Weissenberg effect, viscoelasticity

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]. 

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. 

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. 

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

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

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). 

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). 

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... 

Viscoelastic fluids exhibit elastic recovery from deformations that occur during flow. The Weissenberg effect and die swell have been discussed previously. Another very simple example is the stirring of concentrated polymer solutions rapidly, then stopping. Elastic effects make the fluid move backward for a time. 

Figure 2.8 Weissenberg effect showing how the viscoelastic fluid climbs up the stirrer-rod when stirred at moderate speeds. (Reprinted from Ref. 34 with kind permission from Chapman Hall, Andover, UK.)...

Basic description of non-Newtoruan fluids is provided so that concepts of shear rate dependent viscosities with or without elastic behavior, yield stress with or without shear rate dependent viscosities and time dependent viscosities at fixed shear rates get classified. The filled polymer systems fall into the category of pseudoplastic fluids with or without yield stress and also often depict the behavior of thixotropic fluids. Their viscoelasticity may give rise to various anamolous effects that are discussed in Chapter 2, such as the Weissenberg effect, extrudate swell, drawn resonance, melt fracture and so on. 

However, these simple empirical expressions are far from universal, and fail to account for effects specific to nonlinear behavior, such as the appearance of finite first and second normal stress differences (Tyy = Ni(y) and <7yy — steady shear flow. (For a linear viscoelastic material in shear, ctxx, Cyy and a-zz are equal to the applied pressure, usually atmospheric pressure.) TTiese may be linked to the development of molecular anisotropy in polymer melts subject to flow, and are responsible for the Weissenberg effect, which refers to the tendency for a nonlinear viscoelastic fluid to climb a rotating rod inserted into it, as well as practically important phenomena such as die swell [20]. 

Fig. 1.1 Illustration of the Weissenberg effect due to a rotating rod in a viscoelastic fluid (a) compared to a rod rotating in a Newtonian fluid (b). (See Fredrickson, (1964) for two viscoelastic fluids examples.)...

Figure 6-34 Weissenberg effect with mixing of viscoelastic liquid.

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