Weissenberg normal stress effect

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. 

The fact is that, in the long history of polymer processing, engineering and design has always been ahead of theory. The development of screwless (or disc-type) extruders, innovative for their time, on the basis of the earlier-discovered normal stress effect (which received the name of the Weissenberg effect) was, apparently, one.of the few exclusions. However, this example has clearly demonstrated the potential and the role of theoretical research in the progress of technology. 

Figure 3.10 Example of the "Weissenberg Effect" for a viscoelastic solution. Stirrer is rotated (n=200 s 1) in a glass beaker containing aqueous PEO solution (c=1wt.-%. Polyox WSR 301). The solution climbs up the stirrer shaft due to normal stress effects...

The Weissenberg effect is clearly manifested in the increase in diameter of extruded profiles of a variety of molten polymers. The extrusion swelling (Figure 3.32), more commonly known as die swell, arises probably due to a combination of normal stress effects and a possible elastic recovery consequent to prior compression before the melt or liquid enters the die. 

The experiments to which Weissenberg refers were done during World War II in England on materials for flame throwers. One goal of this research was to improve predictions of the pressure drop through the spray nozzles (Russell. 1946). Gum rubber in gasoline, polymethyl methacrylate in benzene, and similar materials were studied. Figure 4.1.1 shows some of the experiments that were used to demonstrate normal stress effects. 

Another well-known phenomenon is the Weissenberg effect, which occurs when a long vertical rod is rotated in a viscoelastic liquid. Again, the shearing generates a tension along the streamlines, which are circles centred on the axis of the rod. The only way in which the liquid can respond is to flow inwards and it therefore climbs up the rod until the hydrostatic head balances the force due to the normal stresses. 

Viscoelastic fluids have elastic properties in addition to their viscous properties. When under shear, such fluids exhibit a normal stress in addition to a shear stress. For example, if a vertical rod is partly immersed and rotated in a non-viscoelastic liquid the rod s rotation will create a centrifugal force that drives liquid outwards toward the container walls, as shown in Figure 6.16(a). If, on the other hand, the liquid is viscoelastic then as the liquid is sheared about the rod s axis of rotation, a stress normal to the plane of rotation is created which tends to draw fluid in towards the centre. At some rotational speed, the normal force will exceed the centrifugal force and liquid is drawn towards and up along the rod see Figure 6.16(b). This is called the Weissenberg effect. Viscoelastic fluids flow when stress is applied, but some of their deformation is recovered when the stress is removed [381]. 

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. 

The high normal stress differences in comparison to the shear stress cause flow phenomena which may influence many technical processes. One example is the Weissenberg Effect (see Fig. 3.10), which arises when a shaft rotates within a viscoelastic fluid. The first normal stress difference leads to a pressure distribution which causes the fluid to climb up the stirrer shaft. This effect occurs when processing polymer color dispersions or mixing cake dough. 

Other dimensionless groups similar to the Deborah number are sometimes used for special cases. For example, in a steady shearing flow of a polymeric fluid at a shear rate y, the Weissenberg number is defined as Wi = yr. This group takes its name from the discoverer of some unusual effects produced by normal stress differences that exist in polymeric fluids when Wi 1, as discussed in Section 1.4.3. Use of the term Weissenberg number is usually restricted to steady flows, especially shear flows. For suspensions, the Peclet number is defined as the shear rate times a characteristic diffusion time to [see Eq. (6-12) and Section 6.2.2]. 

The steady-state flow behavior is not only nonlinear but also characterized by the development of normal stresses, which are completely absent in a simple Newtonian fluid. Thus, a steady shear flow in the x-y plane,, not only leads to a (nonlinear) shearing stress, X but also leads to normal stresses, Ojjx vv zz Associatea with these normal stresses are many distinctive phenomena exhibited by polymeric fluids, such as the Weissenberg effect, where a polymer being stirred by a turning shaft tends to climb up the shaft instead of being thrown outward by centrifugal action (22). 

An extrudate jet swells owing to normal stresses generated in a moving melt (Weissenberg effect) under shear stresses (71,74). Sheared flow of polymer melts under shearing forces is accompanied by forced changes in macromolecule conformations as compared with the equilibrium condition. This results in creation... 

For a one-dimensional steady shear flow of a fluid between two planes, the velocities of an infinitesimal element of fluid in the y- and z-directions are zero. The velocity in the x-direction is a function of y only. Note that in addition to the shear stress Tyx (refer to t subsequently), there are three normal stresses denoted by Txx, Tyy, within the sheared fluid. Weissenberg in 1947 [6] was the first to observe that the shearing motion of a viscoelastic fluid gives rise to tmequal normal stresses, known as Weissenberg effects. Since the pressure in a non-Newtonian fluid cannot be deflned, and as the normal stress differences... 

Normal stresses originally recognized by Weissenberg [W3] through observation of rod climbing effects in soap-hydrocarbon liquid suspensions and polymer solution systems began to be measured on thermoplastics in the 1960s [C9, K9]. White and Tokita [W24] noted their occurrence in gum... 

The inequality of normal stresses is responsible for a number of visually noticeable Non-Newtonian effects. These include the Weissenberg rod-climbing effect where the fluid climbs up a rotating rod rather than dipping near the rod, and the extrudate swell, see Tanner (2000) and Boger and Walters (1993) for more details. 

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