Shear rate capillary

This section describes two common experimental methods for evaluating i], Fj, and IG as functions of shear rate. The experiments involved are the steady capillary and the cone-and-plate viscometric flows. As noted in the previous section, in the former, only the steady shear viscosity function can be determined for shear rates greater than unity, while in the latter, all three viscometric functions can be determined, but only at very low shear rates. Capillary shear viscosity measurements are much better developed and understood, and certainly much more widely used for the analysis of polymer processing flows, than normal stress difference measurements. It must be emphasized that the results obtained by both viscometric experiments are independent of any constitutive equation. In fact, one reason to conduct viscometric experiments is to test the validity of any given constitutive equation, and clearly the same constitutive equation parameters have to fit the experimental results obtained with all viscometric flows. 

M 14. Merz, E. H., and R. E. Colwell A high shear rate capillary rheometer for polymer melts. ASTM Bulletin 232, 63—66 (1958). 

The cone and plate rheometers are useful at relatively low shear rates. For higher shear rates capillary rheometers are employed. They are usually constructed from metals. The molten polymer is forced through the capillary at a constant displacement rate. Also, they may be constructed to suit various specific shear stresses encountered in commercial operation. Their big disadvantage is that shear stress in the capillary tubes varies from maximum at the walls to zero at the center. On the other hand, stable operation at much higher shear rates is possible. Determination, however, of rjo is usually not possible due to limitations of the instruments. At low shear rates, one can determine the steady-state viscosity from measurements of the volumetric flow rates, Q and the pressure drop ... 

For a PET with a given molecular weight and at constant, extrusion temperature, shear rate, capillary diameter, there were made determinations on capillaries with different entrance angles. Some of the characteristics of the obtained extrudates with the length between 5 and 8 cm were determined. 

Development of a high shear rate capillary viscometer for engine oils, ... 

Figure 29. Apparent viscosity, rj pp, of the chiral nematic cholesteryl acetate as a function of temperature for different shear rates. Capillary flow (s ) 10 (V), 50(x),100(n),l000 ( ), 5000 ( ) rotational shear (s" ) lO (A), and normal liquid behavior at very high shear rate (O) (redrawn from [115]).

Merz, E. H. and Colwell, R. E., A High Shear Rate Capillary Rheometer for Polymer Melts, ASTM Bull. No. 232 (Sept. 1958). 

Figure 3. Viscosity vs. frequency (RMS) or shear rate (capillary) curves at 250°C obtained at different operational conditions (see Table 2).

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... 

Flow processes iaside the spinneret are governed by shear viscosity and shear rate. PET is a non-Newtonian elastic fluid. Spinning filament tension and molecular orientation depend on polymer temperature and viscosity, spinneret capillary diameter and length, spin speed, rate of filament cooling, inertia, and air drag (69,70). These variables combine to attenuate the fiber and orient and sometimes crystallize the molecular chains (71). 

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. 

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. 

More recent developments in the rolling ball area include an automated micro viscometer, the Paar AMV 200, from Paar Physica. The specimen to be measured is introduced into a glass capillary down which a gold-covered steel ball roUs. The rolling time is measured automatically. The shear stress may be varied by changing the inclination angle of the capillary tube. The shear rate range is 10 1000, which makes the instmment useflil for... 

A number of viscometers have been developed for securing viscosity data at temperatures as low as 0 °C (58,59). The most popular instmments in current use are the cone plate (ASTM D3205), parallel plate, and capillary instmments (ASTM D2171 and ASTM D2170). The cone plate can be used for the deterniination of viscosities in the range of 10 to over 10 Pa-s (10 P) at temperatures of 0—70°C and at shear rates from 10 to 10 5 . Capillary viscometers are commonly used for the deterniination of viscosities at 60 —135°C. 

In this apparatus the plastic to be tested is heated in a barrel and then forced through a capillary die as shown in Fig. 5.16, Normally the ram moves at a constant velocity to give a constant volume flow rate, Q. From this it is conventional to calculate the shear rate from the Newtonian flow expression. 

