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Figure 7. Schematic of the hole-pressure geometry for a transverse slot. The curvature of the streamlines near the mouth of the slot is shown. The fluid elasticity (Nt) results in a tension along the curved streamlines that tends to lift out of the slot.

The exit pressure technique has been used to calculate the normal stress differences (87,88). As it is difficult to measure the pressure at the die exit directly, exit pressure is usually obtained by linear extrapolation of the pressure profile from the region of fully developed flow in the die. The expressions for the normal stress differences for a slit die are (89):

However, this method is controversial. Critical analyses of the method have been done (88-90). The origin of the controversy lies in the fact that for polymers, positive (87,88,91), zero (92), and negative (90,93-97) exit pressures have been obtained. There has been very few published studies using this method on foods. Both positive and negative exit pressures were reported for corn grits, but positive exit pressures only for potato grits (98). Another study examining this method for corn grits showed that products having lower moisture (25-35% db) content gave mostly negative exit pressures, whereas higher moisture values (40 and 45% db) gave positive exit pressures (99). Positive exit pressure was obtained using a capillary die (100). As it is impossible to flush-mount transducers on the walls of the capillary, the presence of hole pressure could lead to erroneous exit pressure values, so the use of a capillary die for this procedure is not recommended.

One assumption in obtaining the expression for the normal stress differences from the exit pressure theory (eq. 6) is that the flow remain fully developed till the die exit. There is evidence that for polymers, the flow does not remain fully developed till the exit (101,102), owing to the presence of exit disturbance. The exit disturbance will lead to a rearrangement of the velocity profile. The velocity rearrangement would lead to an overestimation of the exit pressure (89). Beyond a critical shear stress, the exit disturbance is negligible (88). The value of this stress would depend on the material. For low-density polyethylene this value is 25 kPa. However, there are data in the literature where negative exit pressures were obtained for experiments conducted above the recommended 25 kPa value for wall shear stress. A problem during the extrusion cooking of foods is that at temperatures greater than 100°C the presence of moisture flash at the die exit could cause an additional exit disturbance. Other problems with the exit-pressure method are viscous dissipation in the die and pressure dependence of viscosity of the material. Both these effects could lead to a concave pressure profile and would result in erroneous estimates of exit pressure.

The hole pressure was originally observed as an error in the measurement of normal stress difference using standard geometry rheometers (103). Studies subsequently established the presence of significant hole-pressure errors (104). The interest in the hole pressure arises from the claim that this property can be used for reliable prediction of the elastic properties of viscoelastic fluids. As the fluid passes over a hole or a slot, the stream line for a viscoelastic fluid tends to dip and this leads to the development of normal stresses that tend to lift the fluid (Fig. 8), thus creating a lower pressure at the bottom of the slot or hole

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