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Observation of antisymmetric shock waves in soap-film flows
Phys. Rev. Fluids 7, L082001 – Published 8 August, 2022
DOI: https://doi.org/10.1103/PhysRevFluids.7.L082001
Abstract
Objects inserted in a fast-flowing soap film are observed to cause strong disturbances on the film, resembling shock waves. Currently a prevailing opinion is that these shock waves correspond to sudden increases in film thickness caused by elastic symmetric waves, or the propagation of film thickness changes driven by surface tension variations with the film surface area. Here, we show by laser interferometry that these “shock waves” in fact originate from the antisymmetric waves studied by Taylor, which correspond to the bending of the liquid film with no thickness change. This phenomenon thus forms an example of symmetry breaking. These shock waves maintain an antisymmetric structure, but the structure size varies with the size of the intruding object. Our results indicate that these structures could be objects for studying solitary waves, rather than the traditional shocks corresponding to density jumps in compressible flows.
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References (31)
- M. Quirk and J. Serda, Semiconductor Manufacturing Technology (Prentice Hall, Hoboken, NJ, 2001).
- A. Oron, S. H. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931 (1997).
- A. Patsyk, U. Sivan, M. Segev, and M. A. Bandres, Observation of branched flow of light, Nature (London) 583, 60 (2020).
- G. I. Taylor, The dynamics of thin sheets of fluid II. Waves on fluid sheets, Proc. R. Soc. London, Ser. A 253, 296 (1959).
- J. Lucassen, M. Van den Tempel, A. Vrij, and F. Hesselink, Waves in thin liquid films I. The different modes of vibrations, Proc. K. Ned. Akad. Wet. Ser. B: Phys. Sci. 73, 109 (1970).
- A. Vrij, F. Hesselink, J. Lucassen, and M. Van den Tempel, Waves in thin liquid films II. Symmetrical modes in very thin films and film ruptures, Proc. K. Ned. Akad. Wet. Ser. B: Phys. Sci. 73, 124 (1970).
- Y. Couder, J. M. Chomaz, and M. Rabaud, On the hydrodynamics of soap films, Physica D 37, 384 (1989).
- C. Y. Wen, Y. M. Chen, and S. K. Chang-Jian, A soap film shock tube to study two-dimensional compressible flows, Exp. Fluids 31, 19 (2001).
- C. Y. Wen and J. Y. Lai, Analogy between soap film and gas dynamics. I. Equations and shock jump conditions, Exp. Fluids 34, 107 (2003).
- C. Y. Wen, S. K. Chang-Jian, and M. C. Chuang, Analogy between soap film and gas dynamics. II. Experiments on one-dimensional motion of shock waves in soap films, Exp. Fluids 34, 173 (2003).
- T. Tran, P. Chakraborty, G. Gioia, S. Steers, and W. I. Goldburg, Marangoni Shocks in Unobstructed Soap-Film Flows, Phys. Rev. Lett. 103, 104501 (2009).
- I. Kim and X. L. Wu, Tunneling of micron-sized droplets through soap films, Phys. Rev. E 82, 026313 (2010).
- I. Kim and S. Mandre, Marangoni elasticity of flowing soap films, Phys. Rev. Fluids 2, 082001(R) (2017).
- M. Rivera, P. Vorobieff, and R. E. Ecke, Turbulence in Flowing Soap Films: Velocity, Vorticity, and Thickness Fields, Phys. Rev. Lett. 81, 1417 (1998).
- J. Zhang, S. Childress, A. Libchaber, and M. Shelley, Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature (London) 408, 835 (2000).
- M. A. Rutgers, X. L. Wu, and W. B. Daniel, Conducting fluid dynamics experiments with vertically falling soap films, Rev. Sci. Instrum. 72, 3025 (2001).
- H. Kellay and W. I. Goldburg, Two-dimensional turbulence: a review of some recent experiments, Rep. Prog. Phys. 65, 845 (2002).
- L. B. Jia and X. Z. Yin, Passive Oscillations of Two Tandem Flexible Filaments in a Flowing Soap Film, Phys. Rev. Lett. 100, 228104 (2008).
- T. Schnipper, A. Andersen, and T. Bohr, Vortex wakes of a flapping foil, J. Fluid Mech. 633, 411 (2009).
- G. Boffetta and R. E. Ecke, Two-dimensional turbulence, Annu. Rev. Fluid Mech. 44, 427 (2012).
- Z. Y. Zhou, L. Fang, N. T. Ouellette, and H. T. Xu, Vorticity gradient stretching in the direct enstrophy transfer process of two-dimensional turbulence, Phys. Rev. Fluids 5, 054602 (2020).
- A. Prins, C. Arcuri, and M. Van den Tempel, Elasticity of thin liquid films, J. Colloid Interface Sci. 24, 84 (1967).
- H. Bianco and A. Marmur, Gibbs elasticity of a soap bubble, J. Colloid Interface Sci. 158, 295 (1993).
- E. Fuguet, C. Ràfols, M. Rosés, and E. Bosch, Critical micelle concentration of surfactants in aqueous buffered and unbuffered systems, Anal. Chim. Acta 548, 95 (2005).
- R. Sadeghi and S. Shahabi, A comparison study between sodium dodecyl sulfate and sodium dodecyl sulfonate with respect to the thermodynamic properties, micellization, and interaction with poly(ethylene glycol) in aqueous solutions, J. Chem. Thermodyn. 43, 1361 (2011).
- M. A. Motin, M. H. Mia, and A. N. Islam, Thermodynamic properties of sodium dodecyl sulfate aqueous solutions with methanol, ethanol, -propanol and iso-propanol at different temperatures, J. Saudi Chem. Soc. 19, 172 (2015).
- F. Evans and W. Wennerström, The Colloidal Domain (Wiley, New York, 1999).
- D. Langevin and F. Monroy, Marangoni stresses and surface compression rheology of surfactant solutions. achievements and problems, Adv. Colloid Interface Sci. 206, 141 (2014).
- D. Langevin, Rheology of adsorbed surfactant monolayers at fluid surfaces, Annu. Rev. Fluid Mech. 46, 47 (2014).
- D. M. Wan, H. S. Xiang, and H. T. Xu, A laminar-jet-discharging method for measuring the interfacial tension of deformable surfaces, Meas. Sci. Technol. 31, 035302 (2020).
- X.-L. Wu, R. Levine, M. Rutgers, H. Kellay, and W. I. Goldburg, Infrared technique for measuring thickness of a flowing soap film, Rev. Sci. Instrum. 72, 2467 (2001).
