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Effect of Thermocapillary on Absolute and Convective Instability of Film Flow of Self-Rewetting Fluid

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Abstract

The dynamics of a self-rewetting film falling along a vertical fiber under the influence of gravity are considered. The evolution equation of the interface of the self-rewetting film is established in the framework of a long-wave approximation theory. The effect of thermocapillarity (Marangoni effect) on the absolute/convective instability (AI/CI) is investigated for self-rewetting fluids of which the surface tension is a quadratic function of the temperature at the surface. The effect of thermocapillarity on the Rayleigh-Plateau instability is investigated by examining the dispersion relation. The characteristics of self-rewetting fluids are considered for different Marangoni numbers (Ma) in different regions of absolute/convective instability using a spatio-temporal stability analysis. Numerical simulations of the nonlinear evolution in various regions of absolute/convective instability are also performed. The results of numerical simulations are in excellent agreement with the spatio-temporal stability analysis. The effect of thermocapillarity on absolute and convective instability depends on the difference between the temperature at the interface \(\bar {\varTheta }_{i}\), and the temperature corresponding the minimum surface tension Θ0. The results indicate that the thermocapillarity suppresses the absolute instability and enhances the convective instability as Ma increases when \(\bar {\varTheta }_{i}-{\varTheta }_{0}> 0\), and enhances the absolute instability as Ma increases when \(\bar {\varTheta }_{i}-{\varTheta }_{0}< 0\).

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References

  • Abe, Y., Iwaski, A., Tanaka, K.: Thermal management with self-rewetting fluids. Microgravity Sci. Technol. 16(1-4), 148–152 (2005)

    Article  Google Scholar 

  • Abe, Y.: Self-rewetting fluids. Ann. N.Y. Acad. Sci. 1077(1), 650–667 (2006)

    Article  Google Scholar 

  • Chen, X., Zhu, Z.Q., Liu, Q.S.: Thermodynamics behaviors of macroscopic liquid droplets evaporation from heated substrates. Microgravity Sci. Technol. 27(5), 353–360 (2015)

    Article  Google Scholar 

  • Chen, X., Wang, X., Chen, P.G., Liu, Q.S.: Thermal effects of substrate on Marangoni flow in droplet evaporation: response surface and sensitivity analysis. Int. J. Heat Mass Transfer 113, 354–365 (2017)

    Article  Google Scholar 

  • Dávalos-Orozco, LA, You, X.: Three-dimensional instability of a liquid layer flowing down a heated vertical cylinder. Phys. Fluids 12(9), 2198–2209 (2000)

    Article  Google Scholar 

  • Dávalos-Orozco, LA: Sideband thermocapillary instability of a thin film coating the outside of a thick walled cylinder with finite thermal. Interfacial Phenom. Heat Transfer 5(4), 287–298 (2017)

    Article  Google Scholar 

  • Dávalos-Orozco, LA: Sideband thermocapillary instability of a thin film falling down the inside of a thick-walled cylinder with finite thermal conductivity. Interfacial Phenom. Heat Transfer 6(3), 239–251 (2018)

    Article  Google Scholar 

  • Dávalos-Orozco, LA: Sideband thermocapillary instability of a thin film flowing down the outside of a thick walled cylinder with finite thermal conductivity. Int. J. Nonlin. Mech. 109, 15–23 (2019a)

  • Dávalos-Orozco, LA: Nonlinear sideband thermocapillary instability of a thin film coating the inside of a thick walled cylinder with finite thermal conductivity in the absence of gravity. Microgravity Sci. Technol. https://doi.org/10.1007/s12217-019-09751-5 (2019b)

  • Ding, Z., Wong, T.N.: Falling liquid films on a slippery substrate with Marangoni effects. Int. J. Heat Mass Tran. 90, 689–701 (2015)

    Article  Google Scholar 

  • Ding, Z., Wong, T.N.: Three-dimensional dynamics of thin liquid films on vertical cylinders with Marangoni effect. Phys. Fluids 29(1), 011701 (2017)

    Article  Google Scholar 

  • Ding, Z., Liu, R., Wong, T.N., Yang, C.: Absolute instability induced by Marangoni effect in thin liquid film flows on vertical cylindrical surfaces. Chem. Eng. Sci. 177, 261–269 (2018)

    Article  Google Scholar 

  • Ding, Z., Liu, Z., Liu, R., Yang, C.: Breakup of ultra-thin liquid films on vertical fiber enhanced by Marangoni effect. Chem. Eng. Sci. https://doi.org/10.1016/j.ces.2018.12.058 (2019)

  • Ding, Z., Liu, Z., Liu, R., Yang, C.: Thermocapillary effect on the dynamics of liquid films coating the interior surface of a tube. Int. J. Heat Mass Tran. 138, 524–533 (2019)

    Article  Google Scholar 

  • Duprat, C., Ruyer-Quil, C., Kalliadasis, S.: Absolute and convective instabilities of a viscous film flowing down a vertical fiber. Phys. Rev. Lett. 98(24), 244502 (2007)

    Article  Google Scholar 

  • Frenkel, A.L.: Nonlinear theory of strongly undulating thin films flowing down vertical cylinders. Europhys Lett. 31(1), 347–384 (1999)

    Google Scholar 

  • Gannon, M.G.L., Faber, T.E.: The surface tension of nematic liquid crystals. Phil. Mag. A. 37(1), 117–135 (1978)

    Article  Google Scholar 

  • Goren, S.L.: The instability of an annular thread of fluid. J. Fluid Mech. 12(02), 309–319 (1962)

    Article  MathSciNet  Google Scholar 

  • Hu, Y., Lium, T., Li, X.: Heat transfer enhancement of micro oscillating heat pipes with self-rewetting Fluid. Int. Commun. Heat Mass 28(8), 1025–1033 (2014)

    Google Scholar 

  • Huerre, P., Monkwitz, P.A.: Local and global instabilities inspatially developing flows. Annu. Rev. Fluid Mech 37(1), 357–392 (2005)

    Article  Google Scholar 

  • Kliakhandler, I.L., Davis, S.H., Bankoff, S.G.: Viscous beads on vertical fibre. J. Fluid Mech. 429, 381–390 (2001)

    Article  Google Scholar 

  • Liu, R., Liu, Q.S.: Thermocapillarity effect on the dynamics of viscous beads on vertical fiber. Phys. Rev. E. 90(3), 033005 (2014)

    Article  Google Scholar 

  • Liu, R., Ding, Z., Zhu, Z.: Thermocapillarity Eeffect on the absolute and convective instabilities of film flows fown a fibre. Int. J. Heat Mass Tran. 112, 918–925 (2017)

    Article  Google Scholar 

  • Liu, R., Chen, X., Wang, X.: Effects of thermocapillarity on the dynamics of an exterior coating flow of a self-rewetting fluid. Int. J. Heat Mass Tran. 136, 692–701 (2019)

    Article  Google Scholar 

  • Lin, S.P., Liu, W.C.: Instability of film coating of wires and tubes. AIChE J. 21(4), 775–782 (1975)

    Article  Google Scholar 

  • Ono, N., Kaneko, T., Nishigochi, S., Shoji, M.: Measurement of temperature dependence of surface tension of alcohol aqueous solutions by maximum bubble pressure method. J. Therm. Sci. Tech. Jpn. 4(2), 284–293 (2009)

    Article  Google Scholar 

  • Quéré, D.: Thin films flowing on vertical fibers. Europhys. Lett. 13(8), 347–384 (1990)

    Article  Google Scholar 

  • Rayleigh, L.: On the stablitily of liquid jets. P. Lond. Math. Soc. 10, 4–18 (1878)

    Article  MathSciNet  Google Scholar 

  • Restolho, J., Mata, L.J., Saramago, B.: Peculiar surface behavior of some ionic liquids based on active pharmaceutical ingredients. J. Chem.Phys. 134(7), 2262 (2011)

    Article  Google Scholar 

  • Zhang, N.: Innovative heat pipe systems using a new working fluid. Int. Commun. Heat Mass 28(8), 1025–1033 (2001)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 51766002, 11802066), Guangxi Natural Science Foundation (No. 2018GXNSFBA138058), Guangxi’s Key Laboratory Foundation of Manufacturing Systems and Advanced Manufacturing Technology (Grant No. 17-259-05-002Z), and Innovation Project of GUET Graduate Education (Grant No. 2019YCXS005)

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  1. School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin, China

    Longgang Dong, Xuemei Li & Rong Liu

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  1. Longgang Dong
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  2. Xuemei Li
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  3. Rong Liu
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Correspondence to Rong Liu.

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This article belongs to the Topical Collection: Multiphase Fluid Dynamics in Microgravity

Guest Editors: Tatyana P. Lyubimova, Jian-Fu Zhao

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Dong, L., Li, X. & Liu, R. Effect of Thermocapillary on Absolute and Convective Instability of Film Flow of Self-Rewetting Fluid. Microgravity Sci. Technol. 32, 415–422 (2020). https://doi.org/10.1007/s12217-019-09778-8

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