Viscoplastic flow between hinged plates

The incompressible motion of viscoplastic fluid between two semi-infinite rigid plates, hinged at their ends and rotating towards one another at constant angular velocity, generates self-similar flow fields because there is no externally imposed length scale in the absence of inertia. The magnitude of the strain rate scales with the angular velocity of the plates and the dimensionless deviatoric stresses are functions only of the polar angle and a dimensionless measure of the yield stress; they are independent of the radial distance from the corner. These flows feature unyielded regions adjacent to the boundaries for sufficiently large angles between the plates. Moreover, when the dimensionless yield stress is large, there are viscoplastic boundary layers that are attached to the boundary or the plug, the asymptotic structures of which are constructed.