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Slip-enhanced Rayleigh–Plateau instability of a liquid film on a fibre

Published online by Cambridge University Press:  09 January 2023

Chengxi Zhao Open the ORCID record for Chengxi Zhao [Opens in a new window] ,
Yixin Zhang Open the ORCID record for Yixin Zhang [Opens in a new window]  and
Ting Si Open the ORCID record for Ting Si [Opens in a new window]
Chengxi Zhao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Yixin Zhang
Affiliation:
Physics of Fluids Group and Max Planck Center Twente for Complex Fluid Dynamics, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Ting Si*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: tsi@ustc.edu.cn
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Abstract

Boundary conditions at a liquid–solid interface are crucial to dynamics of a liquid film coated on a fibre. Here, a theoretical framework based on axisymmetric Stokes equations is developed to explore the influence of liquid–solid slip on the Rayleigh–Plateau instability of a cylindrical film on a fibre. The new model not only shows that the slip-enhanced growth rate of perturbations is overestimated by the classical lubrication model, but also indicates a slip-dependent dominant wavelength, instead of a constant value obtained by the lubrication method, which leads to larger drops formed on a more slippery fibre. The theoretical findings are validated by direct numerical simulations of Navier–Stokes equations via a volume-of-fluid method. Additionally, the slip-dependent dominant wavelengths predicted by our model agree with the experimental results provided by Haefner et al. (Nat. Commun., vol. 6, issue 1, 2015, 7409).

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A46
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

