Unsheared plug flow

The bulk flow curve of the system studied by Isa et al. fitted a Herschel-Bulkley (HB) form for a yield-stress fluid [8] at small to moderate flow rates. The velocity profile predicted from a HB constitutive relation consists of a central, unsheared plug and shear zones adjacent to the channel walls, which fits qualitatively with what was observed see Fig. 12a. At the same time, however, the size of the central... 

A carbopol solution p = lOOOkg/m ), with Bingham plastic rheology (Tq = 8Pa and plastic viscosity of 50 m Pa-s), is flowing through a 25 mm diameter pipeline. Estimate the pressure drop per metre of pipe when the mean velocity is 1 m/s. Also, estimate the radius of the unsheared plug in the core region. 

As shown in Figure 10, in the presence of a yield stress the central core of the fluid moves as a solid plug which fundamentally affects the stability of flow (Slatter, 1995, 1999). The unsheared plug is treated as a solid body in the centre of the pipe. The flow that the plug represents must be subtracted as it is no longer being treated as part of the fluid flow. The corrected mean velocity in the annulus Vann is then obtained as follows -... 

In many situations, the concentration of a suspension is so high that the flow properties in shear are dominated by the shearing thin slip layer and an almost unsheared solid plug, while for any extensional flow that the paste encounters (such as flow into an orifice or the entrance of a tube) still demands the deformation of the whole paste. In these situations the flow of a typical paste into and along a tube, such as are found in ceramic and battery pastes etc., can be characterised by the formula... 

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