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Falling Films Under Complicated Conditions

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Thin Films of Soft Matter

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 490))

Abstract

A film falling down an inclined plane has been an active topic of fundamental research at the international level for several decades both theoretically and experimentally and is now a classical hydrodynamic instability problem. However, the dynamics of a falling film in the presence of additional complexities, as compared to the classical problem, has largely been ignored by the majority of studies in falling films, even though these complexities are crucial in most situations of practical interest. These additional factors include heated substrates and three-dimensional effects. Here we present very recent and most-up-to-date developments for the problem of a falling film in the presence of these complexities and we outline open questions and issues which have not been resolved.

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Bibliography

  • S.V. Alekseenko, V.A. Antipin, V.V. Guzanov, S.M. Kharlamov, and D.M. Markovich. Three-dimensional solitary waves on falling liquid film at low reynolds numbers. Phys. Fluids, 17:121704, 2005.

    Article  Google Scholar 

  • S.V. Alekseenko, V.E. Nakoryakov, and B.G. Pokusaev. Wave Flow of Liquid Films. Begell House, New York, 1994.

    Google Scholar 

  • N.J. Balmforth, G.R. Ierley, and E.A. Speigel. Chaotic pulse trains. SIAM J. Appl. Maths, 54:1291–1334.

    Google Scholar 

  • T.B. Benjamin. Wave formation in laminar flow down an inclined plane. J. Fluid Mech., 2:554–574, 1957.

    Article  MathSciNet  Google Scholar 

  • D.J. Benney. Long waves on liquid films. J. Math. Phys., 45:150–155, 1966.

    MATH  MathSciNet  Google Scholar 

  • H.-C. Chang. Wave evolution on a falling film. Annu. Rev. Fluid Mech., 26:103–136, 1994.

    Article  Google Scholar 

  • H.-C. Chang and E.A. Demekhin. Solitary wave formation and dynamics on falling films. Adv. Appl. Mech., 32:1–58, 1996.

    Article  Google Scholar 

  • H.-C. Chang and E.A. Demekhin. Complex Wave Dynamics on Thin Films. Elsevier, New York, 2002.

    Google Scholar 

  • H.-C. Chang, E.A. Demekhin, and E. Kalaidin. Interaction dynamics of solitary waves on a falling film. J. Fluid Mech., 294:123–154, 1995a.

    Article  MATH  MathSciNet  Google Scholar 

  • H.-C. Chang, E.A. Demekhin, and E. Kalaidin. Generation and suppression of radiation by solitary pulses. SIAM J. Appl. Maths, 58:1246–1277, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  • H.-C. Chang, E.A. Demekhin, and D.I. Kopelevich. Laminarizing effects of dispersion in an active-dissipative nonlinear medium. Physica D, 63:299–320, 1993.

    Article  MATH  Google Scholar 

  • H.-C. Chang, E.A. Demekhin, and D.I. Kopelevich. Stability of a solitary pulse against wave packet disturbances in an active medium. Phys. Rev. Lett., 75:1747–1750, 1995b.

    Article  Google Scholar 

  • K.J. Chu and A.E. Dukler. Statistical characteristics of thin, wavy films. part 2. studies of the substrate and its wave structure. AIChE J., 20:695–706, 1976.

    Article  Google Scholar 

  • B.I. Cohen, J.A. Krommes, W.M. Tang, and M.N. Rosenbluth. Non-linear saturation of the dissipative trapped-ion mode coupling. Nucl. Fusion, 16:971–992, 1976.

    Google Scholar 

  • E.A. Demekhin, I.A. Demekhin, and V.Ya. Shkadov. Solitons in flowing layer of a viscous fluid. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 4:9–16, 1983.

    MathSciNet  Google Scholar 

  • E.A. Demekhin and M.A. Kaplan. Construction of exact numerical solutions of the stationary traveling type for viscous thin films. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 3:23–41, 1989.

    Google Scholar 

  • E.A. Demekhin, M.A. Kaplan, and V.Ya Shkadov. Mathematical models of the theory of viscous liquid films. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 6:73–81, 1987.

    Google Scholar 

  • E.J. Doedel, A.R. Champneys, T.F. Fairgrieve, Y.A. Kuznetsov, B. Sandstede, and X.-J. Wang. AUTO 97: Continuation and bifurcation software for ordinary differential equations. Montreal Concordia University (Available via FTP from ftp.cs.concordia.ca in directory pub/doedel/auto), 1997.

    Google Scholar 

  • C. Elphick, G.R. Ierley, O. Regev, and E.A. Spiegel. Interacting structures with galilean invariance. Phys. Rev. A, 44:1110–1122, 1991.

