Abstract
The present work discusses both the linear and nonlinear stability conditions of a viscous falling film down the outer surface of a solid vertical cylinder which moves in the direction of its axis with a constant velocity. After studying the linear conditions, a generalized nonlinear kinematic model is then derived to present the physical system. Applying the boundary conditions, analytical solutions are obtained using the long-wave perturbation method. In the first step, the normal mode method is used to characterize the linear behaviors. In the second step, the nonlinear film flow model is solved by using the method of multiple scales, to obtain Ginzburg-Landau equation. The influence of some physical parameters is discussed in both linear and nonlinear steps of the problem, and the results are displayed in many plots showing the stability criteria in various parameter planes.
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References
Lin, C.C.: The Theory of Hydrodynamic Stability. Cambridge University Press, Cambridge (1955)
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Oxford University Press, Oxford (1961)
Lin, S.P., Wang, C.Y.: Encyclopedia Fluid Mechanics. Ed. Cheremisioff, Gulf. Houston (1986)
Yih, C.S.: Stability of parallel laminar flow with a free surface. In: Proceedings of the Second US National Congress of Applied Mechanics. USA, 623–628 (1954)
Benney, D.J.: Long waves on liquid film. J. Math. Phys. 45, 150–155 (1966)
Lin, S.P.: Finite amplitude side-band stability of a viscous film. J. Fluid Mech. 63, 417–429 (1974)
Nakaya, C.: Equilibrium state of periodic waves on the fluid film down a vertical wall. J. Phys. Soc. JPN. 36, 921–926 (1974)
Krishna, M.V.G., Lin, S.P.: Nonlinear stability of a viscous film with respect to three-dimensional side-band disturbance. Phys. Fluids 20, 1039–1044 (1977)
Pumir, A., Manneville, P., Pomeau, Y.: On solitary waves running down on inclined plane. J. FluidMech. 135, 27–50 (1983)
Hwang, C.C., Weng, C.I.: Finite-amplitude stability analysis of liquid films down a vertical wall with and without interfacial phase change. Int. J. Multiphase Flow. 13, 803–814 (1987)
Lin, S.P., Liu, W.C.: Instability of film coating of wires and tubes. AIChE J. 21, 775–782 (1975)
Rosenau, P., Oron, A.: Evolution and breaking of liquid film flowing on a vertical cylinder. Phys. Fluids A1, 1763–1766 (1989)
Hung, C.I., Chen, C.K., Tsai, J.S.: Weakly nonlinear stability analysis of condensate film flow down a vertical cylinder. Int. J. Heat Mass Transfer. 39, 2821–2829 (1996)
Edwards, D.A., Brenner, H., Wasan, D.T.: Interfacial Transport Processes and Rheology. Butterworth-Heinemann, a Division of Reed Publishing, USA (1991)
Chen, C.I., Chen, C.K., Yang, Y.T.: Perturbation analysis to the nonlinear stability characterization of thin condensate falling film on the outer surface of a rotating vertical cylinder. Int. J. Heat Mass Transfer. 47, 1937–1951 (2004)
Zakaria, K.: Nonlinear instability of a liquid jet in the presence of a uniform electric field. Fluid Dynamics Research. 26, 405–420 (2000)
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Zakaria, K., Gamiel, Y. Viscous falling film instability around a vertical moving cylinder. Acta Mech Sin 28, 253–265 (2012). https://doi.org/10.1007/s10409-012-0003-0
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DOI: https://doi.org/10.1007/s10409-012-0003-0