

ROLL WAVES ON VERTICAL FALLING LIQUID FILM
Nakoryakov V.E.^{1}, Ostapenko V.V.^{2}, Bartashevich M.V.^{1,3}
^{1} Institute of Thermophysics SB RAS, Novosibirsk, Russia ^{2} Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia ^{3} Novosibirsk State University, Novosibirsk, Russia
Citation:
Nakoryakov, V.E., Ostapenko, V.V. and Bartashevich, M.V., (2013) Roll waves on vertical falling liquid film, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(12), PP. 189  193.

Keywords: roll waves; continuous and discontinuous solutions; heat and masstransfer; film condensation and evaporation 
Abstracts:
The mathematical model of thin liquid film flowing down a vertical wall in the rollwave regime is considered taking into account heat and mass transfer through the interface. The families of continuous and discontinuous solutions, where the progressive waves are conjugated with each other or with the “residual” film thickness through the strong and weak discontinuities, have been constructed. These solutions qualitatively simulate the condensing and evaporating liquid film flowing down a vertical heat transfer surface. In spite of the large number of the theoretical and experimental studies devoted to different types and regimes of film flows (for example, rivulet flows, film flows in cocurrent gas flow, film flows on structured surfaces), the physics of wave formation on the surface of thin liquid layers is investigated insufficiently. In particular, the hydrodynamics of film flows with the heat and mass transfer through the liquidgas interface is still poorly understood. In this paper we consider the model problem of thin liquid film flowing down a vertical wall in the rollwave regime involving heat and mass transfer through the interface. The families of discontinuous and continuous solutions of the rollwave equation have been constructed. 
References:
Nusselt W. Zeitschrift der VDI. 60.  H. 2728.  1916.
Alekseenko S.V., Nakoryakov V.E., Pokusaev B.G. Wave Flow of Liquid Films.  New York: Begell House.  1994.  335 P.
Капица П.Л. Волновое течение тонких слоев вязкой жидкости // ЖЭТФ.  1948. Т. 18.  № 1.  С.328.
Шкадов В.Я. Волновые режимы течения тонкого слоя вязкой жидкости под действием силы тяжести // Изв. АН СССР. МЖГ. 1967. № 1.  С. 4351.
Nakoryakov V.E., Shreiber I.R. Waves on the surface of a thin layer of viscous liquid // Journal of Applied Mechanics and Technical Physics  1973.  V. 14.  N 2.  P. 237241.
Nakoryakov V.E., Pokusaev B.G., Alekseenko S.V. Stationary twodimensional rolling waves on a vertical film of fluid // Journal of Engineering Physics and Thermophysics.  1976.  V.30.  No. 5.  P.517521.
V.A. Buchin, G.A. Shaposhnikova, Flow of shallow water with a periodic system of jumps over a vertical surface // Doklady Physics. 2009, V.54, N.5, P.248251.
Ganchev B.G. Cooling of Nuclear Reactor Elements By Falling Film Flow  Energoatomizdat: Moskva.  1987.  191 P.
Nakoryakov V.E., Ostapenko V.V., Bartashevich M.V. Heat and mass transfer in the liquid film on a vertical wall in rollwave regime // International Journal of Heat and Mass Transfer.  2012.  Vol. 55, Is. 2324.  P. 65146518.
Ostapenko V.V. Hyperbolic systems of conservation laws and their application to the shallow water theory.  Novosibirsk.  NSU.  2004.  180 P.


