Bagley end correction

Figure 3-17 Illustration of Bagley End Correction Technique. Pressure drop units in pounds per square inch as in Brodkey (1967).

In order to perform the Bagley end correction (13) shear viscosity measurements are made at a constant diameter using different lengths. In cases where long capillaries are used the end corrections may be neglected. 

Also worth noting in connection with the foregoing discussion is the experimental observation of a nonzero gauge pressure at the capillary exit PeK (Curve b of Fig. 12.5). Thus one must take into consideration end corrections, both entrance and exit, and not only entrance corrections alone, as was done by Bagley. Sakiades (6) was the first to report the existence of Pex for polymer solutions, and Han and his co-workers have studied it extensively using polymer melts (7-9). It has been found that Pex/APent is between 0.15 and 0.20, and that, although APent does not depend on L/Dq, Pex decreases up to L/Dq = 10, then remains constant (9). 

Bagley EB (1957) End corrections in the capillary flow of polyethylene. J Appl Phvs 28 624-7. 

With various grades of polyethylene, Bagley found that e invariably reached a plateau value at the stress corresponding to melt fracture (Figure 8.7). This behavior is not always observed with other polymers, but the end correction method is widely used to reconcile melt flow behavior when results from capillary rheometers with variable L R ratios must be compared. 

Next the pressure change across the different capillaries must be calculated and corrected for the end-effect pressure loss using a Bagley correction. 

The first correction is for entrance and end effects and was suggested by Bagley (1957). Due to these effects, in the calculation of the shear stress at the wall one has to use an effective flow length Le(p. 

As mentioned earlier, calculations from measurements are always made on the basis of Newtonian behaviour. This results in apparent quantities which have to be corrected. These corrections are necessary because of the reduced wall adhesion of many polymers (especially with a large filler content), and to this end the Rabinowitsch correction is applied to the shear rate. Also, owing to pressure losses on entry into the capillaries (when measuring with a capillary viscometer), the Bagley correction is applied to the shear stress T. 

If ptot is plotted versus L/R at constant Q, the intercept gives Pe. ThisisillustratedforapolyethylenemeltinFigure6.2.9. Sometimes the intercept on the abscissa is used to express the correction as an extra die length e (Bagley, 1957). For short dies the end effects can be very significant. For example, for L/R = A in Figure 6.2.9 the intercept is about 70% of ptot. 

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