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Thermally-driven coalescence in thin liquid film flowing down a fibre

Published online by Cambridge University Press:  06 April 2021

Hangjie Ji Open the ORCID record for Hangjie Ji [Opens in a new window] ,
Claudia Falcon Open the ORCID record for Claudia Falcon [Opens in a new window] ,
Erfan Sedighi Open the ORCID record for Erfan Sedighi [Opens in a new window] ,
Abolfazl Sadeghpour Open the ORCID record for Abolfazl Sadeghpour [Opens in a new window] ,
Y. Sungtaek Ju Open the ORCID record for Y. Sungtaek Ju [Opens in a new window]  and
Andrea L. Bertozzi Open the ORCID record for Andrea L. Bertozzi [Opens in a new window]
Hangjie Ji*
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA90095, USA
Claudia Falcon
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA90095, USA
Erfan Sedighi
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA90095, USA
Abolfazl Sadeghpour
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA90095, USA
Y. Sungtaek Ju
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA90095, USA
Andrea L. Bertozzi
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA90095, USA Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA90095, USA
*
†Email address for correspondence: [email protected]
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Abstract

This paper presents a study on the dynamics of a thin liquid film flowing down a vertical cylindrical fibre under a streamwise thermal gradient. Previous works on isothermal flows have shown that the inlet flow and fibre geometry are the main factors that determine a transition from the absolute to the convective instability flow regimes. Our experiments demonstrate that an irregular wavy pattern and bead coalescence, which are commonly seen in the convective regime, can also be triggered by applying a thermal gradient along the fibre. We develop a lubrication model that accounts for gravity, temperature-dependent viscosity and surface tension to describe the thermal effects on downstream bead dynamics. Numerical simulations of the model show good agreement between the predicted droplet coalescence dynamics and the experimental data.

