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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. [ABSTRACT FROM AUTHOR]

It is shown that the boundary layer which develops from rest in a loosely coiled pipe of circular cross-section, following the imposition of a constant pressure gradient, terminates in singular behaviour at the inside bend after a finite time. This singularity of the boundary-layer equations is interpreted as an eruption of boundary-layer fluid into the interior or core flow. This result complements earlier work by Stewartson et al. [1] who consider the steady inlet flow to a curved pipe at high Dean number. In that case a singularity also develops, now at a finite distance from the entrance at the inside bend, which is again interpreted in terms of a boundary-layer collision or eruption. [ABSTRACT FROM AUTHOR]