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Long-Wave Perturbation Method to Investigate Nonlinear Stability of the Thin Power Law Liquid Film Flowing Down on a Vertical Cylinder

Published online by Cambridge University Press:  05 May 2011

P. -J. Cheng  and
K. -C. Liu
P. -J. Cheng*
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan, Taiwan 74448, R.O.C.
K. -C. Liu*
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan, Taiwan 74448, R.O.C.
*
*Associate Professor, corresponding author
**Professor
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Abstract

The influence of both the flow index and the cylinder size on the nonlinear hydrodynamic stability of a thin power law liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weakly nonlinear dynamics of the film flow for stability analysis. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained. The modeling results indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Keywords

Thin filmStability analysisFlow indexPower law liquid.
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 3 , September 2008 , pp. 241 - 252
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

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References

1.Krantz, W. B. and Zollars, R. L., “The Linear Hydrodynamic Stability of Film Flow Down a Vertical Cylinder,” AICHEJ., 22, pp. 930–934 (1976).CrossRefGoogle Scholar
2.Rosenau, P. and Oron, A., “Evolution and Breaking of Liquid Film Flowing on a Vertical Cylinder,” Phys. Fluids, A1, pp. 1763–1766 (1989).Google Scholar
3.Davalos-Orozco, L. A. and Ruiz-Chavarria, G., “Hydrodynamic Instability of a Liquid Layer Flowing Down a Rotating Cylinder,” Phys. Fluids, A5, pp. 2390–2404 (1993).Google Scholar
4.Hung, C. I., Chen, C. K. and Tsai, J. S., “Weakly Nonlinear Stability Analysis of Condensate Film Flow Down a Vertical Cylinder,” Int. J. Heat Mass Transfer, 39, pp. 2821–2829(1996).Google Scholar
5.Chen, C. I., Chen, C. K. and 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. of Heat and Mass Transfer, 47, pp. 1937–1951 (2004).Google Scholar
6.Chang, C. L., “Nonlinear Stability Analysis of Thin Micropolar Film Flows Traveling Down on a Vertical Moving Plate,” J. Phys. D, Appl. Phys., 39, pp. 984–992 (2006).Google Scholar
7.Gupta, A. S., “Stability of a Visco-Elastic Liquid Film Flowing down an Inclined Plane,” J. Fluid Mech., 28, pp. 17–28 (1967).Google Scholar
8.Hwang, C. C., Chen, J. L., Wang, J. S. and Lin, J. S., “Linear Stability of Power Law Liquid Film Flows down an Inclined Plane,” J. Phys. D, Appl. Phys., 27, pp. 2297–2301 (1994).Google Scholar
9.Miladinova, S., Lebon, G. and Toshev, E., “Thin-Film Flow of a Power-Law Liquid Falling down an Inclined Plate,” J. Non-Newtonian Fluid Mech., 122, pp. 69–78 (2004).Google Scholar
10.Gorla, R. S. R., “Rupture of the Thin Power-Law Liquid Film on a Cylinder,” Transactions of the ASME, J. of Appl. Mech., 68, pp. 294–297 (2001).Google Scholar
11.Perazzo, C. A. and Gratton, J., “Steady and Traveling Flows of a Power-Law Liquid Over an Incline,” J. Non-Newtonian Fluid Mech., 118, pp. 57–64 (2004).Google Scholar
12.Edwards, D. A., Brenner, H. and Wasan, D. T., Interfacial Transport Processes and Rheology, Butterworth-Heinemann, a Division of Reed Publishing, (USA) Inc. (1991).Google Scholar
13.Benjamin, T. B., “Wave Formation in Laminar Flow down an Inclined Plane,” J. Fluid Mech., 2, pp. 554–574 (1957).Google Scholar
14.Yih, C. S., “Stability of Liquid Flow down an Inclined Plane,” Phys. Fluids, 6, pp. 321–334 (1963).Google Scholar
15.Krishna, M. V. G. and Lin, S. P., “Nonlinear Stability of a Viscous Film with Respect to Three-Dimensional Side-Band Disturbance,” Phys. Fluids, 20, pp. 1039–1044 (1977).Google Scholar
16.Ginzburg, V. L. and Landau, L. D., “Theory of Super-Conductivity,” J. Exptl. Theoret. Phys., (USSR) 20, pp.1064–1082 (1950).Google Scholar