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The Quarterly Journal of Mechanics and Applied Mathematics 1991 44(2):173-192; doi:10.1093/qjmam/44.2.173
© 1991 by Oxford University Press
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MOVING CONTACT LINES IN SLENDER FLUID WEDGES

A. C. KING

( Department of Mathematics, University of Keele Keele, Staffordshire ST5 5BG )

A wedge of fluid is held at rest with its upper edge a free surface and its lower edge in contact with a solid boundary. If the wedge angle of this static system differs from the contact angle of the fluid-solid combination then an adjustment of the wedge angle to a constant dynamic contact angle results when the system is released from rest. The induced motion in the fluid is of a self-similar type and is sustained by surface-tension forces. In the case of a slender fluid wedge of angle {varepsilon} whose dynamic contact angle is O({varepsilon}) the rather complicated equations of motion can be reduced by a perturbation procedure to a novel two-point boundary-value problem. Asymptotic and numerical solutions to this are found and the displacement of the contact point and the free surface are investigated for a variety of parameter values.


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