Normal stress extruder

In the normal stress extruder we first want to evaluate the pressure at the center as a function of disk outer radius, frequency of rotation, and rheological properties. We do this in the absence of radial flow (i.e., for a closed discharge condition), which will give us the... 

Fig. 6.28 Schematic view of the normal stress extruder. Polymer melt is placed between the disks. The upper disk is attached to a rotating shaft at frequency of rotation fi. A pressure profile of increasing pressure toward the center develops, and the melt is extruded through the die.

We find the maximum pressure rise at the center of the disk to be proportional to the square of flR/H, which is the shear rate at r = R. Moreover, by comparing Eq. 6.5-18 to Eqs. 6.5-10 and 6.5-11, we find that this pressure rise is the sum of the primary and secondary normal stress-difference functions —[(tn — T22) + (J22 — T33)] at r = R, less centrifugal forces. Since lL is probably negative, it opposes pressurization hence, the source of the pressurization in the normal stress extruder is the primary normal stress difference function ffq. 

Example 6.9 The Maximum Pressure in the Normal-Stress Extruder Calculate the maximum pressure (at closed discharge) in a normal stress extruder of two 25-cm radius disks at 0.5 cm apart, shearing Low Density Polyethylene (LDPE) at 60rpm and 200°C. 

So far we have neglected radial flow, but in a normal stress extruder the objective is to extrude the polymer melt through a die. Such flow, however, implies a pressure loss in the inward radial direction, consequently reducing the maximum pressure at the die entrance. The die resistance determines the ensuing flow rate at steady flow conditions, the pressure rise in the radial direction equals the pressure drop across the die. 

The normal stress extruder can also be used for melting, as shown in Fig. 6.30. However, because of the limited pressurization capability, various modifications have... 

Fig. 6.30 Schematic representation of a plasticating normal stress extruder.

B. Maxwell, A New Method of Solving the Feeding and Melting Zone Problems in the Normal Stress Extruder, Presented at the 31st Annu. Tech. Conf. of the Society Plastics Engineers, Montreal Canada (1975). 

As the polymer is sheared, normal stresses will generate a centripetal pumping action. Thus, the polymer can be extruded through the central opening in the stationary plate in a continuous fashion. Because normal stresses generate the pumping action, this machine is sometimes referred to as a normal stress extruder. 

Mitsoulis, E., Valchopoulos, J. and Mirza, F. A., 1985. A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell. Poly. Eng. Sci. 25, 677 -669. 

The melt-spinning process used to convert mesophase pitch into fiber form is similar to that employed for many thermoplastic polymers. Normally, an extruder melts the pitch and pumps it into the spin pack. Typically, the molten pitch is filtered before being extruded through a multi-holed spinnerette. The pitch is subjected to high extensional and shear stresses as it approaches and flows through the spinnerette capillaries. The associated torques tend to orient the liquid crystalline pitch in a regular transverse pattern. Upon emerging from the... 

The reasons for such a layered structure are, in our view [20, 21], the lateral temperature gradients that are observed when the extrudate is cooled upon leaving the channel and lateral pressure gradients. The resultant effect of both gradients determines layer order in the flow with intermittent gas content (0.5 to 1 %). The lateral pressure gradient is conditioned by normal stresses in the flow. This was discussed in [8, 9]. 

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 extruders designed in a cone—plate or plate—plate configuration, where the polymer enters at the periphery and exits at the axis. 

The amplitude of shear velocity is a determinant of the degree of thixotropic destruction of a material s structure, independently of the frequency of vibration effect. The effect of reversible viscosity drop is also observed at ultrasonic frequencies. Vibrothixotropy of concentrated polyisobutylene (PIB) solution was sMudied earlier at a frequency of acoustic treatment of 18 kHz and an amplitude of up to 15 mcm74). The first difference of normal stresses determined by the degree of extrudate s swelling... 

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. 

The coefficients Ti and b2, like non-Newtonian viscosity, are also found to be shear rate dependent. The non-Newtonian property of exhibiting normal stresses in shear flows plays an important role in processing under situations in which shear stresses vanish, as in extrudate swell, discussed later in this section. 

Normal stress differences also have practical relevance for extrusion They assist in centering the shaft in the extruder when processing thermoplastics as the rotation of the screw generates radial forces (from the shaft to the wall). 

Although Eq. 3.11 does not fit with all experimental data in literature, the dependence of the extrudate swell on the first normal stress difference is nevertheless shown by B°c Figure 3.11 was used to determine the extrudate swell of the PEO solution, where B = Bex = 1.6. For polymer melts, B can even reach values of 2 or more. The extrudate swell has practical relevance for extrusion, e.g., in pipe or sheet extrusion. 

Thermotropic LCPs have high melt elasticity, but exhibit little extrudate swell. The latter has been attributed to a yield stress and to long relaxation times (60). The relaxation times for LCPs are normally much longer than for conventional polymers. Anomalous behavior such as negative first normal stress differences, shear-thickening behavior and time-dependent effects have also been observed in the. rheology of LCPs (56). Several of these phenomena are discussed for poly(benzylglutamate) solutions in the chapter by Moldenaers et al. 

As discussed by Weber et al. (1978), the same mechanism appears to have operated in experiments performed by Mandl et al. (1977), during which continuous clay smears were produced in a ring-shear apparatus by extruding material from a sheared-off clay band. In these experiments, the much smaller difference between the fault-parallel and the fault-normal stress within the plastic clay, as compared with that in the sand, must have caused the observed extrusion. 

There are four popular measures of liquid elasticity the first normal stress difference, the extrudate swell, B, the Bagley entrance-exit pressure drop correction, P, and the storage shear modulus, G. For multiphase systems there Is no simple correlation between and G, although the Sprigg s theoretical relation (51) ... 

Four measures of melt elasticity have been used the first normal stress difference, Nj, the storage modulus, G , and the two indirect ones, the entrance-exit pressure drop, P. (or Bagley correction), and the extrudate swell, B. In homogeneous melts, the four measures are in a... 

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