Helical flow arising from the yielded annular flow of a Bingham fluid

The Bingham fluid model was developed to represent viscoplastic materials that change from rigid bodies at low stress to viscous fluids at high stress - a process termed yielding. Such a fluid model is used in the modeling of slurries, which occur frequently in food processing and other engineering applications. We consider the flow of a Bingham fluid between infinitely long coaxial cylinders, when the inner cylinder rotates. This is of relevance to a number of applications, including rheometry. We assume a yielded flow, comprising an inner fluid zone and an outer solid zone; and apply a perturbation procedure to analyze the changes in the characteristics of this during a transition from pure annular fluid motion (no axial flow) to a helical fluid motion, where a small axial fluid flow rate is imposed. This analysis gives explicit expressions for the changed fluid velocity field as well as movement in the location of the solid-fluid boundary.