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 surf ace of constant shear stress is calculated by use of the Mellin transform. For wedge angles below a critical value the asymptotic solution near the ve rtex is given by a local similarity solution. The respective stream functio n grows quadratically with the distance from the origin. For supercritical wedge angles the similarity solution breaks down and the leading order solu tion 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 fun ction. The asymptotic dependence of the stream function found here is the s ame 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 no nzero constant shear stress is extended to infinity. The relevance of the p resent result for technical flow systems is pointed out by comparison with the numerically calculated flow in a thermocapillary liquid bridge.