Skip to main content Accessibility help
×
Home

Dynamics of thin liquid films on vertical cylindrical fibres

  • H. Ji (a1), C. Falcon (a1), A. Sadeghpour (a2), Z. Zeng (a2), Y. S. Ju (a2) and A. L. Bertozzi (a1) (a2)...

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.

Copyright

Corresponding author

Email address for correspondence: hangjie@math.ucla.edu

References

Hide All
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81 (2), 739805.10.1103/RevModPhys.81.739
Chang, H.-C. & Demekhin, E. A. 1999 Mechanism for drop formation on a coated vertical fibre. J. Fluid Mech. 380, 233255.10.1017/S0022112098003632
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, 354364.10.1016/j.ces.2017.10.013
Chinju, H., Uchiyama, K. & Mori, Y. H. 2000 String-of-beads flow of liquids on vertical wires for gas absorption. AIChE J. 46 (5), 937945.10.1002/aic.690460508
Coullet, P., Mahadevan, L. & Riera, C. S. 2005 Hydrodynamical models for the chaotic dripping faucet. J. Fluid Mech. 526, 117.10.1017/S0022112004002307
Craster, R. V. & Matar, O. K. 2006 On viscous beads flowing down a vertical fibre. J. Fluid Mech. 553, 85105.10.1017/S0022112006008706
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 11311198.10.1103/RevModPhys.81.1131
Dreyer, K. & Hickey, F. R. 1991 The route to chaos in a dripping water faucet. Am. J. Phys. 59 (7), 619627.10.1119/1.16783
Duprat, C., Ruyer-Quil, C. & Giorgiutti-Dauphiné, F. 2009 Spatial evolution of a film flowing down a fiber. Phys. Fluids 21 (4), 042109.10.1063/1.3119811
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.98.244502
Frenkel, A. L. 1992 Nonlinear theory of strongly undulating thin films flowing down vertical cylinders. Europhys. Lett. 18 (7), 583588.10.1209/0295-5075/18/7/003
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.10.1103/RevModPhys.57.827
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/ncomms8409
Halpern, D. & Wei, H.-H. 2017 Slip-enhanced drop formation in a liquid falling down a vertical fibre. J. Fluid Mech. 820, 4260.10.1017/jfm.2017.202
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic Press.
Kalliadasis, S. & Chang, H.-C. 1994 Drop formation during coating of vertical fibres. J. Fluid Mech. 261, 135168.10.1017/S0022112094000297
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2011 Falling Liquid Films, vol. 176. Springer Science & Business Media.
Kliakhandler, I. L., Davis, S. H. & Bankoff, S. G. 2001 Viscous beads on vertical fibre. J. Fluid Mech. 429, 381390.10.1017/S0022112000003268
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, 540574.10.1017/jfm.2017.756
Münch, A., Wagner, B. A. & Witelski, T. P. 2005 Lubrication models with small to large slip lengths. J. Engng Maths 53 (3–4), 359383.10.1007/s10665-005-9020-3
Oron, A. & Bankoff, S. G. 2001 Dynamics of a condensing liquid film under conjoining/disjoining pressures. Phys. Fluids 13 (5), 11071117.10.1063/1.1355022
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931980.10.1103/RevModPhys.69.931
Quéré, D. 1990 Thin films flowing on vertical fibers. Europhys. Lett. 13 (8), 721726.10.1209/0295-5075/13/8/009
Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31 (1), 347384.10.1146/annurev.fluid.31.1.347
Quéré, D., di Meglio, J.-M. & Brochard-Wyart, F. 1989 Making van der Waals films on fibers. Europhys Lett. 10 (4), 335340.10.1209/0295-5075/10/4/009
Reisfeld, B. & Bankoff, S. G. 1992 Non-isothermal flow of a liquid film on a horizontal cylinder. J. Fluid Mech. 236, 167196.10.1017/S0022112092001381
Ruyer-Quil, C. & Kalliadasis, S. 2012 Wavy regimes of film flow down a fiber. Phys. Rev. E 85 (4), 046302.
Ruyer-Quil, C., Treveleyan, P., Giorgiutti-Dauphiné, F., Duprat, C. & Kalliadasis, S. 2008 Modelling film flows down a fibre. J. Fluid Mech. 603, 431462.10.1017/S0022112008001225
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), 8992.10.1140/epjst/e2009-00884-0
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, 62926299.10.1021/acs.langmuir.7b01277
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), 72797298.10.1016/j.ces.2006.08.033
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.
Snoeijer, J. H. 2006 Free-surface flows with large slopes: beyond lubrication theory. Phys. Fluids 18 (2), 021701.10.1063/1.2171190
Thiele, U. 2011 On the depinning of a drop of partially wetting liquid on a rotating cylinder. J. Fluid Mech. 671, 121136.10.1017/S0022112010005483
Thiele, U. 2018 Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting. Colloids Surf. A 553, 487495.10.1016/j.colsurfa.2018.05.049
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), 821834.10.1002/aic.690380604
Yu, L. & Hinch, J. 2013 The velocity of large viscous drops falling on a coated vertical fibre. J. Fluid Mech. 737, 232248.10.1017/jfm.2013.540
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, 830840.10.1016/j.ijheatmasstransfer.2016.12.066
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed