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Thermocapillary modulation of self-rewetting films

Published online by Cambridge University Press:  27 April 2017

W. Batson Open the ORCID record for W. Batson [Opens in a new window] ,
Y. Agnon  and
A. Oron
W. Batson*
Affiliation:
Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07103, USA Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Y. Agnon
Affiliation:
Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
A. Oron
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: [email protected]
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Abstract

Whereas surface tension decreases linearly with temperature for most fluids, here we consider those that exhibit a well-defined minimum. Specifically, our study is motivated by dilute aqueous mixtures of long-chain alcohols, for which surface tension is typically assumed to be a quadratic function of temperature. Utilization of these so-called ‘self-rewetting fluids’ has grown significantly in the past decade, due to observations that heat transfer is enhanced in applications such as film boiling and pulsating heat pipes. With similar applications in mind, we investigate the dynamics of a thin film with quadratic surface tension which is subjected to a temperature modulation in the bounding gas. A model is developed within the framework of the long-wave approximation, and a time-averaged thermocapillary driving force for destabilization is uncovered that results from the nonlinear surface tension. Linear stability analysis of the nonlinear partial differential equation for the film thickness is used to determine the critical conditions at which this driving force destabilizes the film and numerical investigation of this evolution equation reveals that linearly unstable perturbations saturate to regular periodic solutions (when the modulational frequency is set properly). Properties of these flows such as bifurcation at critical points and long-domain flows, where multiple unstable linear modes interact, are also discussed.

JFM classification

Convection: Marangoni convection Instability: Nonlinear instability Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 562 - 591
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Copyright
© 2017 Cambridge University Press 

