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Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

Published online by Cambridge University Press:  21 April 2006

P. A. Durbin
P. A. Durbin
Affiliation:
NASA Lewis Research Center, Cleveland, OH 44135, USA
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Abstract

It has previously been shown that the no-slip boundary condition leads to a singularity at a moving contact line and that this forces one to admit some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition the length of the slip region becomes a property of the fluid flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 197 , December 1988 , pp. 157 - 169
Copyright
© 1988 Cambridge University Press

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