Weissenberg Effects

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. 

Viscoelastic Measurement. A number of methods measure the various quantities that describe viscoelastic behavior. Some requite expensive commercial rheometers, others depend on custom-made research instmments, and a few requite only simple devices. Even quaHtative observations can be useful in the case of polymer melts, paints, and resins, where elasticity may indicate an inferior batch or unusable formulation. Eor example, the extmsion sweU of a material from a syringe can be observed with a microscope. The Weissenberg effect is seen in the separation of a cone and plate during viscosity measurements or the climbing of a resin up the stirrer shaft during polymerization or mixing. 

Many materials of practical interest (such as polymer solutions and melts, foodstuffs, and biological fluids) exhibit viscoelastic characteristics they have some ability to store and recover shear energy and therefore show some of the properties of both a solid and a liquid. Thus a solid may be subject to creep and a fluid may exhibit elastic properties. Several phenomena ascribed to fluid elasticity including die swell, rod climbing (Weissenberg effect), the tubeless siphon, bouncing of a sphere, and the development of secondary flow patterns at low Reynolds numbers, have recently been illustrated in an excellent photographic study(18). Two common and easily observable examples of viscoelastic behaviour in a liquid are ... 

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. 

For convenience and simplicity, polymers have generally been considered to be isotropic in which the principle force is shear stress. While such assumptions are acceptable for polymers at low shear rates, they fail to account for stresses perpendicular to the plane of the shear stress, which are encountered at high shear rates. For example, an extrudate such as the formation of a pipe or filament expands when it emerges from the die in what is called the Barus or Weissenberg effect or die swell. This behavior is not explained by simple flow theories. 

Almost every biological solution of low viscosity [but also viscous biopolymers like xanthane and dilute solutions of long-chain polymers, e.g., carbox-ymethyl-cellulose (CMC), polyacrylamide (PAA), polyacrylnitrile (PAN), etc.] displays not only viscous but also viscoelastic flow behavior. These liquids are capable of storing a part of the deformation energy elastically and reversibly. They evade mechanical stress by contracting like rubber bands. This behavior causes a secondary flow that often runs contrary to the flow produced by mass forces (e.g., the liquid climbs the shaft of a stirrer, the so-called Weissenberg effect ). 

In (b), the pi numbers and 7ho T as well as ye/yn, have to be added (7 = din /dT). Besides this, completely other phenomena can occur (e.g., creeping of a viscoelastic liquid on a rotating stirrer shaft opposite to gravity—the so-called Weissenberg effect) that require additional parameters (in this case g) to be incorporated into the relevance list. 

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 9.9 The Weissenberg effect (a) Newtonian liquid and (b) viscoelastic liquid...

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]. 

Figure 6.16 The centrifugal effect in a non-elastic liquid (a), and the Weissenberg effect in in a viscoelastic liquid (b).

Fig. 3.3 A 9, 52-mm D aluminum rod rotating at 10 rps in a wide-diameter cylinder containing (a) Newtonian oil, and (b) polyisobutylene (PIB) solution, which exhibits the rod-climbing Weissenberg effect [from G. S. Beavers and D. D. Joseph, J. Fluid Mech., 69, 475 (1975)]. (c) Schematic representation of the flow direction flow-induced causing rod climbing. For Newtonian fluids, Tn = 0, since the small and simple Newtonian fluid molecules are incapable of being oriented by the flow.

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. 

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...

In addition, it can happen that in the non-Newtonian case completely new phenomena take place (e.g. shaft climbing by a viscoelastic fluid against the acceleration due to gravity, the so-called Weissenberg effect), this calling for additional parameters (in this case g). 

While chemical engineers are well-grounded in the mechanics of Newtonian fluids, it is the non-Newtonian character of polymers that controls their processing. Three striking examples [6] of the differences between Newtonian and typical polymeric liquids (either melts or concentrated solutions) are shown schematically in Fig. 1. The upper portion of the figure refers to the Weissenberg effect [7], or rod-climbing, exhibited by polymers excellent photos may be found in Bird et al. [4] as well. When a rod is rotated in a Newtonian fluid, a vortex develops near the rod due to centripetal acceleration of the fluid. When the same experiment is repeated with a polymeric fluid, however, the fluid climbs the rod. In the center... 

Weight-average molecular mass, 18 Weissenberg effect, 526 number, 57,556 Wet fastness, 881 Wide-line NMR, 368,373, 374 WLF... 

If we choose the coefficients p and s in (6.1.7) to be nonzero constants, then we arrive at the Reiner-Rivlin model, which additively combines the Newton model with a tensor-quadratic component. In this case the constants p and e are called, respectively, the shear and the dilatational (transverse) viscosity. Equation (6.1.7) permits one to give a qualitative description of specific features of the mechanical behavior of viscoelastic fluids, in particular, the Weissenberg effect (a fluid rises along a rotating shaft instead of flowing away under the action of the centrifugal force). 

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