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The spread of an oil slick onto calm water is considered from a theoretical viewpoint. The equations of motion are derived for the gravity-inertial and gravity-viscous flow regimes (in which the spreading force of gravity is balanced by, respectively, inertia and viscous drag at the water surface). Approximate formulations for the viscous drag are suggested. The initial growth of the one-dimensional slick is described. For both one-dimensional and radial slicks, similarity solutions are obtained for the flow regimes which give adequate agreement with available experimental data. Approximate solutions are also given for the surface tension-viscous region, in which the slick becomes so thin that surface tension rather than gravity is the primary spreading mechanism. Based on these solutions, a general picture of the slick development is presented.
Fanneløp et al. (Sat,) studied this question.