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Dynamics of thin liquid films on vertical cylindrical fibres

Published online by Cambridge University Press:  19 February 2019

H. Ji Open the ORCID record for H. Ji [Opens in a new window] ,
C. Falcon Open the ORCID record for C. Falcon [Opens in a new window] ,
A. Sadeghpour ,
Z. Zeng ,
Y. S. Ju Open the ORCID record for Y. S. Ju [Opens in a new window]  and
A. L. Bertozzi Open the ORCID record for A. L. Bertozzi [Opens in a new window]
H. Ji*
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA
C. Falcon
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA
A. Sadeghpour
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
Z. Zeng
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
Y. S. Ju
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
A. L. Bertozzi
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
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Abstract

Recent experiments on thin films flowing down a vertical fibre with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of travelling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the travelling wave solution of the model.

JFM classification

Instability: Instability Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 303 - 327
Copyright
© 2019 Cambridge University Press 

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References

Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81 (2), 739–805.10.1103/RevModPhys.81.739Google Scholar
Chang, H.-C. & Demekhin, E. A. 1999 Mechanism for drop formation on a coated vertical fibre. J. Fluid Mech. 380, 233–255.10.1017/S0022112098003632Google Scholar
Chao, Y., Ding, Z. & Liu, R. 2018 Dynamics of thin liquid films flowing down the uniformly heated/cooled cylinder with wall slippage. Chem. Engng Sci. 175, 354–364.10.1016/j.ces.2017.10.013Google Scholar
Chinju, H., Uchiyama, K. & Mori, Y. H. 2000 String-of-beads flow of liquids on vertical wires for gas absorption. AIChE J. 46 (5), 937–945.10.1002/aic.690460508Google Scholar
Coullet, P., Mahadevan, L. & Riera, C. S. 2005 Hydrodynamical models for the chaotic dripping faucet. J. Fluid Mech. 526, 1–17.10.1017/S0022112004002307Google Scholar
Craster, R. V. & Matar, O. K. 2006 On viscous beads flowing down a vertical fibre. J. Fluid Mech. 553, 85–105.10.1017/S0022112006008706Google Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 1131–1198.10.1103/RevModPhys.81.1131Google Scholar
Dreyer, K. & Hickey, F. R. 1991 The route to chaos in a dripping water faucet. Am. J. Phys. 59 (7), 619–627.10.1119/1.16783Google Scholar
Duprat, C., Ruyer-Quil, C. & Giorgiutti-Dauphiné, F. 2009 Spatial evolution of a film flowing down a fiber. Phys. Fluids 21 (4), 042109.10.1063/1.3119811Google Scholar
Duprat, C., Ruyer-Quil, C., Kalliadasis, S. & Giorgiutti-Dauphiné, F. 2007 Absolute and convective instabilities of a viscous film flowing down a vertical fiber. Phys. Rev. Lett. 98 (24), 244502.10.1103/PhysRevLett.98.244502Google Scholar
Frenkel, A. L. 1992 Nonlinear theory of strongly undulating thin films flowing down vertical cylinders. Europhys. Lett. 18 (7), 583–588.10.1209/0295-5075/18/7/003Google Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.10.1103/RevModPhys.57.827Google Scholar
Haefner, S., Benzaquen, M., Bäumchen, O., Salez, T., Peters, R., McGraw, J. D., Jacobs, K., Raphaël, E. & Dalnoki-Veress, K. 2015 Influence of slip on the Plateau–Rayleigh instability on a fibre. Nat. Commun. 6, 7409.10.1038/ncomms8409Google Scholar
Halpern, D. & Wei, H.-H. 2017 Slip-enhanced drop formation in a liquid falling down a vertical fibre. J. Fluid Mech. 820, 42–60.10.1017/jfm.2017.202Google Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic Press.Google Scholar
