Effect of long undulated bottoms on thin gravity-driven films Authors
First Online: 04 August 2005 Received: 30 October 2004 Revised: 24 February 2005 DOI:
Cite this article as: Wierschem, A., Lepski, C. & Aksel, N. Acta Mechanica (2005) 179: 41. doi:10.1007/s00707-005-0242-2 Summary
We carry out a perturbation analysis for steady gravity-driven film flow over undulations of moderate steepness that are long compared to the film thickness and study the linear stability of the flow in the framework of Floquet analysis. The effect of geometric nonlinearities on the instability becomes relevant for moderate bottom variations. We find that the critical Reynolds number for the onset of surface waves is higher than that for a flat bottom. At higher inclination angles, the theoretical results are in good quantitative agreement with experiment. At inclination angles where the flat part of the undulation is close to being horizontal, the basic solution for the steady flow fails to describe the flow in the flat part, and the linear stability analysis overestimates the critical Reynolds number.
Kistler S. F., Schweizer P. M. (eds.): Liquid film coating. London: Chapman & Hall 1997.
Webb, R. L. 1994Principles of enhanced heat transfer Wiley New York Alekseenko, S. V., Ye Nakoryakov, V. , Pokusaev, B. G. 1994Wave flow of liquid films Begell House New York Wang, C. Y. 1981 Liquid film flowing slowly down a wavy incline AIChE 27 207 212 CrossRef Wang, C. Y. 1984 Thin film flowing down a curved surface Z. Angew. Math. Phys. 35 533 544 CrossRef Scholle, M., Wierschem, A., Aksel, N. 2004 Creeping films with vortices over strongly undulated bottoms Acta Mech. 168 167 193 CrossRef Pozrikidis, C. 1988 The flow of a liquid film along a periodic wall J. Fluid Mech. 188 275 300 Bontozoglou, V., Papapolymerou, G. 1997 Laminar film flow down a wavy incline Int. J. Multiphase Flow 23 69 79 CrossRef Malamataris, N. A., Bontozoglou, V. 1999 Computer aided analysis of viscous film flow along an inclined wavy wall J. Comp. Phys. 154 372 392 CrossRef Bontozoglou, V. 2000 Laminar film flow along a periodic wall CMES 1 133 142 Zhao, L., Cerro, R. I. 1992 Experimental characterization of viscous film flows over complex surfaces Int. J. Multiphase Flows 18 495 516 CrossRef Wierschem, A., Scholle, M., Aksel, N. 2002 Comparison of different theoretical approaches to experiments on film flow down an inclined wavy channel Exp. Fluids 33 429 442 Wierschem, A., Scholle, M., Aksel, N. 2003 Vortices in film flow over strongly undulated bottom profiles at low Reynolds numbers Phys. Fluids 15 426 435 CrossRef MathSciNet Wierschem, A., Aksel, N. 2004 Hydraulic jumps and standing waves in gravity-driven flows of viscous liquids in wavy open channels Phys. Fluids 16 3868 3877 CrossRef Wierschem, A., Aksel, N. 2004 Influence of inertia on vortices created in films creeping over strongly undulated substrates Phys. Fluids 16 4566 4574 CrossRef Chang, H.-C., Demekhin, E. A. 2002Complex wave dynamics on thin films Elsevier Amsterdam Yih, C. S. 1963 Stability of liquid flow down an inclined plane Phys. Fluids 6 321 334 Tougou, H. 1978 Long waves on a film flow of a viscous fluid down an inclined uneven wall J. Phys. Soc. Jpn. 44 1014 1019 CrossRef Vlachogiannis, M., Bontozoglou, V. 2002 Experiments on laminar film flow along a periodic wall J. Fluid Mech. 457 133 156 CrossRef Wierschem, A., Aksel, N. 2003 Instability of a liquid film flowing down an inclined wavy plane Physica D 186 221 237 Schmid, P. J., Henningson, D. S. 2001Stability and transition in shear flows Springer New York Liu, J., Paul, J. D., Gollub, J. P. 1993 Measurements of the primary instabilities of film flows J. Fluid Mech. 250 69 101 Copyright information
© Springer-Verlag Wien 2005