Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-29T03:55:15.897Z Has data issue: false hasContentIssue false
  • English
  • Français

Gasdynamic-Like Equations for Oblique Shock Waves and Nozzle Flows in Soap Films

Published online by Cambridge University Press:  05 May 2011

C.-Y. Wen  and
J.-Y. Lai
C.-Y. Wen*
Affiliation:
Department of Mechanical and Automation Engineering, Da-Yeh University, Chang-Hwa, Taiwan 51505, R.O.C.
J.-Y. Lai*
Affiliation:
Department of Mechanical and Automation Engineering, Da-Yeh University, Chang-Hwa, Taiwan 51505, R.O.C.
*
* Professor
* Professor
Get access

Abstract

The governing equations for oblique shock waves and nozzle flows in soap films are formulated based on their very specific property equations. The θ-β-M relation for oblique shock waves and the width-velocity relation for quasi-one-dimensional nozzle flows are presented. The results are similar to those of compressible gases. On short time scales, the analogy of soap films to two-dimensional (2-D) compressible gases with a specific heat ratio of γ = 1.0 that is shown by Wen and Lai [1], Wen, et al. [2] and Chomaz [3] is again demonstrated. The present results supplement the theory of compressible flows in soap films.

Keywords

Oblique shock wavesNozzle flowsSoap filmAnalogy
Type
Articles
Information
Journal of Mechanics , Volume 20 , Issue 1 , March 2004 , pp. 69 - 76
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Wen, C. Y. and Lai, J. Y., “Analogy between Soap Film and Gas Dynamics. I. Equations and Shock Jump Conditions,” Experiments in Fluids, 34(1), pp. 107–114 (2003).CrossRefGoogle Scholar
2.Wen, C. Y., Chang-Jian, S. K. and Chuang, M. J., “Analogy between Soap Film and Gas Dynamics. II. Experiments on One-Dimensional Motion of Shock Waves in Soap Films,” Experiments in Fluids, 34(2), pp. 173–180 (2003).CrossRefGoogle Scholar
3.Chomaz, J. M., “The Dynamics of a Viscous Soap Film with Soluble Surfactant,” J. Fluid Mech., 442, pp. 387–409 (2001).CrossRefGoogle Scholar
4.Couder, Y., Chomaz, J. M. and Rabaud, M., “On the Hydrodynamics of Soap Films,” Physica D, 37, pp. 384–405 (1989).CrossRefGoogle Scholar
5.Mysels, K. J., Shinoda, K. and Frankel, S., Soap Films, Studies of Their Thinning, Pergamon Press (1959).Google Scholar
6.Couder, Y., “The Observation of a Shear Flow Instability in a Rotating System with a Soap Membrane,” J. Phys. Lett., 42, pp. 429–431 (1981).CrossRefGoogle Scholar
7.Gharib, M. and Derango, P., “A Liquid Film (Soap Film) Tunnel to Study Two-Dimensional Laminar and Turbulent Shear Flows,” Physica D, 37, pp. 406–416(1989).CrossRefGoogle Scholar
8.Kellay, H., Wu, X. L. and Goldburg, W., “Experiments with Turbulent Soap Films,” Phys. Rev. Lett., 74, pp. 3975–3978 (1995).CrossRefGoogle ScholarPubMed
9.Couder, Y., “Two-Dimensional Grid Turbulence in a Thin Liquid Film,” J. Phys. Lett., 45, pp. 353–360 (1984).CrossRefGoogle Scholar
10.Beizaie, M. and Gharib, M., “Fundamentals of a Liquid (Soap) Film Tunnel,” Exp. Fluids, 23, pp. 130–140 (1997).CrossRefGoogle Scholar
11.Wu, X., Martin, B. K., Kellay, H. and Goldburg, W., “Hydrodynamic Convection in a Two-Dimensional Couette Cell,” Phys. Rev. Lett., 75, pp. 236–239 (1995).CrossRefGoogle Scholar
12.Rutgers, M. A., Wu, X. L., Bhagavatula, R., Petersen, A. A. and Goldburg, W. I., “Two Dimensional Velocity Profiles and Laminar Boundary Layers in Flowing Soap Films,” Phys. Fluids, 8, pp. 2847–2854 (1996).CrossRefGoogle Scholar
13.Rivera, M., Vorobieff, P. and Ecke, R. E., “Turbulence in Flowing Soap Films: Velocity, Vorticity and Thickness Fields,” Phys. Rev. Lett., 81, pp. 1417–1420(1998).CrossRefGoogle Scholar
14.Wen, C.-Y. and Lin, C.-Y., “Two-Dimensional Vortex Shedding of a Circular Cylinder,” Phys. Fluids, 13(3), pp. 557–560 (2001).CrossRefGoogle Scholar
15.McEntee, W. R. and Mysels, K. J., “The Bursting of Soap Films. I. An Experimental Study,” J. Phys. Chem., 73, pp. 3018–3028 (1969).CrossRefGoogle Scholar
16.Frankel., S. and Mysels, K. J., “The Bursting of Soap Films. II. A Theoretical Study,” J. Phys. Chem., 73, pp. 3029–3038 (1969)CrossRefGoogle Scholar
17.Liang, N. Y., “The Bursting of Soap Films,” PhD Dissertation, National Taiwan University, Taiwan (1997).Google Scholar
18.Wen, C. Y., Chen, Y. M. and Chang-Jian, S. K., “A Soap Film Shock Tube to Study Two-Dimensional Compressible Flows,” Exp. Fluids, 31, pp. 19–25 (2001).CrossRefGoogle Scholar
19.Gibbs, J. W., The Collected Works, Longmans Green, New York (1931).Google Scholar
20.Boys, C. V., In Soap Bubbles and the Forces Which Mould Them, Society for Promoting Christian Knowledge, London (1890); Anchor, New York (1959).Google Scholar
21.Rusanov, A. L. and Krotov, V. V., “Gibbs Elasticity of Liquid Films,” Prog. Surf. Membr. Sci., 13, pp. 415–525 (1979).CrossRefGoogle Scholar
22.Thompson, P. A., Compressible-fluid dynamics. The Rensselaer Polytechnic Institute Press (1988).Google Scholar
23.Lucassen, J., VanDen Tempel, M. Den Tempel, M., Vrij, A. and Hesselink, F., “Waves in Thin Liquid Films I. The Fifferent Modes of Vibration,” Proc. K. Ned. Akad. Wetensch. B 73: pp. 109–124 (1970).Google Scholar