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The Quarterly Journal of Mechanics and Applied Mathematics 1989 42(1):99-113; doi:10.1093/qjmam/42.1.99
© 1989 by Oxford University Press
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STOKES FLOW NEAR A MOVING CONTACT LINE WITH YIELD-STRESS BOUNDARY CONDITION

P. A. DURBIN

( Department of Aerospace and Mechanical Engineering, The University ofArizona Tucson, Arizona 85721, USA )

The low-Reynolds-number, Stokes-flow equations are solved in a wedge-shaped region bounded by a moving wall and a stress-free meniscus. The moving-contact-line singularity is removed by invoking the yield-stress boundary condition. A solution is found by Mellin transformation, followed by application of the Wiener—Hopf method. Formulae are obtained for the length of the slip region and for the surface shear stress, both as functions of the contact angle. The role of the present analysis as an inner solution for more general cases of flow near moving menisci is discussed.


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