Shear rate, melt

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

As it seems that the dispersive mixing of the additives could be improved by increasing the melt shear rate, in the video conference the 3D simulation expert proposes a modification of the screw configuration as well as the screw speed. This is accepted by the team leader, a new MOREX simulation is done and the compounding extruder configuration is fixed. 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

Polyolefin melts have a high degree of viscoelastic memory or elasticity. First normal stress differences of polyolefins, a rheological measure of melt elasticity, are shown in Figure 9 (30). At a fixed molecular weight and shear rate, the first normal stress difference increases as MJM increases. The high shear rate obtained in fine capillaries, typically on the order of 10 , coupled with the viscoelastic memory, causes the filament to swell (die swell or... 

Many industrially important fluids cannot be described in simple terms. Viscoelastic fluids are prominent offenders. These fluids exhibit memory, flowing when subjected to a stress, but recovering part of their deformation when the stress is removed. Polymer melts and flour dough are typical examples. Both the shear stresses and the normal stresses depend on the history of the fluid. Even the simplest constitutive equations are complex, as exemplified by the Oldroyd expression for shear stress at low shear rates ... 

Between 50 and 300°C, PTEE obeys the relationship between stress T and the apparent shear rate 7 r =. Melting of PTEE begins near... 

C. Above this temperature, the shear stress at constant shear rate increases and the rheological exponent rises from 0.25 toward 0.5 at the final melting point (68). 

Like other thermoplastics, they exhibit melt fracture (32) above certain critical shear rates. In extmsion, many variables control product quaUty and performance (33). 

Extrusion. Like other thermoplastics. Teflon PEA resin exhibits melt fracture above certain critical shear rates. Eor example, samples at 372°C and 5-kg load show the following behavior ... 

Melt Viscosity. As shown in Tables 2 and 3, the melt viscosity of an acid copolymer increases dramatically as the fraction of neutralization is increased. The relationship for sodium ionomers is shown in Figure 4 (6). Melt viscosities for a series of sodium ionomers derived from an ethylene—3.5 mol % methacrylic acid polymer show that the increase is most pronounced at low shear rates and that the ionomers become increasingly non-Newtonian with increasing neutralization (9). The activation energy for viscous flow has been reported to be somewhat higher in ionomers than in related acidic... 

Fig. 1. Melt viscosity as a function of shear rate for (—) linear BPA polycarbonate and (-) branched polycarbonate. To convert Pa-s to poise, multiply...

Fig. 6. Melt viscosity dependence on shear rate for various polymers A, low density polyethylene at 210°C B, polystyrene at 200°C C, UDEL P-1700 polysulfone at 360°C D, LEXAN 104 polycarbonate at 315°C and E, RADEL A-300 polyethersulfone at 380°C.

The other models can be appHed to non-Newtonian materials where time-dependent effects are absent. This situation encompasses many technically important materials from polymer solutions to latices, pigment slurries, and polymer melts. At high shear rates most of these materials tend to a Newtonian viscosity limit. At low shear rates they tend either to a yield point or to a low shear Newtonian limiting viscosity. At intermediate shear rates, the power law or the Casson model is a useful approximation. 

The value for n is often given as 2/3, but polymer melts have shown a wide range of values. The constant d is associated with mpture of the linkages in the stmcture of the fluid. The effect of different values of a, ie, at the same values of T q and, is shown in Figure 4. As d increases, breakdown occurs at lower and lower shear rates. 

Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The stmcture can be estabUshed from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often ia a Newtonian region. This 2ero-shear viscosity, T q, is related directly to the molecular weight of polymer melts and concentrated polymer solutions. 

Processing PC resins by extmsion or injection-molding methods requires melt temperatures of 290—320°C. High melt viscosity at low shear rates prevents mold flash and drool. At injection shear rates, apparent viscosities decrease, and easy melt flow allows manufacture of large, complex parts. 

At the same time it is not surprising that polymer melts are non-Newtonian and do not obey such simple rules. Fortunately, if we make certain assumptions, it is possible to analyse flow in certain viscometer geometries to provide measurements of both shear stress (t) and shear rate (7) so that curves relating the two (flow curves) may be drawn. 

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