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The Quarterly Journal of Mechanics and Applied Mathematics 1998 51(4):553-561; doi:10.1093/qjmam/51.4.553
© 1998 by Oxford University Press
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Surface tension effects in a wedge

ND Fowkes and MJ Hood

( Mathematics Department, University of Western Australia, Nedlands, Western Australia 6009, Australia )

The linearized Laplace-Young capillary equation has been solved for the depth of liquid contained in a region bounded by vertical walls at an arbitrary wedge angle 2{alpha} using the Kantorovich-Lebedev transform. These solutions accurately describe the surface displacement for surface contact angles {gamma} close enough to {pi}/2, for both convex and concave (re-entrant) wedge angles.

By matching solutions of the linearized Laplace-Young equation solutions on the exactly known one-dimensional nonlinear Laplace-Young wall solutions, far-field approximations are obtained for arbitrary contact angle {gamma} situations for possibly a restricted range of wedge angles.


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