The axial flow of a Bingham plastic in a narrow eccentric annulus

Abstract

This paper describes analytical and numerical solutions for the flow of a Bingham plastic in an eccentric annulus. Analytical solutions are obtained by expanding in powers of δ, the ratio of the difference in radii of the bounding cylinders to their mean. The solution over most of the annulus is similar to that in a slot of uniform width, containing a central plug-like region over which the velocity is independent of the radial variable. However, unlike the uniform-slot solution, the velocity in the plug varies around the annulus and the stress exceeds the yield stress. This simple structure is supplemented by true plugs (over which the velocity is constant and the stress is below the yield stress) at the widest and, in some cases, the narrowest parts of the annulus. A simple criterion is given for conditions under which the fluid ceases to flow on the narrow side and bounds are obtained for the extent of the motionless region and for the true plugs.The predictions of the theory have been compared to numerical results over a wide range of eccentricities, radius ratios, fluid properties and flow parameters. Good quantitative agreement has been reached for radius ratios in excess of about 0.7. In particular the extent and location of pseudo-plugs and true plugs are confirmed.