Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-18T18:59:37.615Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrified coating flows on vertical fibres: enhancement or suppression of interfacial dynamics

Published online by Cambridge University Press:  24 October 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 investigate the evolution and stability of a wetting viscous fluid layer flowing down the surface of a cylinder, and surrounded by a conductive gas. The inner cylinder is an electrode kept at constant voltage, and a second, concentric electrode encloses the system whose potential is allowed to vary spatially. This induces electrostatic forces at the interface in competition with surface tension and viscous stresses. Asymptotic methods are used to derive a long-wave axisymmetric model governing the interfacial position and charge density. The resulting system of equations is investigated both analytically and numerically to determine its stability characteristics in the linear and nonlinear regimes.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) MHD and Electrohydrodynamics: MHD and Electrohydrodynamics Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 735 , 25 November 2013 , pp. 427 - 456
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.)

References

Bandyopadhyay, D. & Sharma, A. 2007 Electric field induced instabilities in thin confined bilayers. J. Colloid Interface Sci. 311 (2), 595–608.CrossRefGoogle ScholarPubMed
Benjamin, T. B. 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2 (6), 554–573.CrossRefGoogle 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, 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, 066305.CrossRefGoogle ScholarPubMed
Conroy, D. T., Matar, O. K., Craster, R. V. & Papageorgiou, D. T. 2011a Breakup of an electrified, perfectly conducting, viscous thread in an ac field. Phys. Rev. E 83, 066314.CrossRefGoogle Scholar
Conroy, D. T., Matar, O. K., Craster, R. V. & Papageorgiou, D. T. 2011b Breakup of an electrified viscous thread with charged surfactants. Phys. Fluids 23 (2), 022103.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2005 Electrically induced pattern formation in thin leaky dielectric films. Phys. Fluids 17 (3), 032104.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2006 On viscous beads flowing down a vertical fibre. J. Fluid Mech. 553, 85–105.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131–1198.CrossRefGoogle Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.CrossRefGoogle Scholar
Darabi, J., Ohadi, M. M. & Desiatoun, S. V. 2000a Falling film and spray evaporation enhancement using an applied electric field. J. Heat Transfer 122 (4), 741–748.CrossRefGoogle Scholar
Darabi, J., Ohadi, M. M. & Dessiatoun, S. V. 2000b Augmentation of thin falling-film evaporation on horizontal tubes using an applied electric field. J. Heat Transfer 122 (2), 391–398.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. Nature 389 (6653), 827–829.CrossRefGoogle Scholar
Duprat, C., Ruyer-Quil, C., Kalliadasis, S. & Giorgiutti-Dauphiné, F. 2007 Absolute and convective instabilities of a viscous film flowing down a vertical fibre. Phys. Rev. Lett. 98 (24), 244502.CrossRefGoogle Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69 (3), 865–930.CrossRefGoogle Scholar
Eral, H. B., Augustine, D. M., Duits, M. H. G. & Mugele, F. 2011 Suppressing the coffee stain effect: how to control colloidal self-assembly in evapourating drops using electrowetting. Soft Matt. 7 (10), 4954–4958.CrossRefGoogle 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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Hickox, C. E. 1971 Instability due to viscosity and density stratification in axisymmetric pipe flow. Phys. Fluids 14 (2), 251–262.CrossRefGoogle Scholar
Keast, P. & Muir, P. H. 1991 Algorithm 688: EPDCOL: a more efficient PDECOL code. ACM Trans. Math. Softw. 17, 153–166.CrossRefGoogle Scholar
Kliakhandler, I. L., Davis, S. H. & Bankoff, S. G. 2001 Viscous beads on vertical fibre. J. Fluid Mech. 429, 381–390.CrossRefGoogle 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, 311–343.CrossRefGoogle Scholar
