Pressure-driven flow of a yield-stress fluid in an annular channel with internal torque

Various industrial problems involve transport of fluids with a yield stress along annular channels driven by an axial pressure gradient, where the inner cylinder can also rotate to aid mobilisation of the material. This problem is considered here for the case of a Bingham fluid, which is undeformed if the applied stress lies below the fluid's yield stress. Unlike for a Newtonian fluid, where the steady-state velocity field is simply a composite of axial Poiseuille flow and azimuthal shear flow, the velocity components for a Bingham fluid are inherently coupled by the rheological non-linearity. The resulting steady behaviour is thus rather more complex, and can take qualitatively different forms, with different regions of the fluid remaining rigid and unyielded. The phase space delineating different flow regimes, and the associated behaviour of the fluxes and flow resistance, are outlined as a function of the applied torque and pressure drop, channel geometry and rheological properties. Flow stability and the possible implications for industrial applications are also discussed.