Abstract
Wavy downflow of viscous fluid films is studied. The full Navier-Stokes equations are used to calculate the hydrodynamic characteristics of the flow. The stability of calculated nonlinear waves to arbitrary two-dimensional perturbations is considered within the framework of the Floquet theory. It is shown that, for small values of the Kapitza number, the waves are stable over a wide range of wavelengths and values of the Reynolds number. It is found that, as the Kapitza number increases, the parameter range where nonlinear waves are calculated is divided into a series of alternating zones of stable and unstable solutions. A large number of narrow zones where the solutions are stable are revealed on the wavelength-Reynolds number parameter plane for large values of the Kapitza number. Optimal regimes of film downflow that correspond to the minimum value of average film thickness for nonlinear waves with different wavelengths are determined. The basic characteristics of these waves are calculated in a wide range of Reynolds and Kapitza numbers.
Similar content being viewed by others
References
W. Nusselt, “Die Oberflächenkondensation des Wasserdampfes,” Z. VDI 60, 541–546 (1916).
P. L. Kapitza, “Wave Flow of Thin Layers of a Viscous Fluid. 1. Free Flow,” Zh. Exp. Teor. Fiz. 18(1), 3–28 (1948).
P. L. Kapitza and S. P. Kapitza, “Wave Flow of Thin Layers of a Viscous Fluid. 3. Experimental Study of Wave Flow Regime,” Zh. Exp. Teor. Fiz. 19(2) 105–120 (1949).
K. I. Chu and A. E. Dukler, “Statistical Characteristics of Thin, Wavy Films. 2. Studies of the Substrate and Its Wave Structure,” AIChE J. 20, 695–706 (1974).
S. V. Alekseenko, V. E. Nakoryakov, and B. G. Pokusaev, “Wave Formation on a Vertical Falling Liquid Film,” AIChE J. 31, 1446–1460 (1985).
J. Liu, J. D. Paul, and J. P. Gollub, “Measurements of the Primary Instabilities of Film Flow,” J. Fluid Mech. 250, 69–101 (1993).
H.-C. Chang and E. A. Demekhin, Complex Wave Dynamics on Thin Films (Elsevier, New York, 2002).
S. Kalliadasis, C. Ruyer-Quil, B. Scheid, and M. G. Velarde, Falling Liquid Films (Springer, London, 2012). (Appl. Math. Sci., Vol. 176.)
V. Ya. Shkadov, “Wavy Flow of a Thin Layer of a Viscous Fluid under Gravity,” Izv. Akad. Nauk SSSR, Mekh. Zhid. Gaza, No. 1, 43–51 (1967).
T. R. Salamon, R. C. Armstrong, and R. A. Brown, “Traveling Waves on Inclined Films: Numerical Analysis by the Finite-Element Method,” Phys. Fluids 6, 2202–2220 (1994).
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).
N. T. Malamataris, M. Vlachogiannis, and V. Bontozoglou, “Solitary Waves on Inclined Films: Flow Structure and Binary Interactions,” Phys. Fluids 14, 1143–1154 (2002).
N. T. Malamataris and V. Balakotaiah, “Flow Structure underneath the Large Amplitude Waves of a Vertically Falling Film,” AIChE J. 54, 1725–1740 (2008).
G. F. Dietze, A. Leefken, and R. Kneer, “Investigation of the Backflow Phenomenon in Falling Liquid Films,” J. Fluid Mech. 595, 435–459 (2008).
Yu. Ya. Trifonov, “Stability of Wavy Downflow of Films Calculated by the Navier-Stokes Equations,” Prikl. Mekh. Tekh. Fiz. 49(2), 98–112 (2008) [J. Appl. Mech. Tech. Phys. 49 (2), 239–252 (2008)].
Y. Trifonov, “Stability and Bifurcations of the Wavy Film Flow Down a Vertical Plate: The Results of Integral Approaches and Full-Scale Computations,” Fluid Dyn. Res. 44, 031.418 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.Ya. Trifonov.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 55, No. 2, pp. 188–198, March–April, 2014.
Rights and permissions
About this article
Cite this article
Trifonov, Y.Y. Waves on down-flowing fluid films: Calculation of resistance to arbitrary two-dimensional perturbations and optimal downflow conditions. J Appl Mech Tech Phy 55, 352–361 (2014). https://doi.org/10.1134/S0021894414020187
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894414020187