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References

Abe, Y. 2006 Self-rewetting fluids. Ann. N. Y. Acad. Sci. 1077, 650–667.CrossRefGoogle ScholarPubMed
Aveyard, R., Binks, B. P. & Mead, J. 1985 Interfacial tension minima in oil+water+surfactant systems. Effects of salt, temperature and alkane in systems containing ionic surfactants. J. Chem. Soc. Faraday Trans. 81, 2169–2177.CrossRefGoogle Scholar
Batson, W., Agnon, Y. & Oron, A. 2015 Mass variation of a thin liquid film driven by an acoustic wave. Phys. Fluids 27, 062106.Google Scholar
Bénard, H. 1900 Les tourbillons cellulaires dans une nappe liquide. Ref. Gén. Sci. Pure Apple. 11, 1261–1271.Google Scholar
Boyd, J. P. 2001 Chebyshev and Fourier Spectral Methods, 2nd edn. (Revised). Dover.Google Scholar
Fracescantonio, N., Savino, R. & Abe, Y. 2008 New alcohol solutions for heat pipes: Marangoni effect and heat transfer enhancement. Intl J. Heat Mass Transfer 51, 6199–6207.Google Scholar
Frisk, D. P. & Davis, E. J. 2015 The enhancement of heat transfer by waves in stratified gas–liquid flow. Intl J. Heat Mass Transfer 15, 1537–1552.Google Scholar
Fumoto, K., Ishida, T., Kawanami, T. & Inamura, T. 2015 Experimental study on pulsating heat pipe using self-rewetting fluid as a working fluid: visualization of thin liquid film and surface wave. Heat Pipe Sci. Tech. 6, 65–76.Google Scholar
Gannon, M. G. J. & Faber, T. E. 1978 The surface tension of nematic liquid crystals. Phil. Mag. A 37, 117–135.Google Scholar
Goren, S. L. & Mani, R. V. S. 1968 Mass transfer through horizontal liquid films in wavy motion. AIChE J. 14, 57–61.CrossRefGoogle Scholar
Guianvarc’h, C., Bruneau, M. & Gavioso, R. M. 2014 Acoustics and precondensation phenomena in gas–vapor saturated mixtures. Phys. Rev. E 89, 023208.Google ScholarPubMed
Haimovich, O. & Oron, A. 2010 Nonlinear dynamics of a thin liquid film on an axially oscillating cylindrical surface. Phys. Fluids 22, 032101.Google Scholar
Holman, J. P. 2010 Heat Transfer. McGraw-Hill.Google Scholar
Hu, Y., Liu, T., Li, X. & Wang, S. 2014 Heat transfer enhancement of micro oscillating heat pipes with self-rewetting fluid. Intl J. Heat Mass Transfer 70, 496–503.CrossRefGoogle Scholar
Kalliadasis, S., Kiyashko, A. & Demekhin, E. A. 2003 Marangoni instability of a thin liquid film heated from below by a local heat source. J. Fluid Mech. 475, 377–408.Google Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films. (Applied Mathematical Sciences, vol. 176) , Springer.CrossRefGoogle Scholar
Karapetsas, G., Sahu, K. C., Sefiane, K. & Matar, O. K. 2014 Thermocapillary-driven motion of a sessile drop: effect of non-monotonic dependence of surface tension on temperature. Langmuir 30, 4310–4321.CrossRefGoogle ScholarPubMed
Legros, J. C. 1986 Problems related to nonlinear variations of surface tension. Acta Astron. 13, 697–703.Google Scholar
Mehl, J. B. & Moldover, M. R. 1982 Precondensation phenomena in acoustic measurements. J. Chem. Phys. 77, 455–465.Google Scholar
Nepomnyashchy, A., Velarde, M. & Colinet, P. 2001 Interfacial Phenomena and Convection. CRC.Google Scholar
Noda, D. & Ueda, Y. 2013 A thermoacoustic oscillator powered by vaporized water and ethanol. Am. J. Phys. 81, 124–126.CrossRefGoogle Scholar
Ono, N., Kaneko, T., Nishiguchi, S. & Shoji, M. 2009 Measurement of temperature dependence of surface tension of alcohol aqueous solutions by maximum bubble pressure method. J. Therm. Sci. Tech. Japan 4, 284–293.Google Scholar
Or, A. C. & Kelly, R. E. 2002 The effects of thermal modulation upon the onset of Marangoni–Bénard convection. J. Fluid Mech. 456, 161–182.CrossRefGoogle Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.Google Scholar
Oron, A. & Rosenau, P. 1994 On a nonlinear thermocapillary effect in thin liquid layers. J. Fluid Mech. 273, 361–374.Google Scholar
Pearson, J. R. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500.Google Scholar
Plechkova, N. V. & Seddon, K. R. 2008 Applications of ionic liquids in the chemical industry. Chem. Soc. Rev. 37, 123–150.Google Scholar
Raspet, R., Slaton, W. V., Hickey, C. J. & Hiller, R. A. 2002 Theory of inert gas-condensing vapor thermoacoustics: propagation equation. J. Acoust. Soc. Am. 112, 1414–1422.Google Scholar
Restolho, J., Mata, J. L. & Saramango, B. 2011 Peculiar surface behavior of some ionic liquids based on active pharmaceutical ingredients. J. Chem. Phys. 134, 074702.Google Scholar
Savino, R., Cecere, A., VanVaerenbergh, S., Abe, Y., Pizzirusso, G., Tzevelecos, W., Mojahed, M. & Galand, Q. 2013 Some experimental progresses in the study of self-rewetting fluids for the selene experiment to be carried in the thermal platform 1 hardware. Acta Astron. 89, 179–188.Google Scholar
Savino, R., Paola, R. D., Cecere, A. & Fortezza, R. 2010 Self-rewetting heat transfer fluids and nano brines for space heat pipes. Acta Astron. 67, 1030–1037.Google Scholar
Scriven, L. E. & Sternling, C. V. 1964 On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech. 19, 321–340.Google Scholar
Shanahan, M. E. & Sefiane, K. 2014 Recalcitrant bubbles. Sci. Rep. 4, 4727.Google Scholar
Sitar, A. & Golobic, I. 2015 Heat transfer enhancement of self-rewetting aqueous n-butanol solutions boiling in microchannels. Intl J. Heat Mass Transfer 81, 198–206.CrossRefGoogle Scholar
Smorodin, B. L., Mikishev, A. B., Nepomnyashchy, A. A. & Myznikova, B. I. 2009 Thermocapillary instability of a liquid layer under heat flux modulation. Phys. Fluids 21, 062102.Google Scholar
Smyrlis, Y. S. & Papageorgiou, D. T. 1991 Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation, a case study. Proc. Natl Acad. Sci. USA 88, 11129–11132.Google Scholar
Swift, G. W. 1988 Thermoacoustic engines. J. Acoust. Soc. Am. 84, 1145–1180.CrossRefGoogle Scholar
Thiele, U. & Knobloch, E. 2004 Thin liquid films on a slightly inclined heated plate. Physica D 190, 213–248.Google Scholar
Tripathi, M. K., Sahu, K. C., Karapetsas, G., Sefiane, K. & Matar, O. K. 2015 Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature. J. Fluid Mech. 763, 82–108.Google Scholar
VanHook, S. J., Schatz, M. F., Swift, J. B., McCormick, W. D. & Swinney, H. L. 1997 Long-wavelength surface-tension-driven Bénard convection: experiment and theory. J. Fluid Mech. 345, 45–78.CrossRefGoogle Scholar
Vochten, R. & Pétré, G. 1973 Study of heat reversible adsorption at air-solution interface 2. Experimental determination of heat of reversible adsorption of some alcohols. J. Colloid Interface Sci. 42, 320–327.Google Scholar
Wu, S. 2015 Study of self-rewetting fluid applied to loop heat pipe. Intl J. Therm. Sci. 98, 374–380.CrossRefGoogle Scholar
Zhang, N. 2001 Innovative heat pipe systems using a new working fluid. Intl Commun. Heat Mass Transfer 28 (8), 1025–1033.Google Scholar