McBride, S. E., Moroney, R. M. & Chiang, W. 1998 Electrohydrodynamic pumps for high-density microfluidic arrays. In Micro Total Analysis Systems, 98, pp. 45–48. Springer.CrossRefGoogle Scholar
Mestel, A. J. 1994 The electrohydrodynamic cone-jet at high Reynolds number. J. Aerosol. Sci. 25 (6), 1037–1047.CrossRefGoogle Scholar
Novbari, E. & Oron, A. 2009 Energy integral method model for the nonlinear dynamics of an axisymmetric thin liquid film falling on a vertical cylinder. Phys. Fluids 21 (6), 062107.CrossRefGoogle Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.CrossRefGoogle Scholar
Ozen, O., Aubry, N., Papageorgiou, D. T. & Petropoulos, P. G. 2006a Electrohydrodynamic linear stability of two immiscible fluids in channel flow. Electrochim. Acta 51 (25), 5316–5323.CrossRefGoogle Scholar
Ozen, O., Papageorgiou, D. T. & Petropoulos, P. G. 2006b Nonlinear stability of a charged electrified viscous liquid sheet under the action of a horizontal electric field. Phys. Fluids 18 (4), 042102.CrossRefGoogle Scholar
Pantzali, M. N., Mouza, A. A. & Paras, S. V. 2008 Counter-current gas–liquid flow and incipient flooding in inclined small diameter tubes. Chem. Engng Sci. 63 (15), 3966–3978.CrossRefGoogle Scholar
Pease, L. F. III & Russel, W. B. 2002 Linear stability analysis of thin leaky dielectric films subjected to electric fields. J. Non-Newtonian Fluid Mech. 102 (2), 233–250, a collection of papers dedicated to Professor Andreas Acrivos on the occasion of his retirement from the Benjamin Levich Institute for Physiochemical Hydrodynamics and the City College of the CUNY.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. s1–10 (1), 4–13.CrossRefGoogle Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29 (1), 27–64.CrossRefGoogle Scholar
Shankar, V. & Sharma, A. 2004 Instability of the interface between thin fluid films subjected to electric fields. J. Colloid Interface Sci. 274 (1), 294–308.CrossRefGoogle ScholarPubMed
Shin, Y. M., Hohman, M. M., Brenner, M. P. & Rutledge, G. C. 2001 Experimental characterization of electrospinning: the electrically forced jet and instabilities. Polymer 42 (25), 09955–09967.CrossRefGoogle Scholar
Shlang, T. & Sivashinsky, G. I. 1982 Irregular flow of a liquid film down a vertical column. J. Phys. 32 (3), 459–466.Google Scholar
Sisoev, G. M., Craster, R. V., Matar, O. K. & Gerasimov, S. V. 2006 Film flow down a fibre at moderate flow rates. Chem. Engng Sci. 61 (22), 7279–7298.CrossRefGoogle Scholar
Trifonov, Y. Y. 2004 Steady-state traveling waves on the surface of a viscous liquid film falling down on vertical wires and tubes. AIChE J. 38 (6), 821–834.CrossRefGoogle Scholar
Tseluiko, D. & Kalliadasis, S. 2011 Nonlinear waves in counter-current gas–liquid film flow. J. Fluid Mech. 673, 19–59.CrossRefGoogle Scholar
Tseluiko, D. & Papageorgiou, D. T. 2006 Wave evolution on electrified falling films. J. Fluid Mech. 556, 361–386.CrossRefGoogle Scholar
Tseluiko, D., Saprykin, S., Duprat, C., Giorgiutti-Dauphiné, F. & Kalliadasis, S. 2010 Pulse dynamics in low-Reynolds-number interfacial hydrodynamics: experiments and theory. Physica D: Nonlinear Phenomena 239 (20–22), 2000–2010.CrossRefGoogle Scholar
Verma, R., Sharma, A., Kargupta, K. & Bhaumik, J. 2005 Electric field induced instability and pattern formation in thin liquid films. Langmuir 21 (8), 3710–3721.CrossRefGoogle ScholarPubMed
Wang, Q., Mählmann, S. & Papageorgiou, D. T. 2009 Dynamics of liquid jets and threads under the action of radial electric fields: microthread formation and touchdown singularities. Phys. Fluids 21 (3), 032109.CrossRefGoogle Scholar
Wang, Q. & Papageorgiou, D. T. 2011 Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities. J. Fluid Mech. 683, 27–56.CrossRefGoogle 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. Math 77 (3), 430–440.CrossRefGoogle Scholar
Yih, C.-S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6 (3), 321–334.CrossRefGoogle Scholar