Stokes flow before plane boundary with mixed stick-slip boundary conditions

doi:10.1007/s10483-011-1459-8

Abstract

Abstract: A general theorem for the Stokes flow over a plane boundary with mixed tick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.

Key words: Stokes flow, Stokes stream function, stick-slip boundary conditions, harmonic function, biharmonic function

2010 MSC Number:

76D07

N. AKHTAR;G. A. H. CHOWDHURY;S.K.SEN. Stokes flow before plane boundary with mixed stick-slip boundary conditions. Applied Mathematics and Mechanics (English Edition), 2011, 32(6): 795-804.

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