Other Pressure Rheometers

Several other channel geometries have been used as rheometers, particularly annular flows. In addition in this section we describe the important indexer squeezing flow between parallel plates. 

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Piston Cylinder (Extrusion). Pressure-driven piston cylinder capillary viscometers, ie, extmsion rheometers (Fig. 25), are used primarily to measure the melt viscosity of polymers and other viscous materials (21,47,49,50). A reservoir is connected to a capillary tube, and molten polymer or another material is extmded through the capillary by means of a piston to which a constant force is appHed. Viscosity can be determined from the volumetric flow rate and the pressure drop along the capillary. The basic method and test conditions for a number of thermoplastics are described in ASTM D1238. Melt viscoelasticity can influence the results (160). 

Another type of rotational viscometer is the hehcal-screw rheometer (176). This iastmment is basically a screw-type metering pump that does not pump. The measure of force is the pressure difference resulting from the rotational motion. It is possible to use a bank of pressure transducers of different sensitivities to measure viscosity over a wide range. The iastmment can be used for high temperature rheometry and to foUow polymerkation, shear and heat degradation, and other developments. 

At this point it should be noted that the conclusion drawn from flow birefringence measurements, viz. that p22 — p33 of polymer systems is very small compared with pn — pn is not always supported by other types of measurement. With the aid of pressure measurements in the walls of various rheometers (e.g. cone-and-plate apparatus) results have been obtained by a number of authors (refs. 26, 43, 44), showing that p23 — p33 should be positive and can have values up to 20 per cent of Pn Pta- 1-7 suggests for the investigated polyisobutylene solution... 

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... 

In other words, apparent viscosity (as well as other apparent values in polymer rheology, snch as apparent shear rate and apparent shear stress) is a value calculated assuming Newtonian behavior and considering all pressure drops within the capillary (when using a capillary rheometer). A nonlinearity between shear rate and shear stress is typically observed for polymer melts. The fluid may behave like Newtonian at a very low shear rates to give a limiting viscosity iJq. 

In a dynamic experiment, a small-amplitude oscillatory shear is imposed to a molten polymer confined in the rheometer. The shear stress response of the polymeric system can be expressed as in Equation 22.14. In this equation, G and G" are dynamic moduli related to the elastic storage energy and dissipated energy of the system, respectively. For a viscoelastic fluid, two independent normal stress differences, namely, first and second normal stress differences can be defined. These quantities are calculated in terms of the differences of the components of the stress tensor, as indicated in Equation 22.15a and 22.15b, and can be obtained, for instance, from the radial pressure distribution in a cone-and-plate rheometer [5]. Some other experiments used in the determination of the normal stress differences can be found elsewhere [9, 22] ... 

These rheometers are widely used to study the rheological behavior of molten polymers. As shown in Figure 3.35 the fluid is forced from a reservoir into and through a fine-bore tube, or capillary, by either mechanical or pneumatic means. The fluid is maintained at isothermal conditions by electrical temperature control methods. Either the extrusion pressure or volumetric flow rate can be controlled as the independent variable with the other being the measured dependent variable. 

The particular ESM extruder was modified in such a manner that it can be used with a measuring barrel serving as a large capillary rheometer, whereby an auger in lieu of a pressure piston forces the material into the nozzle. This means that the pressure drop is measured analogously to the capillary rheometer. The results of this test produce the yield point and the apparent flow curve of the body, amongst other readings. 

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 ... 

If the capillary rheometer is used to compare different polymers, it is not necessary to go through the various correction procedures. However, if one wants to know the absolute values of the viscosity, it is important to apply the various correction factors. The most important corrections are the correction of the shear rate for non-Newtonian fluid behavior (often referred to as Rabinowitsch correction) and the correction of the shear stress for entrance effects (often referred to as Bagley correction). These are the most common corrections applied to capillary rheometers. Other corrections that are sometimes considered are corrections for viscous heating, corrections for the effect of pressure on viscosity, corrections for compressibility, correction for time effects, etc. If many corrections are applied to the data, the whole measurement and data analysis procedure can become very complex and time consuming. 

This rheometer is similar in all respects to that discussed in section 3.2.1 except for the fact that it has a slit orifice cross-section rather than a circular one. The major credit for the development of the concept and use of this rheometer goes to Han [69,71,72] though others [73] have also used it for polymer melt studies. The instrument makes use of a series of flush mounted transducers located along the flow channel wall which measure the pressure gradients along the flow direction. These are then converted into wall shear stress values [69] as follows ... 

The majority of published work on extrusion behaviour deals with compounded stock. Those papers reporting work on raw rubbers have usually been on the use of capillary rheometers to determine extrusion properties at higher shear rates than are possible with Mooney viscometers. Capillary rheometers are, in principle, quite simple to use, and the application of electronic, minicomputer and laser technology has reduced the operation and data analysis to a routine task. There are no standard ASTM or other test procedures, but under a specific set of conditions, once a material is characterized, the data can be used as standard for comparison of all subsequent batches. It is readily possible to characterize a raw rubber by an extrusion experiment to determine the viscosity/shear rate curve, extrudate swell, and stress relaxation.Both Sezna and Karg have shown how the Monsanto Processability Tester (MPT), a modified, computerized extrusion rheometer, can be used in predicting mixing behaviour. The MPT (shown schematically in Fig. 7) is a most versatile instrument. It has a larger than conventional barrel for minimal pressure drop in the barrel, a pressure transducer at the entrance to the orifice, a microprocessor system, and a laser device for... 

Char strength is a crucial parameter because it has to accommodate internal pressure and external stresses to avoid the formation of cracks. Figure 6.16 describes the evolution of the force applied on the top of the intumescent char as a function of the gap between the rheometer plates (Figure 6.16a). EVA-APP/PA6 -OMMT exhibits better char resistance than the other formulations, those of EVA-APP/PA6-NPSi and EVA-APP/PA6 are significantly lower, and EVA -APP/PA6-OLDH exhibits intermediate behavior. This suggests that high char strength should be required to get the best performance associated with reasonable expansion. 

In Eqs. 196 and 197, Pq is the exit pressure which can be well approximated by the pressure drop through an orifice of the same radius as the die and n is the PL exponent which is obtained from capillary data (with die radius and length given by R and L, respectively). Cogswell s method, as well as other alternative methods for obtaining the uniaxial viscosity, have been compared against direct measurements in an extensional rheometer by Laun and Schuch [23]. 

In rheology we generally assume that a material is incompressible. The deviations from simple Hookean or Newtonian behavior due to nonlinear dependence on deformation or deformation history are usually much greater than the influence of compressibility. We discuss the influence of pressure briefly in Chapters 2 and 6. For incompressible materials the overall pressure cannot influence material behavior. In other words, increasing the barometric pressure in the room should not change the reading from a rheometer. For incompressible materials the isotropic pressure is determined solely by the boundary conditions and the equations of motion (see Sections 1.7 and 1.8). 

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