Viscosity measurement shear flow capillary method

Measurements of viscosities in nematics Cl.l Shear flow capillary method... 

One encounters the following difficulties in the interpretation of the data from the experiments with interfacial dilatation. As discussed in Ref. 58, the shear viscosity, T jh, does not influence the total stress, 67, only for interfacial flow of perfect spherical symmetry. If the latter requirement is not fulfilled by a given experimental technique, its output data will be influenced by a mixture of dissipative effects (not only -r d but also -qsh and tr). The apparent interfacial viscosity thus determined is not a real interfacial property insofar as it depends on the specific method of measurement. For example, the apparent interfacial viscosity measured by the capillary-wave methods [189-196] depends on the frequency the apparent interfacial viscosity measured by the Langmuir trough method [197,198] is a sum of the dilatational and shear viscosities ("q + -q h) for the methods employing nonspherical droplet deformation, like the spinning-drop method [199-201], the apparent surface viscosity is a complex function of the dilatational and shear interfacial viscosities. 

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. 

Numerous methods for measuring fluid viscosity exist, for example, capillary tube flow methods (Ostwald viscometer), Zahn cup method, falling sphere methods, vibrational methods, and rotational methods. Rotational viscometers measure the torque required to turn an object immersed or in contact with a fluid this torque is related to the fluid s viscosity. A well-known example of this type of system is the Couette viscometer. However, it should be noted that as some CMP slurries may be non-Newtonian fluids, the viscosity may be a function of the rotation rate (shear rate). An example of this is the dilatant behavior (increasing viscosity unda increasing shear) of precipitated slurries that have symmetrical particles [33]. Furthermore, the CMP polisher can be thought of as a large rotational plate viscometer where shear rates can exceed 10 s and possibly affect changes to the apparoit viscosity. The reader can refer to the comprehensive review of viscosity measurement techniques in the book by Viswanath et aL [34]. 

The rotational viscometers and the capillary rheometers described in sections 3.1 and 3.2 are those applicable for shear flows. However, there are processing operations that involve extensional flows. These flows have to be treated differently for making mecisurements of extensional viscosity. The extensional viscosity of a material is a measure of its resistance to flow when stress is applied to extend it. In general, measurement of steady-state extensional viscosity has proven to be extremely difficult. Steady extensional rate would be achieved by pulling Ihe ends of the sample apart such that I = Zq exp(ef) or in other words, at a rate that increases exponentially with time. Steady-state is reached when the force is constant. However, often d e sample breaks before steady-state is achieved or the limits of the equipment are exceeded or at the other extreme, die forces become too small for the transducer to differentiate between noise etnd response signal. Nevertheless, there have been various methods attempted for the measurement of extensional viscosity. 

A typical example of extensional flow is the flow at the entrance of a capillary die. Cogswell [83] has shown that the pressure losses through sudi dies can be used as a measure of the extensional viscomty. This method has not lined popularity because of the skepticism in acc ting the complex converging-flow patterns at the die entrance as representative of true extensional flow with constant extensional rate. Cogswell [84] did suggest later that the die should be lubricated to reduce the shear flow and the profile of the die wall should vary at all cross sections in such a way as to ensure constant extensional rate along the die axis. Such a rheometer has been known to be developed and used for extensional viscosity data of polystyrene melt [85]. 

The most frequently employed methods for measuring viscosities are based on flow through a capillary tube. The pressure under which the liquid flows furnishes the shearing stress. 

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

A number of experimental methods have been applied to measure the melt viscosity of polymers (53-55,65), but capillary extrusion techniques probably are generally preferred. Rotational methods are also used, and some permit the measurement of normal stress effects resulting from elasticity as well as of viscosity. Slit rheometers can also be used to measure normal stress (66). Oscillatory shear measurements are useful for measuring the elasticity of poljmier melts (57,58). Controlled stress methods have also been applied (59). Squeeze film flow has also been proposed as a geometry suitable for processibility testing of polymer melts... 

Mooney viscosities of MNR-ADS blends were found to be much higher than those of MNR-STR 5L blends. Rheological measurements were carried out the same method as described above.The apparent values of shear stress, shear rate and shear viscosity were calculated using the derivation of the Poiseuille law for capillary flow as shown in Equations (18.1) to (18.3). Plots of the apparent shear stress versus apparent shear rate for various blend compositions of MNR-STR/STR 5L and MNR-ADS/ADS were shown in Figures 18.32 and 18.33, respectively. Straight lines of the flow curve were observed for all sets of the test. The results corresponded to the power law equation proposed by Ostwald as shown in Equation 18.4. 

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