The local flow in a wedge between a rigid wall and a surface of constant shear stress

The viscous incompressible flow in a wedge between a rigid plane and a surface of constant shear stress is calculated by use of the Mellin transform. For wedge angles below a critical value the asymptotic solution near the vertex is given by a local similarity solution. The respective stream function grows quadratically with the distance from the origin. For supercritical wedge angles the similarity solution breaks down and the leading order solution for the stream function grows with a power law having an exponent less than two. At the critical angle logarithmic terms appear in the stream function. The asymptotic dependence of the stream function found here is the same as for the 'hinged plate' problem. It is shown that the validity of the Stokes flow assumption is restricted to a vanishingly small distance from the vertex when the wedge angle is above critical and when the region of nonzero constant shear stress is extended to infinity. The relevance of the present result for technical flow systems is pointed out by comparison with the numerically calculated flow in a thermocapillary liquid bridge.