 1997 Cone-jet analytical extension of Taylor’s electrostatic solution and the asymptotic universal scaling laws in electrospraying. Phys. Rev. Lett. 79 (2), 217–220.CrossRefGoogle Scholar
Gañán-Calvo, A. M. & Montanero, J. M. 2009 Revision of capillary cone-jet physics: electrospray and flow focusing. Phys. Rev. E 79 (6), 066305.CrossRefGoogle ScholarPubMed
Hammond, P. S. 1983 Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe. J. Fluid Mech. 137, 363–384.Google Scholar
Kalliadasis, S. & Chang, H.-C. 1994 Drop formation during coating of vertical fibres. J. Fluid Mech. 261, 135–168.Google Scholar
Kerchman, V. I. & Frenkel, A. L. 1994 Interactions of coherent structures in a film flow: simulations of a highly nonlinear evolution equation. Theor. Comput. Fluid Dyn. 6 (4), 235–254.Google Scholar
Li, B., Li, Y., Xu, G.-K. & Feng, X.-Q. 2009 Surface patterning of soft polymer film-coated cylinders via an electric field. J. Phys.: Condens. Matter 21 (44), 445006.Google Scholar
Lister, J. R., Rallison, J. M., King, A. A., Cummings, L. J. & Jensen, O. E. 2006 Capillary drainage of an annular film: the dynamics of collars and lobes. J. Fluid Mech. 552, 311–344.Google Scholar
Lister, J. R., Rallison, M. & Rees, S. J. 2010 The nonlinear dynamics of pendent drops on a thin film coating the underside of a ceiling. J. Fluid Mech. 647, 239–264.Google Scholar
Mestel, A. J. 1996 Electrohydrodynamic stability of a highly viscous jet. J. Fluid Mech. 312, 311–326.Google Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. R. Soc. Lond. A 10, 4–13.Google Scholar
Ruyer-Quil, C., Treveleyan, P., Giorgiutti-Dauphin, F., Duprat, C. & Kalliadasis, S. 2008 Modelling film flows down a fibre. J. Fluid Mech. 603, 431–462.Google Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.Google Scholar
Scheid, B., Ruyer-Quil, C. & Manneville, P. 2006 Wave patterns in film flows: modelling and three-dimensional waves. J. Fluid Mech. 562, 183–222.Google Scholar
Shlang, T. & Sivashinsky, G. I. 1982 Irregular flow of a liquid film down a vertical column. J. Phys. 43 (3), 459–466.Google Scholar
Witelski, T. P. & Bowen, M. 2003 ADI schemes for higher-order nonlinear diffusion equations. Appl. Numer Maths 45 (2), 331–351.Google Scholar
Wray, A. W., Matar, O. & Papageorgiou, D. T. 2012 Non-linear waves in electrified viscous film flow down a vertical cylinder. IMA J. Appl. Maths 77 (3), 430–440.Google Scholar
Wray, A. W., Papageorgiou, D. T. & Matar, O. K. Electrified coating flows on vertical fibres: enhancement or suppression of interfacial dynamics. J. Fluid Mech. 735, 427–456.Google Scholar