REFERENCES

Berny, A., Deike, L., Séon, T. & Popinet, S. 2020 Role of all jet drops in mass transfer from bursting bubbles. Phys. Rev. Fluids 5 (3), 033605.CrossRefGoogle Scholar
Brochard-Wyart, F., De Gennes, P.G., Hervert, H. & Redon, C. 1994 Wetting and slippage of polymer melts on semi-ideal surfaces. Langmuir 10 (5), 1566–1572.CrossRefGoogle 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.CrossRefGoogle Scholar
Chen, H., Ran, T., Gan, Y., Zhou, J., Zhang, Y., Zhang, L., Zhang, D. & Jiang, L. 2018 Ultrafast water harvesting and transport in hierarchical microchannels. Nat. Mater. 17 (10), 935–942.CrossRefGoogle ScholarPubMed
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 (3), 1131.CrossRefGoogle Scholar
Deblais, A., Herrada, M.A., Hauner, I., Velikov, K.P., Van Roon, T., Kellay, H., Eggers, J. & Bonn, D. 2018 Viscous effects on inertial drop formation. Phys. Rev. Lett. 121 (25), 254501.CrossRefGoogle ScholarPubMed
Deng, D., Nave, J., Liang, X., Johnson, S.G. & Fink, Y. 2011 Exploration of in-fiber nanostructures from capillary instability. Opt. Express 19 (17), 16273–16290.CrossRefGoogle ScholarPubMed
Ding, Z. & Liu, Q. 2011 Stability of liquid films on a porous vertical cylinder. Phys. Rev. E 84 (4), 046307.CrossRefGoogle ScholarPubMed
Ding, Z., Wong, T.N., Liu, R. & Liu, Q. 2013 Viscous liquid films on a porous vertical cylinder: dynamics and stability. Phys. Fluids 25 (6), 064101.CrossRefGoogle Scholar
Ding, Z., Xie, J., Wong, T.N. & Liu, R. 2014 Dynamics of liquid films on vertical fibres in a radial electric field. J. Fluid Mech. 752, 66–89.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 fiber. Phys. Rev. Lett. 98 (24), 244502.CrossRefGoogle Scholar
Eggers, J. & Dupont, T.F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262, 205–221.CrossRefGoogle Scholar
Frenkel, A.L. 1992 Nonlinear theory of strongly undulating thin films flowing down vertical cylinders. Europhys. Lett. 18 (7), 583.CrossRefGoogle Scholar
Goren, S.L. 1962 The instability of an annular thread of fluid. J. Fluid Mech. 12 (2), 309–319.CrossRefGoogle Scholar
Goren, S.L. 1964 The shape of a thread of liquid undergoing break-up. J. Colloid Sci. 19 (1), 81–86.CrossRefGoogle Scholar
Haefner, S. 2015 Rayleigh–Plateau-type instabilities in thin liquid films. PhD thesis, Saarland University.Google 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 (1), 7409.CrossRefGoogle ScholarPubMed
Halpern, D., Li, Y. & Wei, H. 2015 Slip-induced suppression of Marangoni film thickening in surfactant-retarded Landau–Levich–Bretherton flows. J. Fluid Mech. 781, 578–594.CrossRefGoogle Scholar
Halpern, D. & Wei, H. 2017 Slip-enhanced drop formation in a liquid falling down a vertical fibre. J. Fluid Mech. 820, 42–60.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
Huang, P., Guasto, J.S. & Breuer, K.S. 2006 Direct measurement of slip velocities using three-dimensional total internal reflection velocimetry. J. Fluid Mech. 566, 447–464.CrossRefGoogle Scholar
Ji, H., Falcon, C., Sadeghpour, A., Zeng, Z., Ju, Y.S. & Bertozzi, A.L. 2019 Dynamics of thin liquid films on vertical cylindrical fibres. J. Fluid Mech. 865, 303–327.CrossRefGoogle Scholar
Kalliadasis, S. & Chang, H. 1994 Drop formation during coating of vertical fibres. J. Fluid Mech. 261, 135–168.CrossRefGoogle Scholar
Kavokine, N., Bocquet, M. & Bocquet, L. 2022 Fluctuation-induced quantum friction in nanoscale water flows. Nature 602 (7895), 84–90.CrossRefGoogle ScholarPubMed
Kavokine, N., Netz, R.R. & Bocquet, L. 2021 Fluids at the nanoscale: from continuum to subcontinuum transport. Annu. Rev. Fluid Mech. 53, 377–410.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
Lauga, E., Brenner, M. & Stone, H. 2007 Microfluidics: The No-Slip Boundary Condition, pp. 1219–1240. Springer.Google Scholar
Lee, C.L., Chan, T.S., Carlson, A. & Dalnoki-Veress, K. 2022 Multiple droplets on a conical fiber: formation, motion, and droplet mergers. Soft Matt. 18, 134495.CrossRefGoogle ScholarPubMed
Liang, X., Deng, D., Nave, J. & Johnson, S.G. 2011 Linear stability analysis of capillary instabilities for concentric cylindrical shells. J. Fluid Mech. 683, 235–262.CrossRefGoogle Scholar
Liao, Y., Li, Y., Chang, Y., Huang, C. & Wei, H. 2014 Speeding up thermocapillary migration of a confined bubble by wall slip. J. Fluid Mech. 746, 31–52.CrossRefGoogle Scholar
Liao, Y., Li, Y. & Wei, H. 2013 Drastic changes in interfacial hydrodynamics due to wall slippage: slip-intensified film thinning, drop spreading, and capillary instability. Phys. Rev. Lett. 111 (18), 1364–1370.CrossRefGoogle ScholarPubMed
Liu, R. & Ding, Z. 2021 Coating flows down a vertical fibre: towards the full Navier–Stokes problem. J. Fluid Mech. 914, A30.CrossRefGoogle Scholar
Maali, A. & Bhushan, B. 2012 Measurement of slip length on superhydrophobic surfaces. Phil. Trans. R. Soc. Lond. A 370 (1967), 2304–2320.Google ScholarPubMed
Maali, A., Colin, S. & Bhushan, B. 2016 Slip length measurement of gas flow. Nanotechnology 27 (37), 374004.CrossRefGoogle ScholarPubMed
Martínez-Calvo, A., Moreno-Boza, D. & Sevilla, A. 2020 The effect of wall slip on the dewetting of ultrathin films on solid substrates: linear instability and second-order lubrication theory. Phys. Fluids 32 (10), 102107.CrossRefGoogle Scholar
Mostert, W. & Deike, L. 2020 Inertial energy dissipation in shallow-water breaking waves. J. Fluid Mech. 890, A12.CrossRefGoogle Scholar
Plateau, J.A.F. 1873 Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires, vol. 2. Gauthier-Villars.Google Scholar
Popinet, S. 2014 Basilisk. URL: http://basilisk.fr.Google Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 49–75.CrossRefGoogle Scholar
Quéré, D. 1990 Thin films flowing on vertical fibers. Europhys. Lett. 13 (8), 721.CrossRefGoogle Scholar
Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31, 347–384.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 1, 4–13.CrossRefGoogle Scholar
Rayleigh, Lord 1892 XVI. On the instability of a cylinder of viscous liquid under capillary force. Lond. Edinb. Dubl. Phil. Mag. J. Sci. 34, 145–154.CrossRefGoogle 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.CrossRefGoogle Scholar
Secchi, E., Marbach, S., Niguès, A., Stein, D., Siria, A. & Bocquet, L. 2016 Massive radius-dependent flow slippage in carbon nanotubes. Nature 537 (7619), 210–213.CrossRefGoogle ScholarPubMed
Tomo, Y., Nag, S. & Takamatsu, H. 2022 Observation of interfacial instability of an ultrathin water film. Phys. Rev. Lett. 128 (14), 144502.CrossRefGoogle ScholarPubMed
Tomotika, S. 1935 On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. R. Soc. Lond. A 150 (870), 322–337.Google Scholar
Wei, H., Tsao, H. & Chu, K. 2019 Slipping moving contact lines: critical roles of de Gennes's ‘foot’ in dynamic wetting. J. Fluid Mech. 873, 110–150.CrossRefGoogle Scholar
Yu, L. & Hinch, J. 2013 The velocity of ‘large’ viscous drops falling on a coated vertical fibre. J. Fluid Mech. 737, 232–248.CrossRefGoogle 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.CrossRefGoogle Scholar
Zhang, M., Zheng, Z., Zhu, Y., Zhu, Z., Si, T. & Xu, R.X. 2022 Combinational biomimetic microfibers for high-efficiency water collection. Chem. Engng J. 433, 134495.CrossRefGoogle Scholar
Zhang, Y., Sprittles, J.E. & Lockerby, D.A. 2020 Nanoscale thin-film flows with thermal fluctuations and slip. Phys. Rev. E 102 (5), 053105.CrossRefGoogle ScholarPubMed
Zhang, Y., Sprittles, J.E. & Lockerby, D.A. 2021 Thermal capillary wave growth and surface roughening of nanoscale liquid films. J. Fluid Mech. 915, A135.CrossRefGoogle Scholar
Zhao, C., Liu, J., Lockerby, D.A. & Sprittles, J.E. 2022 Fluctuation-driven dynamics in nanoscale thin-film flows: physical insights from numerical investigations. Phys. Rev. Fluids 7 (2), 024203.CrossRefGoogle Scholar
Zhao, C., Sprittles, J.E. & Lockerby, D.A. 2019 Revisiting the Rayleigh–Plateau instability for the nanoscale. J. Fluid Mech. 861, R3.CrossRefGoogle Scholar