The correction factor for converting apparent shear rates at the wall of a circular cylindrical capillary to true shear rates is (3n + l)/4n, where n is the power law index of the polymer melt being extruded. 

Viscosities of the blends and composites were measured in shear flow with a Gottfert Rheograph 2002 capillary viscosimeter. The shear rate was investigated from 100-10000 s" . The L D ratio of the capillary die was 30 mm 1 mm. Rabinowitch correction was made to the measurements, but Bagley correction was not applied. 

During a steady-state capillary flow, several shear-induced effects emerge on blend morphology [4-6]. It is, for instance, frequently observed that TLCP domains form a fibrillar structure. The higher the shear rate, the higher the aspect ratio of the TLCP fibrils [7]. It is even possible that fibers coalesce to form platelet or interlayers. 

The shear viscosity, especially as measured with capillary rheometers characterized by high shear rates, is hardly sensitive to material structure since the investigator usually has to deal with the substantially destroyed structure in the molten sample. Melt stretching experiments would normally provide much more information [33]. 

If it is known that a particular form of relation, such as the power-law model, is applicable, it is not necessary to maintain a constant shear rate. Thus, for instance, a capillary tube viscometer can be used for determination of the values of the two parameters in the model. In this case it is usually possible to allow for the effects of wall-slip by making measurements with tubes covering a range of bores and extrapolating the results to a tube of infinite diameter. Details of the method are given by Farooqi and Richardson. 21 ... 

A capillary rheometer is another type of instmment, in which the uncured mbber is extmded through a small orifice and the change in dimensions of the extmdate is measured with a laser [2]. This instmment generates high shear rates, compared to Mooney rheometer. The capillary rheometer can thus represent flow of compounds on mbber processing machinery, such as injection molds. 

If the intrinsic viscosity is large (i.e., greater than about 4 deciliters per gram), the viscosity is likely to be appreciably dependent on the rate of shear in the range of operation of the usual capillary viscometer. Measurements in a viscometer permitting operation at a series of rates of shear extending to very low rates are then required in order to extrapolate nsp/c to its limiting value at a shear rate of zero. Extrapolation to infinite dilution does not eliminate the effect on this ratio of a dependence on shear rate. 

A quite different approach to rheo-NMR was taken by Xia and Callaghan [12], in an NMR microscopy measurement of the velocity profile of a high molecular weight polymer solution flowing through a capillary. In this study anomalous polymer diffusion was found at a radius within the pipe at which the local shear rate exceeded... 

There are commercially available in-line or on-line viscometer devices. In-line devices are installed directly in the process while on-line devices are used to analyze a side stream of the process. Most devices are based on measuring the pressure drop and flow rate through a capillary. The viscosity is either determined at a single shear rate or, at most, a few shear rates. Complex fluids, on the other hand, exhibit a viscosity that cannot be so easily characterized. In order to capture enough information that allows, for example, a molecular weight distribution to be inferred, it is necessary to determine the shear viscosity over reasonably wide ranges of shear rates. 

Fig. 22. Radius of drops produced by capillary breakup (solid lines) and binary breakup (dotted lines) in a hyperbolic extensional flow for different viscosity ratios (p) and scaled shear rate (p,cylo) (Janssen and Meijer, 1993). The initial amplitude of the surface disturbances is ao = 10 9 m. Note that significantly smaller drops are produced by capillary breakup for high viscosity ratios.

Viscosity measurements were carried out using Cannon-Fenske viscometers of appropriate capillary diameter so as to keep the efflux time between 200-300 seconds. Approximate shear rate at the wall was calculated using the equation... 

The concentration at which a steep rise in this curve begins has been termed as the critical or threshold concentration (2,3). Figure 6 shows such typical curves for PTF and BTF in n-hexane. Despite the fact that different shear rates are involved in capillary viscometry, it can be qualitatively said that at a given concentration, PTF viscosified n-hexane better than BTF. It is clear from Figure 6 that the critical concentration for these two compounds is above 0.7%, while analogous tri-n-alkyltin fluorides showed a critical concentration of less than 0.4% (3). This may be due to the presence of bulky Me3Si-groups nearer to the Sn-F bond, which causes some steric hindrance to auto-association. 

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