Kalliadasis, S. & Chang, H.-C. 1994 Drop formation during coating of vertical fibres. J. Fluid Mech. 261, 135–168.10.1017/S0022112094000297Google Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2011 Falling Liquid Films, vol. 176. Springer Science & Business Media.Google Scholar
Kliakhandler, I. L., Davis, S. H. & Bankoff, S. G. 2001 Viscous beads on vertical fibre. J. Fluid Mech. 429, 381–390.10.1017/S0022112000003268Google Scholar
Lopes, A., von Borries, T. U. & Hazel, A. L. 2018 On the multiple solutions of coating and rimming flows on rotating cylinders. J. Fluid Mech. 835, 540–574.10.1017/jfm.2017.756Google Scholar
Münch, A., Wagner, B. A. & Witelski, T. P. 2005 Lubrication models with small to large slip lengths. J. Engng Maths 53 (3–4), 359–383.10.1007/s10665-005-9020-3Google Scholar
Oron, A. & Bankoff, S. G. 2001 Dynamics of a condensing liquid film under conjoining/disjoining pressures. Phys. Fluids 13 (5), 1107–1117.10.1063/1.1355022Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.10.1103/RevModPhys.69.931Google Scholar
Quéré, D. 1990 Thin films flowing on vertical fibers. Europhys. Lett. 13 (8), 721–726.10.1209/0295-5075/13/8/009Google Scholar
Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31 (1), 347–384.10.1146/annurev.fluid.31.1.347Google Scholar
Quéré, D., di Meglio, J.-M. & Brochard-Wyart, F. 1989 Making van der Waals films on fibers. Europhys Lett. 10 (4), 335–340.10.1209/0295-5075/10/4/009Google Scholar
Reisfeld, B. & Bankoff, S. G. 1992 Non-isothermal flow of a liquid film on a horizontal cylinder. J. Fluid Mech. 236, 167–196.10.1017/S0022112092001381Google Scholar
Ruyer-Quil, C. & Kalliadasis, S. 2012 Wavy regimes of film flow down a fiber. Phys. Rev. E 85 (4), 046302.Google Scholar
Ruyer-Quil, C., Treveleyan, P., Giorgiutti-Dauphiné, F., Duprat, C. & Kalliadasis, S. 2008 Modelling film flows down a fibre. J. Fluid Mech. 603, 431–462.10.1017/S0022112008001225Google Scholar
Ruyer-Quil, C., Trevelyan, S. P. M. J., Giorgiutti-Dauphiné, F., Duprat, C. & Kalliadasis, S. 2009 Film flows down a fiber: modeling and influence of streamwise viscous diffusion. Eur. Phys. J. Special Topics 166 (1), 89–92.10.1140/epjst/e2009-00884-0Google Scholar
Sadeghpour, A., Zeng, Z. & Ju, Y. S. 2017 Effects of nozzle geometry on the fluid dynamics of thin liquid films flowing down vertical strings in the Rayleigh–Plateau regime. Langmuir 33, 6292–6299.10.1021/acs.langmuir.7b01277Google 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), 7279–7298.10.1016/j.ces.2006.08.033Google Scholar
Smolka, L. B., North, J. & Guerra, B. K. 2008 Dynamics of free surface perturbations along an annular viscous film. Phys. Rev. E 77 (3), 036301.Google Scholar
Snoeijer, J. H. 2006 Free-surface flows with large slopes: beyond lubrication theory. Phys. Fluids 18 (2), 021701.10.1063/1.2171190Google Scholar
Thiele, U. 2011 On the depinning of a drop of partially wetting liquid on a rotating cylinder. J. Fluid Mech. 671, 121–136.10.1017/S0022112010005483Google Scholar
Thiele, U. 2018 Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting. Colloids Surf. A 553, 487–495.10.1016/j.colsurfa.2018.05.049Google Scholar
Trifonov, Y. 1992 Steady-state traveling waves on the surface of a viscous liquid film falling down on vertical wires and tubes. AIChE J. 38 (6), 821–834.10.1002/aic.690380604Google Scholar
Yu, L. & Hinch, J. 2013 The velocity of large viscous drops falling on a coated vertical fibre. J. Fluid Mech. 737, 232–248.10.1017/jfm.2013.540Google Scholar
Zeng, Z., Sadeghpour, A., Warrier, G. & Ju, Y. S. 2017 Experimental study of heat transfer between thin liquid films flowing down a vertical string in the Rayleigh–Plateau instability regime and a counterflowing gas stream. Intl J. Heat Mass Transfer 108, 830–840.10.1016/j.ijheatmasstransfer.2016.12.066Google Scholar