Hole pressure normal stress from

Normal stress measurements versus wall shear stress for a 1 % solution of polyacrylamide at 25°C in annular flows —N2 from axial annular flow, N] from (solid line) tangential annular flow, N from (dashed line) cone and plate, and Ph the hole pressure error. Adapted from Osmers and Lobo (1976),... 

For rotating coaxial cylinder geometry, the radial gradient in pressure across the gap between the cylinders, measured, at a point well removed from either end, would in the absence of hole effects be related to the primary normal stress difference ... 

While the cone and plate geometry is the preferred arrangement to obtain the steady viscometric functions, it is limited to low shear rates — usually, to those less than 10 s . At higher shear rates encountered in processing ( 10-10 s ), it is customary to resort to capillary rheometry to measure the shear viscosity. Unfortunately, the normal stress differences cannot be obtained from this test. To get N at high shear rates one can, however, employ a slit device based on the so-called hole pressure effect [21]. 

However, two other methods for obtaining normal stress data from slit rheometry have had reasonable success the exit pressure and particularly the pressure hole method. These are discussed in Sections 6.3.2 and 6.3.3. 

Comparison of shear and normal stress determined by parallel plates (solid symbols) and slit rheometer with hole pressure (open symbols) for a polyisobutylene solution at room temperature. From Lodge (1989). 

Normal stress versus shear stress for a polystyrene melt at 190°C cone and plate (o) and transverse pressure holes of two different widths (A). From Baird et al. (1986). 

Figure 5.4.3 compares Ni and Wz as determined from total thrust in the cone and plate to values obtained from the pressure distribution. Figure 6.2.13 and Table 6.2.2 compare N from cone and plate to extrudate swell. Figures 6.3.4,6.3.6, and 6.3.7 do the same for N determined by exit pressure and hole pressure. These comparisons helped us to decide which mediods were reliable and over what range of measurement The same ccndd be said of the normal stress comparisons made for axial annular and tangential annular flow in Figure 6.4.2. 

Slit rheometers are more difficult to build and use but are preferred for research studies, because the flat flow channel makes it possible to mount pressure sensors and to make optical measurements. It has been proposed that measurement of the exit pressure or hole pressure [129] might be used to infer the first normal stress difference using a slit rheometer [9,p. 309], but these approaches have been little used because of the difficulty of measuring the small pressures or pressure differences involved. As in the case of capillary rheometers, there are established methods for calculating the true wall shear stress and shear rate from experimental slit data [9, 81]. 

Lodge, A. S. Normal stress differences from hole pressure measurements . Chapter 10 of Rheological Measurement. 2 edit., ed. by AA. Collyer and D. W. Clegg, Chapman Hall, London (1998)... 

Here the solution of Dugdale will be followed since it clearly shows a significant feature of the model. A flat elliptical hole of length 2c is considered in an infinite plate loaded in tension by a stress a remote from and normal to the ellipse. The ends of the ellipse terminate in small plastic zotees whose boundaries are under uniform internal pressure stresses (see Fig. 2.2). For these internal stresses static equilibrium is achievai by imposing equal and compressive opposite stresses ct,.. This... 

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