PMID: 15244935Jul 13, 2004Paper

Falling films and the Marangoni effect

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
V Ya ShkadovV P Shkadova

Abstract

The instability of a falling liquid film of an aqueous surfactant solution along a vertical slope with surfactant adsorption-desorption at its open surface originating surface stresses (Marangoni effect) is investigated. The diffusion of surfactant to the film surface from the bulk and desorption of surfactant to the gas phase are taken into account. The Navier-Stokes and Fick equations are reduced to a system of simpler hence, analytically and numerically, more tractable nonlinear evolution equations albeit with nine dimensionless parameters. The linear stability analysis yields a dispersion equation that is numerically solved and eigenvalues are obtained for various values of significant dimensionless parameters. A very rich picture of instabilities appears. In addition to the earlier known (Kapitza) hydrodynamic mode there are up to four new (Marangoni-driven) diffusion modes. Two modes travel with the liquid velocity on the film surface and the other two travel on their own downstream and upstream, respectively. One diffusion mode could be identified, in the reference frame moving with the liquid on the film surface, as a monotonic instability mode hence leading to a patterned film surface. All other modes are oscillatory o...Continue Reading

References

Apr 12, 1993·Physical Review Letters·J Liu, J P Gollub
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Carlos Alberto Perazzo, Julio Gratton

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Citations

Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Aashish Jain, V Shankar
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Antonio Pereira, Serafim Kalliadasis
Feb 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rui Zheng, Thomas A Witten
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hsien-Hung Wei

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