    Article  Google Scholar 

  • C. Elphick, E. Meron, and E.A. Spiegel. Spatiotemporal complexity in traveling patterns. Phys. Rev. Lett., 61:496–499, 1998.

    Article  MathSciNet  Google Scholar 

  • A.L. Frenkel and K. Indireshkumar. Wavy flows down an inclined plane: Perturbation theory and general evolution equation for the film thickness. Phys. Rev. E, 60:4143–4157, 1999.

    Article  MathSciNet  Google Scholar 

  • B. Gjevik. Spatially varying finite-amplitude wave trains on falling liquid films. Acta Polytech. Scand. Mech. Eng. Ser., 61:1–16, 1971.

    Google Scholar 

  • P. Glendinning and C. Sparrow. Local and global behavior near homoclinic orbits. J. Stat. Phys., 35:645–696, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  • D. Gottlieb and S.A. Orszag. Numerical Analysis of Spectral Methods: Theory and Applications. SIAM, Philadelphia, 1977.

    MATH  Google Scholar 

  • D.A. Goussis and R.E. Kelly. Surface waves and thermocapillary instabilities in a liquid film flow. J. Fluid Mech., 223:24–45, 1991.

    Article  Google Scholar 

  • K. Indireshkumar and A.L. Frenkel. Mutually penetrating motion of self-organizing two-dimensional patterns of solitonlike structures. Phys. Rev. E, 55:1174–1177, 1997.

    Article  Google Scholar 

  • A. Joets and R. Ribota. Localized, time-dependent state in the convection of a nematic liquid crystal. Phys. Rev. Lett., 60:2164–2167, 1988.

    Article  Google Scholar 

  • S.W. Joo, S.H. Davis, and S.G. Bankoff. Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers. J. Fluid Mech., 230:117–146, 1991.

    Article  MATH  Google Scholar 

  • S. Kalliadasis, E.A. Demekhin, C. Ruyer-Quil, and M.G. Velarde. Thermocapillary instability and wave formation on a film falling down a uniformly heated plane. J. Fluid Mech., 492:303–338, 2003a.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Kalliadasis, A. Kiyashko, and E.A. Demekhin. Marangoni instability of a thin liquid film heated from below by a local heat source. J. Fluid Mech., 475:377–408, 2003b.

    Article  MATH  Google Scholar 

  • P.L. Kapitza. Wave flow of thin layers of a viscous fluid: I. Free flow. Zh. Eksp. Teor. Fiz., 18:3–28, 1948.

    Google Scholar 

  • P.L. Kapitza and S.P. Kapitza. Wave flow of thin layers of a viscous fluid: III. Experimental study of undulatory flow conditions. Zh. Eksp. Teor. Fiz., 19:105–120, 1949.

    Google Scholar 

  • T. Kawahara. Formation of saturated solitons in a nonlinear dispersive system with instability and dissipation. Phys. Rev. Lett., 51:381–383, 1983.

    Article  Google Scholar 

  • T. Kawahara and S. Toh. Pulse interactions in an unstable dissipative-dispersive nonlinear system. Phys. Fluids, 31:2103–2111, 1988.

    Article  MathSciNet  Google Scholar 

  • E.A. Kuznetsov, A.M. Rubechik, and V.E. Zakharov. Soliton stability in plasmas and hydrodynamics. Phys. Rep., 142:103–165, 1986.

    Article  MathSciNet  Google Scholar 

  • S.P. Lin. Finite amplitude side-band stability of a viscous film. J. Fluid Mech., 63: 417–429, 1974.

    Article  MATH  Google Scholar 

  • S.P. Lin and M.V.G. Krishna. Stability of liquid film with respect to initially finite three-dimensional disturbances. Phys. Fluids, 20:2005–2001, 1977.

    Article  MATH  Google Scholar 

  • C. Nakaya. Waves on a viscous fluid film down a vertical wall. Phys. Fluids, 7:1143–1154, 1989.

    Google Scholar 

  • V.I. Nekorkin and M.G. Velarde. Solitary waves, soliton bound states and chaos in a dissipative korteweg-de vries equation. Int. J. Bifurcation Chaos, 4:1135–1146, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  • A.A. Nepomnyashchy. Stability of wave regimes in a film flowing down an inclined plane. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 3:28–34, 1974.

    Google Scholar 

  • T. Ooshida. Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number. Phys. Fluids, 11:3247–3269, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  • A. Oron, S.H. Davis, and S.G. Bankoff. Long-scale evolution of thin liquid films. Rev. Mod. Phys., 69:931–980, 1997.

