Pressure-Driven Rheometers

Shear modulus versus time after a step strain for a poly-dimethylsiloxane. The inset graph shows that the commanded strain is reached in 3ms. Stress reaches a maximum in 6ms due to transducer inertia. Low torque signal and transducer hysteresis are limiting at long time. 

As with drag flow rtieometers, there are two basic design types one features controlled drive pressure and measurement of flow rate, and the other uses controlled flow rate and measures pressure drop. Pressure is controlled by a hydrostatic head, external gas or hydraulic pressure, or even a weight. Flow rate can be controlled by motion of a driving piston. Whoriow (1992) has an extensive review of pressure driven iheometer design. 

Effect of analog filter on torque after cessation of steady shear for a dilute xan-than solution. From Mackay et al. (1992). 

Comparison of G(t) by different methods. Adapted from Meissner (1972). 

Hydrostatic head viscometers. (a) In the Ostwald design, liquid is filled exactly to mark C then sucked through the narrow capillary section to above mark A. The time for the meniscus to fall from. 4 to S is proportional to viscosity. (b) The side arm of the Ubbelehde design eliminates the need to fill with a precise volume, (c) The Cannon-Fenske design reverses the flow from (a) and is used for opaque fluids. The dark meniscus rises from A to B during the timing. (from Van Wazer et al., 1963). 

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Normally pressure-driven rheometers are used only to measure steady shear viscosi. However, several devices have been developed that oscillate the flow rate sinusoidally (Thurston, 1961 Brokate and Cast, 1992). Typically oscillations are large amplitude and the strain field is nonhomogeneous, so G and G" cannot be measured directly. However, such rheometers have been shown to be sensitive to structure in low viscosity liquids ( filastic, 1992). 

Pressure-driven rheometers, particularly capillary instruments, are the rheological work-horses of the plastics industry, as they are relatively simple and easy to use, even for melts at high temperatures. In most capillary rheometers, the flow is generated by a piston moving in a... 

A final source of uncertainty in the analysis of data from pressure-driven rheometers is the possibility of wall slip [132]. In fact, weU-entangled, linear polymers nearly always slip at a sufiSciently high wall shear stress. A large slip velocity often announces itself by the occurrence of an oscillatory shear regime in constant-piston-speed rheometers, or a sudden large jump in flow rate ( spurt ) in pressure-controlled instruments. However, the presence of slip velocities at pressures below those at which these phenomena occur may not be apparent from an inspection of data. 

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). 

The capillary viscometer. The most common and simplest device for measuring viscosity is the capillary viscometer. Its main component is a straight tube or capillary, and it was first used to measure the viscosity of water by Hagen [28] and Poiseuille [60], A capillary rheometer has a pressure driven flow for which the velocity gradient or strain rate and also the shear rate will be maximum at the wall and zero at the center of the flow, making it a non-homogeneous flow. 

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... 

Although the flow in a capillary rheometer is regarded as pressure-driven flow, namely, the shear is generated by the pressure difference along the capillary length, in rotational rheometers the shear is generated between a moving and a fixed surface [9]. 

The concepts of the cone-plate and biconical rheometers developed in the 1940s (Fig. 13). The cone-plate instrument is due to Freeman and Weissenherg [FIO] and intended for modest-viscosity fluids. It has the basis of his rheogo-niometer which also measured normal stresses. The biconical rheometer was developed in the same period by Piper and Scott [P12] of the BRMRA and was from the beginning intended for rubber. Similar instruments are discussed by Turner and Moore [T12] and Montes et al. [M37, M38]. In the latter instruments, the pressure is controlled by charging the rubber into the rheometer by an attached pressure-driven device. 

High density polyethylene CH3CF2CI 200 NR NR Pressure-driven slit die rheometer... 

The flow in Fig. 3 is called a drag flow, the top plate is dragging the material across the stationary plate to create the velocity profile that is shearing the fluid. In contrast, flow in a capillary rheometer is pressure-driven flow. All of the wall area inside the capillary is stationary so that the material has zero velocity at the walls and a maximum velocity along the centerline. Calculating the shear rate in a capillary is not as straightforward as with steady simple shear. Each fluid element still sees steady simple shear, but the shear rate is no longer constant it varies across the radius of the die. It runs... 

A capillary rheometer is a pressure-driven flow, the theme of this chapter, in contrast to the drag flows of Chapter 5. As Hagen first observed, when pressure drives a fluid through a channel, velocity is maximum at the center. The velocity gradient or shear rate and also the shear strain will be maximum at the wall and zero in the center of the flow. Thus all pressure-driven flows are nonhomogeneous. This means that they are only used to measure steady shear functions the viscosity and normal stress coefficients t] y), and Equations 5.1.1-5.1.3 define these functions, and Figure II.3 indicated how they are related to the other material functions. 

The organization of this chapter parallels that of its predecessors in Part II, describing first the design of drag flow rheometers, then pressure-driven ones. Separate sections are devoted to analysis of data, particularly sinusoidal oscillations, and to special designs for process-line rheological measurements. The section on exten-sional rheometry is brief because most of the design issues were discussed in Chapter 7. 

This section first considers the general features of data analysis software and future trends in this area. Then we focus on analysis of transient strain or stress tests, particularly sinusoidal oscillations. We will apply this analysis to data from rotational rheometers, but some of the strategies are also applicable to pressure-driven shear rheometers and extensional rheometers described in the following sections. 

Capillary and slit-die rheometers are used to determine the dependency of viscosity on shear rate. Since most molten polymers exhibit non-Newtonian behavior, it is important to be able to characterize this behavior. Measurements are made using a piston-driven cylinder that drives the molten polymer through a die of precise dimensions. The pressure drop across the die is measured, as is the flow rate through the die. Temperature is precisely controlled throughout the measurement. This test yields precise viscosity measurements as a function of temperature and shear rate. However, measurements tend to have artifacts in them, which need to be corrected in order to obtain true viscosity using Bagley and Rabinowitsch corrections. Capillary rheometers are also used to determine the effects of slip, a phenomenon in which the velocity of the melt at the capillary wall is nonzero. Slip has important implications for highly filled materials. 

Figure 6.2.7 indicates the pressure profile in a typical piston-driven capillary rheometer for polymer melts. The total pressure is made up of a number of contributions ... 

Figure 8.4.3 shows a typical design of a capillary rheometer for polymer melts. The piston is controlled by a ball screw drive or in some cases by gas or hydraulic pressure. In some designs the ball screws are driven by a constant speed motor. In mote sophisticated... 

A Sieglaff-McKelvey capillary rheometer (Tinius-Olsen Testing Machine Company) was used for compression with the barrel plugged and for shear with an appropriate capillary. This rheometer is driven with nitrogen gas pressure applied to a piston, which exerts pressure on the material in the barrel. A barrel of 6.35 mm radius was chosen for this experiment. A predetermined amount of sample was charged and preheated in the barrel for 5 minutes before pressure was applied. Measurements were made at 100 °C and 150 C. 

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