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.

Effective rheology of Bingham fluids in a rough channel

“…Lubrication approximations have been investigated extensively for Newtonian fluids in confined geometries (e.g., [32,33]). For visco-plastic fluids, the limit of lubrication has also been investigated by various authors in different geometries (see [34] for film flows, [22][23][24]35] for confined geometries and [36,37] for experiments). In this case, the lubrication hypothesis becomes very restrictive essentially due to rigidity of the plug regions.…”

Finite element analysis of the duct flow of Bingham plastic fluids: an application of the variational inequality

“…However, the plug zone for Bn 0Á15 still remains intact because of the high yield stress in the plastic¯uid. Some authors 17,20 did not identify the unyielded plug zone at the narrow side of the eccentric annulus. In calculating the velocity ®eld, the latter authors 20 used a relatively large parameter of about 10 78 and a relatively coarse tessellation of the¯ow domain, both of which may lead to poor resolution of the velocity ®eld.…”

“…The same case has been considered previously. 17,20 The numerical parameters used here are e 0Á2 and Bn 0Á15, which correspond to 0Á4 and 0Á5 respectively in the aforementioned works. The difference is due to the different scaling.…”

“…However, the parameter of 10 74 used seemed too large and the resolution of the yield surface was not satisfactory. Walton and Bittleston 20 used the same method to solve the axial¯ow of Bingham¯uids in a narrow eccentric annulus. Bittleston and Hassager 21 calculated the tangential¯ow ®eld of the same¯uids in a concentric annulus.…”

Shallow viscoplastic flow on an inclined plane

“…Hidden at higher order is the resolution of this contradiction: above z = Y , the stresses are not actually below the yield value, but order above it. In other words, the level z = Y (x, y, t) is really a 'fake' yield surface, and the upper region is a 'pseudo-plug' (to use the terminology of Walton & Bittleston 1991).…”