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Inertia and slip effects on the instability of a liquid film coated on a fibre

Published online by Cambridge University Press:  04 March 2024

Chengxi Zhao Open the ORCID record for Chengxi Zhao [Opens in a new window] ,
Ran Qiao Open the ORCID record for Ran Qiao [Opens in a new window] ,
Kai Mu Open the ORCID record for Kai Mu [Opens in a new window] ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Chengxi Zhao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Ran Qiao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Kai Mu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Ting Si*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo
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

To investigate the influence of inertia and slip on the instability of a liquid film on a fibre, a theoretical framework based on the axisymmetric Navier–Stokes equations is proposed via linear instability analysis. The model reveals that slip significantly enhances perturbation growth in viscous film flows, whereas it exerts minimal influence on flows dominated by inertia. Moreover, under no-slip boundary conditions, the dominant instability mode of thin films remains unaltered by inertia, closely aligning with predictions from a no-slip lubrication model. Conversely, when slip is introduced, the dominant wavenumber experiences a noticeable reduction as inertia decreases. This trend is captured by an introduced lubrication model with giant slip. Direct numerical simulations of the Navier–Stokes equations are then performed to further confirm the theoretical findings at the linear stage. For the nonlinear dynamics, no-slip simulations show complex vortical structures within films, driven by fluid inertia near surfaces. Additionally, in scenarios with weak inertia, a reduction in the volume of satellite droplets is observed due to slip, following a power-law relationship.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films Materials Processing Flows: Coating
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 982 , 10 March 2024 , A13
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Assael, M.J., Kalyva, A.E., Antoniadis, K.D., Michael Banish, R., Egry, I., Wu, J., Kaschnitz, E. & Wakeham, W.A. 2010 Reference data for the density and viscosity of liquid copper and liquid tin. J. Phys. Chem. Ref. Data 39 (3), 033105.CrossRefGoogle Scholar
Chakraborty, I., Chubynsky, M.V. & Sprittles, J.E. 2022 Computational modelling of Leidenfrost drops. J. Fluid Mech. 936, A12.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
Chen, X., Yang, M., Zheng, S., Temprano-Coleto, F., Dong, Q., Cheng, G., Yao, N., Stone, H.A., Hu, L. & Ren, Z.J. 2023 Spatially separated crystallization for selective lithium extraction from saline water. Nat. Water. 1, 808–817.CrossRefGoogle Scholar
Chubynsky, M.V., Belousov, K.I., Lockerby, D.A. & Sprittles, J.E. 2020 Bouncing off the walls: the influence of gas-kinetic and van der Waals effects in drop impact. Phys. Rev. Lett. 124 (8), 084501.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 (3), 1131–1198.CrossRefGoogle Scholar
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
Erneux, T. & Davis, S.H. 1993 Nonlinear rupture of free films. Phys. Fluids A 5 (5), 1117–1122.CrossRefGoogle Scholar
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38 (4), 689–711.CrossRefGoogle Scholar
González, A.G., Diez, J.A. & Sellier, M. 2016 Inertial and dimensional effects on the instability of a thin film. J. Fluid Mech. 787, 449–473.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., 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), 1–6.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
Kang, D., Nadim, A. & Chugunova, M. 2017 Marangoni effects on a thin liquid film coating a sphere with axial or radial thermal gradients. Phys. Fluids 29 (7), 072106.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
Kondic, L., González, A.G., Diez, J.A., Fowlkes, J.D. & Rack, P. 2020 Liquid-state dewetting of pulsed-laser-heated nanoscale metal films and other geometries. Annu. Rev. Fluid Mech 52, 235–262.CrossRefGoogle 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
Li, F., Yin, X. & Yin, X. 2008 Instability of a viscous coflowing jet in a radial electric field. J. Fluid Mech. 596, 285–311.CrossRefGoogle Scholar
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
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
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. A 370 (1967), 2304–2320.CrossRefGoogle 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 a 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
Martínez-Calvo, A., Rivero-Rodríguez, J., Scheid, B. & Sevilla, A. 2020 b Natural break-up and satellite formation regimes of surfactant-laden liquid threads. J. Fluid Mech. 883, A35.CrossRefGoogle Scholar
Moreno-Boza, D., Martínez-Calvo, A. & Sevilla, A. 2020 a The role of inertia in the rupture of ultrathin liquid films. Phys. Fluids 32 (11), 112114.CrossRefGoogle Scholar
Moreno-Boza, D., Martínez-Calvo, A. & Sevilla, A. 2020 b Stokes theory of thin-film rupture. Phys. Rev. Fluids 5 (1), 014002.CrossRefGoogle Scholar
Münch, A., Wagner, B.A. & Witelski, T.P. 2005 Lubrication models with small to large slip lengths. J. Engng Maths 53, 359–383.CrossRefGoogle Scholar
Navier, C. 1823 Mémoire sur les lois du Mouvement des Fluides, In Mémoire de l'Académie Royale des Sciences de l'Institut de France, vol. VI, pp. 389–440. Sci. de L'Institut de France, éditeur inconnu.Google Scholar
Oliveira, J.P., Santos, T.G. & Miranda, R.M. 2020 Revisiting fundamental welding concepts to improve additive manufacturing: from theory to practice. Prog. Mater. Sci. 107, 100590.CrossRefGoogle Scholar
Oron, A., Davis, S.H. & Bankoff, S.G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931–980.CrossRefGoogle Scholar
Plateau, J.A.F. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires, vol. 2. Gauthier-Villars.Google 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. Dublin Philos. Mag. J. Sci. 34, 145–154.CrossRefGoogle Scholar
Reitz, B., et al. 2021 Additive manufacturing under lunar gravity and microgravity. Microgravity Sci. Technol. 33, 1–12.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
Schlichting, H. & Kestin, J. 1961 Boundary Layer Theory, vol. 121. Springer.Google 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
Si, T., Li, F., Yin, X. & Yin, X. 2009 Modes in flow focusing and instability of coaxial liquid–gas jets. J. Fluid Mech. 629, 1–23.CrossRefGoogle Scholar
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
Van Ombergen, A., et al. 2023 3D bioprinting in microgravity: opportunities, challenges, and possible applications in space. Adv. Healthc. Mater. 12, 2300443.CrossRefGoogle ScholarPubMed
Weber, C. 1931 Zum zerfall eines flüssigkeitsstrahles. Z. Angew. Math. Mech. 11, 136–154.CrossRefGoogle Scholar
Wei, X., Rivero-Rodríguez, J., Zou, J. & Scheid, B. 2021 Statics and dynamics of a viscous ligament drawn out of a pure-liquid bath. J. Fluid Mech. 922, A14.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, 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
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
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
Zhao, C., Zhang, Y. & Si, T. 2023 a Slip-enhanced Rayleigh–Plateau instability of a liquid film on a fibre. J. Fluid Mech. 954, A46.CrossRefGoogle Scholar
Zhao, C., Zhang, Z. & Si, T. 2023 b Fluctuation-driven instability of nanoscale liquid films on chemically heterogeneous substrates. Phys. Fluids 35 (7), 072016.CrossRefGoogle Scholar
Zhao, C., Zhao, J., Si, T. & Chen, S. 2021 Influence of thermal fluctuations on nanoscale free-surface flows: a many-body dissipative particle dynamics study. Phys. Fluids 33 (11), 112004.CrossRefGoogle Scholar