Bagley-corrected flow curve

Fig. 7 Apparent flow curves and Bagley-corrected flow curves for ceramic compound C (aluminium oxide with ammonium alginate)...

As discussed above, the flow curves of polymer fluids can be obtained by Equations 8.18 and 8.38 (or 8.39), and the viscosities of the fluids can be calculated by Equation 8.41. While deriving these equations, one of the assumptions is that the flow pattern is constant along the pipe. However, in a real capillary flow, the polymer fluid exhibits different flow patterns in the entrance and exit regions of the pipe. For example, the pressure drops at the die entrance and exit regions are different from AP/Z. Therefore, corrections, e.g., Bagley correction, are needed to address the entrance and exit effects. Another assumption is that there is no slip at the wall. However, in a real flow, polymer fluid may slip at the wall and this reduces the shear rate near the wall. The Mooney analysis can be used to address the effect of the wall slip. In addition, the velocity profile shown in Figure 8.13 is a parabolic flow. However, the tme flow in the die orifice is not necessarily a simple parabolic flow, and hence Weissenberg-Rabinowitsch correction often is used to correct the shear rate at the wall for the non-parabohc velocity profile. 

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