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

摘要

A general theorem for the Stokes flow over a plane boundary with mixed stick-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.