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The Quarterly Journal of Mechanics and Applied Mathematics 1979 32(4):355-381; doi:10.1093/qjmam/32.4.355
© 1979 by Oxford University Press
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THE SPREADING OF A VERY VISCOUS LIQUID ON A QUIESCENT WATER SURFACE

N. D. DI PIETRO and R. G. COX

( Department of Civil Engineering and Applied Mechanics, McGill University Montreal )

A theoretical investigation is made into the spreading of a very viscous liquid, with positive spreading coefficient, on a quiescent water surface. When the boundary-layer drag on the spreading layer due to the water is assumed negligible, the equations determining the motion are found by extending the use of lubrication theory to a higher order than that necessary for the situation where boundary-layer drag is important. In this manner the various systems of equations and their regimes of validity are found for situations ranging from those where the effect of boundary-layer drag is dominant to those where it is negligible. Finally various analytic solutions are found for the spreading equations for the case where boundary-layer drag is negligible. Numerical values of layer velocities and sizes are found for typical examples.


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