JFM classification

Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A19
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Batson, W., Agnon, Y. & Oron, A. 2017 Thermocapillary modulation of self-rewetting films. J. Fluid Mech. 819, 562–591.CrossRefGoogle Scholar
Brackbill, J.U., Kothe, D.B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354.CrossRefGoogle Scholar
Chang, H.-C. & Demekhin, E.A. 1999 Mechanism for drop formation on a coated vertical fibre. J. Fluid Mech. 380, 233–255.CrossRefGoogle 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.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
Ding, Z., Liu, Z., Liu, R. & Yang, C. 2019 Breakup of ultra-thin liquid films on vertical fiber enhanced by marangoni effect. Chem. Engng Sci. 199, 342–348.CrossRefGoogle Scholar
Ding, Z., Liu, R., Wong, T.N. & Yang, C. 2018 Absolute instability induced by marangoni effect in thin liquid film flows on vertical cylindrical surfaces. Chem. Engng Sci. 177, 261–269.CrossRefGoogle Scholar
Ding, Z. & Wong, T.N. 2017 Three-dimensional dynamics of thin liquid films on vertical cylinders with Marangoni effect. Phys. Fluids 29 (1), 011701.CrossRefGoogle Scholar
Dong, L., Li, X. & Liu, R. 2020 Effect of thermocapillary on absolute and convective instability of film flow of self-rewetting fluid. Microgravity Sci. Technol. 32, 415–422.CrossRefGoogle Scholar
Duprat, C., Ruyer-Quil, C. & Giorgiutti-Dauphiné, F. 2009 Spatial evolution of a film flowing down a fiber. Phys. Fluids 21 (4), 042109.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
Frenkel, A.L. 1992 Nonlinear theory of strongly undulating thin films flowing down vertical cylinders. Europhys. Lett. 18 (7), 583.CrossRefGoogle Scholar
de Gennes, P.G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.CrossRefGoogle Scholar
Haimovich, O. & Oron, A. 2011 Nonlinear dynamics of a thin nonisothermal liquid film on an axially oscillating cylindrical surface. Phys. Rev. E 84 (6), 061605.CrossRefGoogle Scholar
Hattori, K., Ishikawa, M. & Mori, Y.H. 1994 Strings of liquid beads for gas-liquid contact operations. AIChE J. 40 (12), 1983–1992.CrossRefGoogle Scholar
Issa, R.I., Gosman, A.D. & Watkins, A.P. 1986 The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme. J. Comput. Phys. 62 (1), 66–82.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
Ji, H., Sadeghpour, A., Ju, Y.S. & Bertozzi, A.L. 2020 a Modelling film flows down a fibre influenced by nozzle geometry. J. Fluid Mech. 901, R6.CrossRefGoogle Scholar
Ji, H., Taranets, R. & Chugunova, M. 2020 b On travelling wave solutions of a model of a liquid film flowing down a fibre. arXiv:2006.04994.Google Scholar
Ji, H. & Witelski, T.P. 2017 Finite-time thin film rupture driven by modified evaporative loss. Physica D 342, 1–15.CrossRefGoogle Scholar
Kabova, Y.O., Kuznetsov, V.V. & Kabov, O.A. 2012 Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film. Intl J. Heat Mass Transfer 55 (4), 1271–1278.CrossRefGoogle Scholar
Kalliadasis, S. & Chang, H.-C. 1994 Drop formation during coating of vertical fibres. J. Fluid Mech. 261, 135–168.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
Liu, R., Chen, X. & Wang, X. 2019 Effects of thermocapillarity on the dynamics of an exterior coating flow of a self-rewetting fluid. Intl J. Heat Mass Transfer 136, 692–701.CrossRefGoogle Scholar
Liu, R., Ding, Z. & Chen, X. 2018 The effect of thermocapillarity on the dynamics of an exterior coating film flow down a fibre subject to an axial temperature gradient. Intl J. Heat Mass Transfer 123, 718–727.CrossRefGoogle Scholar
Liu, R., Ding, Z. & Zhu, Z. 2017 Thermocapillary effect on the absolute and convective instabilities of film flows down a fibre. Intl J. Heat Mass Transfer 112, 918–925.CrossRefGoogle Scholar
Migita, H., Soga, K. & Mori, Y.H. 2005 Gas absorption in a wetted-wire column. AIChE J. 51 (8), 2190–2198.CrossRefGoogle Scholar
Mills, A.F. 1995 Heat and Mass Transfer. Richard D. Irwin.Google Scholar
Nozaki, T., Kaji, N. & Mod, Y.H. 1998 Heat transfer to a liquid flowing down vertical wires hanging in a hot gas stream: an experimental study of a new means of thermal energy recovery. Heat Transfer 6, 63–68.Google Scholar
Ruyer-Quil, C. & Kalliadasis, S. 2012 Wavy regimes of film flow down a fiber. Phys. Rev. E 85 (4), 046302.CrossRefGoogle ScholarPubMed
Ruyer-Quil, C., Scheid, B., Kalliadasis, S., Velarde, M.G. & Zeytounian, R.K. 2005 Thermocapillary long waves in a liquid film flow. Part 1. Low-dimensional formulation. J. Fluid Mech. 538, 199–222.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
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. Spec. Top. 166 (1), 89–92.CrossRefGoogle Scholar
Sadeghpour, A., Oroumiyeh, F., Zhu, Y., Ko, D.D., Ji, H., Bertozzi, A.L. & Ju, Y.S. 2021 Experimental study of a string-based counterflow wet electrostatic precipitator for collection of fine and ultrafine particles. J. Air Waste Manage. Assoc. doi:10.1080/10962247.2020.1869627.CrossRefGoogle ScholarPubMed
Sadeghpour, A., Zeng, Z., Ji, H., Ebrahimi, N.D., Bertozzi, A.L. & Ju, Y.S. 2019 Water vapor capturing using an array of traveling liquid beads for desalination and water treatment. Sci. Adv. 5 (4), eaav7662.CrossRefGoogle ScholarPubMed
Scheid, B., Kofman, N. & Rohlfs, W. 2016 Critical inclination for absolute/convective instability transition in inverted falling films. Phys. Fluids 28 (4), 044107.CrossRefGoogle Scholar
Shin-etsu 2005 Shin-etsu silicone silicone fluid dm-fluid performance test results. Retrieved from https://www.shinetsusilicone-global.com/catalog/pdf/kf96_us.pdfGoogle Scholar
Trifonov, Y.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.CrossRefGoogle Scholar
Washburn, E.W. 1921 The dynamics of capillary flow. Phys. Rev. 17 (3), 273.CrossRefGoogle Scholar
Whitaker, S. 1972 Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE J. 18 (2), 361–371.CrossRefGoogle Scholar
Zeng, Z., Sadeghpour, A. & Ju, Y.S. 2018 Thermohydraulic characteristics of a multi-string direct-contact heat exchanger. Intl J. Heat Mass Transfer 126, 536–544.CrossRefGoogle Scholar
Zeng, Z., Sadeghpour, A. & Ju, Y.S. 2019 A highly effective multi-string humidifier with a low gas stream pressure drop for desalination. Desalination 449, 92–100.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