Abstract
The spread of a thin oil film by surface tension gradients from an oil source of unlimited mass on deep water is considered. A similarity solution for the velocity fields of the oil and water, the oil thickness and the rate at which each grow is obtained both for axisymmetric and the previously explored planar spreading. The dimensionless size of the spread, which is oil type independent, is shown to be 1.0754 and 1.4150 for axisymmetric and planar spreading respectively. It is further shown that the oil film equation of state, which relates surface tension to oil thickness, is unique to each oil or oil-surfactant mixture.
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References
Adamson, A.W.Physical Chemistry of Surfaces. Wiley-Interscience, New York (1967).
Borgas, M.S. and Grotberg, J.B., Monolayer flow on a thin film.J. Fluid Mech. 193 (1988) 151–170.
Brown, S.N. and Stewartson, K., Laminar separation,Ann. Rev. Fluid Mech. 1 (1969) 45–72.
Buckmaster, J., Viscous-gravity spreading of an oil slick,J. Fluid Mech. 59 (1973) 481–491.
Camp, D.W. and Berg, J.C., The spreading of oil on water in the surface-tension regime,J. Fluid Mech. 184 (1987) 445–462.
DiPietro, N.D. and Cox, R.G., The spreading of a very viscous liquid on a quiescent water surface,Quart. J. Mech. Appl. Math 32 (1979) 355–381.
DiPietro, N.D. and Cox, R.G., The containment of an oil slick by a boom placed across a uniform stream,J. Fluid Mech. 96 (1980) 613–640.
DiPietro, N.D., Huh, C. and Cox, R.G., The hydrodynamics of the spreading of one liquid on the surface of another,J. Fluid Mech. 84 (1978) 529–549.
Fay, J.A., The spread of oil slicks on a calm sea. In: Hoult, D.P. (ed.),Oil on the Sea. Plenum, New York (1969) pp. 53–63.
Foda, M. and Cox, R.G., The spreading of thin liquid films on a water-air interface.J. Fluid Mech. 101 (1980) 33–51.
Garrett, W.D. and Barger, W.R., Factors affecting uses of monomolecular surface films to control oil pollution on water.Environ. Sci. Tech. 4 (1970) 123–127.
Gaver III, D.P. and Grotberg, J.B., The dynamics of a localized surfactant on a thin film.J. Fluid Mech. 213 (1990) 127–148.
Harkins, W.D.,The Physical Chemistry of Surface Films. Reinhold, New York (1952).
Huh, C., Inoue, M. and Mason, S.G., Unidirectional spreading of one liquid on the surface of another.Can. J. Chem. Engng. 53 (1975) 367–371.
Jensen, O.E., Self-similar surfactant-driven flows.Phys. Fluids 6 (1994) 1084–1094.
Jensen, O.E., The spreading of insoluble surfactant at the free surface of a deep fluid layer.J. Fluid Mech. 293 (1995) 349–378.
Landt, E. and Volmer, M., Spreading velocity of oil on H2O,Z. Phys. Chem. 122 (1926) 398–404.
Ma, P.K.H. and Hui, W.H., Similarity solutions of the two-dimensional unsteady boundary-layer equations.J. Fluid Mech. 216 (1990) 537–559.
Phillips, W.R.C., On a class of unsteady boundary layers of finite extent.J. Fluid Mech. 319 (1996) 151–170.
Sheludko, A.,Colloid Chemistry. Elsevier, Amsterdam (1966).
Stewartson, K., On the impulsive motion of a flat plate in a viscous fluid.Q. J. Mech. Appl. Maths. 4 (1951) 182–198.
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Phillips, W.R.C. On the spreading radius of surface tension driven oil on deep water. Appl. Sci. Res. 57, 67–80 (1996). https://doi.org/10.1007/BF02528764
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DOI: https://doi.org/10.1007/BF02528764