Bagley plots

Fig. 26. Bagley plot of pressure,, drop along a capidary versus capidary aspect ratio, E/R, at A, 7 = 590 s, and B, 7 = 295 s N To convert MPa to psi,...

Figure 7.71 Bagley plots for a polystyrene melt at 200°C. From Z. Tadmor and C. G. Gogos, Principles of Polymer Processing. Copyright 1979 by John Wiley Sons, Inc. This material is used by permission of John WUey Sons, Inc.

Figure 7. Detection of slip from Bagley plots, 1 No slip, 2 Slip effects present.

Fig. 12.6 Bagley plots for a polystyrene (PS) melt at 200°C, from which N(T) can he evaluated AP at L/Dq —> 0 is the entrance pressure drop AP. [Reprinted by permission from J. L. White, Appl. Polym. Symp., No. 20, 155 (1973).]...

Figure 13.13 Bagley plots to determine the effective length of a capillary tube.

It was observed that Bagley plots of pressure drop P vs. L/d were not always linear (45, 47) ... 

The Barus effect can be studied with the aid of the Bagley plot. Solving... 

In the Bagley plot, the pressure is plotted against the nozzle geometry Lj.R at a constant shear rate y. With Newtonian liquids, according to Equation (7-32), for L / = 0,/ will also be 0 the slope of the straight lines is... 

Figure 11-10. Bagley plot of a high-impact poly(styrene) at 189° C at shear gradients of 10, 100, 1000, and 4000 s" from measurements with capillaries of / = 1 mm in diameter ( ) ox R = 0.6 mm (O) and different lengths L. (After BASF.)...

As the construction of the Bagley plot requires considerable experimental effort, in practice a single long (L/R > 60) capillary is usually deemed to provide accurate results on the assumption that all corrections may be safely ignored. This assmnption is not always warranted and the reader is referred to... 

The Bams effect can be studied with the aid of the Bagley plot. Solving equation (7-43) for the pressure p and replacing the shear stress for non Newtonian liquids by (see Section 7.6.2), we obtain... 

Fig. 23. Bagley plot of pressure, p, drop along a capillary versus capillary aspect ratio, L/R, at (A), Y = 590 s and (B), y = 295 s. To convert MPa to psi, multiply by 145.

Construct a Bagley plot from this data (see Fig. 7). The measured pressures are plotted against the LjD of the die for each apparent shear rate. Note. By convention, the Bagley plot... 

The excess pressure drop associated with the entrance and exit is shear-rate dependent for polymer melts. If the excess pressure drop can be measured, then it can be subtracted from the total pressure drop to provide the value for fully developed flow, and the latter can be used to compute the shear stress at a given shear rate. The method commonly used is known as a Bagley plot. Here, the pressure drop as a function of shear rate is measured in capillaries of varying length-to-diameter L/D) ratios. The data are then plotted as pressure drop versus L/D at fixed shear... 

Figure 9.14. Bagley plot for a linear metallocene polyethylene at 150 °C. ASR denotes apparent shear rate. Reprinted with permission from Kim and Dealy, /. RheoL, 45,1413 (2001).

Eqs. 179 and 180 indicate that the shear rate at the die wall has a correction due to the non-Newtonian character of the viscosity. This correction on the shear rate is called the Weissenberg-Rabinowitch correction. The shear stress itself may also need to be corrected so as to account for pressure losses due to elastic effects at the die entrance and exit. This correction is known as the Bagley correction. The Bagley correction can be obtained by repeating the pressure drop measurements with different aspect ratio (L/R) dies. The pressure drop vs. L/R plot which results is called a Bagley plot the intercept on the negative L/R axis represents the additional length of fictitious capillary which corresponds to the extra losses. 

Entrance pressure drop Bagley plot Single die L/R 60... 

Negative curvature rarely occurs in Bagley plots, but an example is shown in Figure 6.2.10. Laun and Hirsch (1989) attributed this to the thixotropy that is, the decrease in viscosity with amount of shear. For this sample only dies (A L/R < 12 could be used to estimate the end effects. 

The most accurate method for determining pe is to make a Bagley plot with at least two short dies of the same diameter. Another approach is to measure p directly with an orifice die and use it to correct data from one long die. This method usually requires using two different transducers because of the great difference in pressure. 

Representation of pressure versus L/R at constant flow rate for a polyethylene melt, often call a Bagley plot. The upward curvature for long dies is due both to compressibility and to the pressure dependence of viscosity. The dam have been fit with the three functions indicated. Evaluating dP/d(L/R) at L/R = 0 for each of these fits gives r i = 275 kPa, r 2 = 244 kl and Zws = 233 kPa. 

Similar to capillary, but no Bagley plots are needed if pressure transducers on the slit wall are used... 

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