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Effects of soluble and insoluble surfactant on laminar interactions of vortical flows with a free surface

Published online by Cambridge University Press:  26 April 2006

Wu-Ting Tsai  and
Dick K. P. Yue
Wu-Ting Tsai
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Department of Oceanography, Ocean University, Keelung, Taiwan, ROC.
Dick K. P. Yue
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

We study the two-dimensional, laminar interactions between a contaminated free surface and a vortical flow below. Two canonical vortical flows are considered: a pair of vortex tubes impinging onto the free surface; and an unstable shear wake behind a body operating on the surface. A quantitative model for free-surface viscous flows in the presence of soluble or insoluble surfactants is developed. For the low to moderate Froude numbers considered here, for which weakly nonlinear free-surface boundary conditions are valid, the surface boundary layer and vorticity production are weak for clean water and the vortical flow evolution does not differ qualitatively from that under a free-slip boundary. When even a small amount of contamination is present, the flow can be dramatically affected. The vortical flow creates gradients in the surfactant surface concentration which leads to Marangoni stresses, strong surface vorticity generation, boundary layers, and even separation. These significantly influence the underlying flow which itself affects surfactant transport in a closed-loop interaction. The resulting flow features are intermediate between but qualitatively distinct from those under either a free- or no-slip boundary. Surfactant effects are most prominent for insoluble surface contamination with likely development of surfactant shocks and associated surface features such as Reynolds ridges. For soluble surfactant with initially uniform bulk concentration, surface concentration variations are moderated by sorption kinetics between the surface and bulk phases, and the overall effects are generally diminished. For initially stratified bulk concentrations, however, the evolution dynamics becomes more varied and surfactant effects may be amplified relative to the insoluble case. The dependence of these results on the properties of the contamination is studied.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 289 , 25 April 1995 , pp. 315 - 349
Copyright
© 1995 Cambridge University Press

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References

Alpers, W. & Hühnerfuss, H. 1989 The damping of ocean waves by surface films: a new look at an old problem. J. Geophy. Res. 94, 6251–6265.Google Scholar
Barger, W. R. 1991 A review of experimental observations and remaining questions concerning formation, persistence, and disappearance of sea slicks. Naval Research Laboratory NRL Rep. 9313.
Barker, S. J. & Crow, S. C. 1977 The motions of two-dimensional vortex pairs in a ground effect. J. Fluid Mech. 82, 659–671.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bernal, L. P., Hirsa, A., Kwon, J. T. & Willmarth, W. W. 1989 On the interaction of vortex rings and pairs with a free surface for various amounts of surface active agent. Phys. Fluids A1, 2001–2004.Google Scholar
Borwankar, R. P. & Wasan, D. T. 1983 The kinetics of adsorption of surface active agents at gas-liquid surfaces. Chem. Engng Sci. 38, 1637–1649.Google Scholar
Dimas, A. A. 1991 Nonlinear interaction of shear flows with a free surface. PhD thesis, MIT, Department of Ocean Engineering.
Dimas, A. A. & Triantafyllou, G. S. 1994 Nonlinear interaction of shear flow with a free surface. J. Fluid Mech. 260, 211–246.Google Scholar
Dommermuth, D. G. & Yue, D. K. P. 1990 A numerical study of three-dimensional viscous interactions of vortices with a free surface. In Proc. 18th Symp. Naval Hydro., Ann Arbor, MI, pp. 727–788.
Edwards, D. A., Brenner, H., & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.
Gaines, G. L. 1966 Insoluble Monolayers at Liquid-Gas Interface. Interscience.
Harper, J. F. 1974 The motion of bubbles and drops in liquids. In Proc. Intl. Colloqu. on Drops and Bubbles., Pasadena, CA, pp. 300–303.
Hirsa, A., Tryggvason, G., Abdollahi-Alibeik, J. & Willmarth, W. W. 1990 Measurement and computations of vortex pair interaction with a clean or contaminated free surface. In Proc. 18th Symp. Naval Hydro., Ann Arbor, MI, pp. 521–531.
Hirsa, A. & Willmarth, W. W. 1994 Measurement of vortex pair interaction with a clean or contaminated free surface. J. Fluid Mech., 259, 25–45.Google Scholar
Lucassen, J. 1982 Effect of surface-active material on the damping of gravity waves: a reappraisal. J. Colloid Interface Sci. 85, 52–58.Google Scholar
Lucassen-Reynders, E. H. 1981 Adsorption at fluid interfaces. In Anionic Surfactants (ed. E.H. Lucassen-Reynders), pp. 1–54. Marcel Dekker.
Lugt, H. J. 1987 Local flow properties at a viscous free surface. Phys. Fluids 30, 3647–3652.Google Scholar
Mattingly, G. E. & Criminale, W. O. 1972 The stability of an incompressible two-dimensional wake. J. Fluid Mech. 51, 233–272.Google Scholar
Miller, R. 1981 On the solution of diffusion controlled adsorption kinetics for any adsorption isotherms. Colloid & Polymer Sci. 259, 375–381.Google Scholar
Pierson, F. W. & Whitaker, S. 1976 Studies of the drop-weight method for surfactant solutions I. mathematical analysis of the adsorption of surfactants at the surface of a growing drop. J. Colloid Interface Sci. 54, 203–218.Google Scholar
Scott, J. C. 1982 Flow beneath a stagnant film on water: the Reynolds ridge. J. Fluid Mech. 116, 283–296.Google Scholar
Scriven, L. E. 1960 Dynamics of a fluid interface. Chem. Engng. Sci. 12, 98–108.Google Scholar
Tempel, M. van den 1965 Damping of waves by surface-active materials. J. Chem. Phys. 42, 2769–2777.Google Scholar
Triantafyllou, G. S. & Dimas, A. A. 1989 Interaction of a two-dimensional separated flow with a free surface at low Froude numbers. Phys. Fluids A1, 1813–1821.Google Scholar
Tryggvason, G., Abdollahi-Alibeik, J., Willmarth, W. W. & Hirsa, A. 1992 Collision of a vortex pair with a contaminated free surface. Phys. Fluids A4, 1215–1229.Google Scholar
Wang, H. T. & Leighton, R. I. 1990 Direct calculation of the interaction between subsurface vortices and surface contaminants. In Proc. 19th Intl. Conf. Offshore Mechanics and Arctic Engineering, Houston, TX, pp. 271–277.
Yeung, R. & Ananthakrishnan, P. 1992 Vortical flows with and without a surface-piercing body. In Proc. 19th Symp. Naval Hydro., Seoul, Korea.