    Article  Google Scholar 

  • A. Oron and O. Gottlieb. Nonlinear dynamics of temporally excited falling liquid films. Phys. Fluids, 14:2622–2636, 2002.

    Article  MathSciNet  Google Scholar 

  • C.D. Park and T. Nosoko. Three-dimensional wave dynamics on a falling film and associated mass transfer. AIChE J., 49:2715–2727, 2003.

    Article  Google Scholar 

  • J.R.A. Pearson. On convective cells induced by surface tension. J. Fluid Mech., 4: 489–500, 1958.

    Article  MATH  Google Scholar 

  • C.-A. Peng, L.A. Jurman, and M.J. McCready. Formation of solitary waves on gassheared liquid layers. Int. J. Multiphase Flow, 17:767–782, 1991.

    Article  MATH  Google Scholar 

  • V.I. Petviashvili and O.Yu. Tsvelodub. Horse-shoe shaped solitons on an inclined viscous liquid film. Dokl. Akad. Nauk SSSR, 238:1321–1324, 1978.

    Google Scholar 

  • A. Pumir, P. Manneville, and Y. Pomeau. On solitary waves running down an inclined plane. J. Fluid Mech., 135:27–50, 1983.

    Article  MATH  Google Scholar 

  • B. Ramaswamy, S. Chippada, and S.W. Joo. A full-scale numerical study of interfacial instabilities in thin film flows. J. Fluid Mech., 325:163–194, 1996.

    Article  MATH  Google Scholar 

  • P. Rosenau, A. Oron, and J.M. Hyman. Bounded and unbounded patterns of the Benney equation. J. Fluid Mech., 4:1102–1104, 1992.

    Google Scholar 

  • G.J. Roskes. Three-dimensional long waves on liquid film. Phys. Fluids, 13:1440–1445, 1970.

    Article  MATH  Google Scholar 

  • C. Ruyer-Quil and P. Manneville. Improved modeling of flows down inclined planes. Eur. Phys. J. B, 15:357–369, 2000.

    Article  Google Scholar 

  • C. Ruyer-Quil and P. Manneville. Further accuracy and convergence results of the modeling of flows down inclined planes by weighted residual approximations. Phys. Fluids, 14:170–183, 2002.

    Article  MathSciNet  Google Scholar 

  • C. Ruyer-Quil, B. Scheid, S. Kalliadasis, M.G. Velarde, and R.Kh Zeytounian. Thermocapillary long waves in a liquid film flow. Part 1. Low-dimensional formulation. J. Fluid Mech., 538:199–222, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  • T.R. Salamon, R.C. Armstrong, and R.A. Brown. Traveling waves on vertical films: Numerical analysis using the finite element method. Phys. Fluids, 6:2202–2220, 1993.

    Article  Google Scholar 

  • S. Saprykin, E.A. Demekhin, and S. Kalliadasis. Two-dimensional wave dynamics in thin films. Part I. Stationary solitary pulses. Phys. Fluids, 17:117105, 2005.

    Article  MathSciNet  Google Scholar 

  • B. Scheid. Evolution and Stability of Falling Liquid Films with Thermocapillary Effects. PhD Thesis. Université Libre de Bruxelles, 2004.

    Google Scholar 

  • B. Scheid, A. Oron, P. Colinet, U. Thiele, and J.C. Legros. Nonlinear evolution of nonuniformly heated falling liquid films. Phys. Fluids, 14:4130–4151, 2002.

    Article  MathSciNet  Google Scholar 

  • B. Scheid, C. Ruyer-Quil, S. Kalliadasis, M.G. Velarde, and R.Kh Zeytounian. Thermocapillary long waves in a liquid film flow. Part 2. Linear stability and nonlinear waves. J. Fluid Mech., 538:223–244, 2005a.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Chemical Engineering, Imperial College London, London, UK

    Serafim Kalliadasis

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  1. Serafim Kalliadasis
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Editors and Affiliations

  1. Imperial College London, UK

    Serafim Kalliadasis

  2. Max-Planck-Institut für Physik Komplexer Systeme, Dresden, Germany

    Uwe Thiele

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Kalliadasis, S. (2007). Falling Films Under Complicated Conditions. In: Kalliadasis, S., Thiele, U. (eds) Thin Films of Soft Matter. CISM International Centre for Mechanical Sciences, vol 490. Springer, Vienna. https://doi.org/10.1007/978-3-211-69808-2_5

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  • DOI: https://doi.org/10.1007/978-3-211-69808-2_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-69807-5

  • Online ISBN: 978-3-211-69808-2

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