Concentric cylinders normal stress climbing

Normal Stress (Weissenberg Effect). Many viscoelastic fluids flow in a direction normal (perpendicular) to the direction of shear stress in steady-state shear (21,90). Examples of the effect include flour dough climbing up a beater, polymer solutions climbing up the inner cylinder in a concentric cylinder viscometer, and paints forcing apart the cone and plate of a cone—plate viscometer. The normal stress effect has been put to practical use in certain screwless extmders designed in a cone—plate or plate—plate configuration, where the polymer enters at the periphery and exits at the axis. 

A graphic example of the consequences of the existence of in stress in simple steady shear flows is demonstrated by the well-known Weissenberg rod-climbing effect (5). As shown in Fig. 3.3, it involves another simple shear flow, the Couette (6) torsional concentric cylinder flow,3 where x = 6, x2 = r, x3 = z. The flow creates a shear rate y12 y, which in Newtonian fluids generates only one stress component 112-Polyisobutelene molecules in solution used in Fig. 3.3(b) become oriented in the 1 direction, giving rise to the shear stress component in addition to the normal stress component in. 

In some ways a simpler approach to obtaining normal stresses from the concentric cylinder system is to use the rod climbing phenomenon quantitatively. Because the flow is complex, analysis requires the assumption of some constitutive relation. Joseph and Fosdick (1973) have done this using the second-order fluid, which should be an exact representation of elastic liquids in the limit of slow flows (see Section 4.3). They derive a power series for the... 

In the foregoing derivations we neglected the inertia term in eq. 5.4.1. We saw with concentric cylinders that inertia causes a depression around the inner cylinder rather than the climb due to viscoelastic normal stresses (Figure 5.3.3). In cone and plate... 

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