Rotary rheometer

The relaxation modulus G(t) is the value of the transient stress per unit strain in a step-strain experiment. This type of experiment may be achieved with modem rotary rheometers with a limited resolution in time (roughly 10 2 s). If one wishes to evaluate G(t) at shorter times, it is necessary to derive G(t) from the high frequency G (co) data by an inverse Carson-Laplace transform. 

We will discuss in this section the variations of the viscoelastic parameters derived from linear viscoelastic measurements all these parameters may be derived from any t3rpe of measurement (relaxation or creep experiment, mechanical spectroscopy) performed in the relevant time or frequency domain. The discussion will be focused however on the complex shear modulus which is the basic function derived from isothermal frequency sweep measurements performed with modem rotary rheometers. 

The first cylindrical rotary rheometer was invented in 1890 by Couette. Rotational rheometers consist of two concentric cylinders, as shown in Figure 7.10. 

Section 8.2 described how different rotary rheometers are designed to control and to measure rotation rate, angular position, torque, temperature, and other variables. Equally important is the analysis of these measurements, conversion of the raw millivolts to material functions. Twenty years ago this was all done by hand, but today commercial rheometers spit out materials functions like G and G" in real time. Data analysis software is becoming a more and more important part of rheometer design. We have already seen that the inertia correction algorithms illustrated in Figure 8.2.11 can significantly extend the performance of controlled stress rheometers. 

Measurements of rheological properties at low shear rates are usually carried out in rotary rheometers such as the cone-and-plate (C-P) or plate-plate (P-P) systems shown in Figures 3.18 and 3.19, respectively. In rotary rheometers one of... 

In this section three topics are discussed (1) the molecular weight dependence of the rheological properties (2) the interrelation between steady shear and dynamic oscillatory shear measurements and (3) the effect of branching. The importance of the second topic rests on the fact that dynamic oscillatory properties are easier to measure and can be obtained at higher equivalent shear rates than are possible for the steady shear flow properties obtained by means of rotary rheometers. 

At the time of writing this article, there are only two instruments in the market in the U.S.A. - the Rheometrics Extensional Rheometer, the RFX, and the Rheometrics Elongation Melt Rheometer, based on Meissner s rotary clamp method. The RFX is based on the opposing jet method. 

The semisolid consistency and the occurrence of slip effects during flow could limit the use of the rotary clamp method, the conveigent flow method or even Sridhar s extensional rheometer for a large number of food products such as mayonnaises and salad dressings. A novel rheometer (15) based on the concept of filament stretching has been developed by Plucinski et al (Fig. 10) to measure the extensional properties... 

FIG. 15.24 Schematic representation of the four roller extensional rheometer, designed by Meissner (1972) to attain high Hencky strains. Two sets of rotary clamps are individually driven by two motors at constant rotation rates. The force in the sample is measured by a transducer F mounted on a leaf spring. From Barnes, Hutton and Walters (Gen Ref 1993). Courtesy Elsevier Science Publishers. 

The operating principle of the YR-1 Rheometer is to drive a spindle through a calibrated spiral spring connected to a motor drive shaft (see Fig. 3). The vane spindle is immersed in the test materiaJ. The resistance of the material to movement is measured by observing increasing torque values as the YR-1 motor rotates. The amount of shaft rotation is measured by the deflection of the calibrated spiral spring inside the instrument. Spring deflection is measured with a rotary transducer. 

A special note should be made concerning the doctoral thesis by Lawrence Malcom in 1976 [36]. This is an excellent study of cartilage friction and deformation, in which a device resembling a rotary plate rheometer was used to investigate the effects of static and dynamic loading on the frictional behavior of bovine cartilage. The contact geometry consisted of a circular cylindrical annulus in contact with a concave hemispherical section. It was found that dynamically loaded specimens in bovine synovial fluid yielded the... 

The oscillatory deep-channel rheometer described by Nagarajan and Wasan (227) can be used to examine the rheological behavior of liquid/liquid interfaces. The method is based on monitoring the motion of tracer particles at an interface contained in a channel formed by two concentric rings, which is subjected to a well-defined flow field. The middle liquid/liquid interface and upper gas/liquid interface are both plane horizon tal layers sandwiched between the adjacent bulk phase. The walls are stationary while the base moves. In the instrument described for dynamic studies of viscoelastic interfaces the base oscillates sinusoidally. This move ment induces shear stresses in the bottom liquid that are transmitted to the interface. The interfaces are viewed from above through a microscope attached to a rotary micrometer stage which is coaxial to the cylinders. 

Since the invention of the rotary damp rheometer (Figure 1(a)) by Meissner [1], the elongational viscosity of linear and branched polyethylene (PE) melts has l n studied extensively. For polypropylene (PP), only a few studies have been published. The measurement of elongational viscosity at constant strain rate or constant tensile stress is of great importance for characterizing the structure of the pol5uner melt. 

Figure 1 (a) Rotary damp rheometer, (b) Rheotens test. For details see Meissner [1]. (Reprinted from Rheol. Acta (1971), by permission of Steinkopff Verlag.)... 

Rheology measurements were carried out by means of a Bohlin Gemini 150 rheometer equipped with a high-frequency extension with a piezo rotary vibrator [9]. A plate-plate geometry of aluminium was used with a diameter of 40 mm. This set-up then allows for measurements up to 2000 Hz. 

FIGURE 4. Meissner s extensional rheometer and rotary clamps. (From Reference 31.)... 

The development of the rotary clamp extensional rheometer has been described by Meissner(32) and further progress has been reviewed more recently. ( 3-35) The polymer sample is immersed in oil and the stretching force is determined by mounting one set of gears on a vertical leaf spring the deflection of the spring is noted by a displacement transducer which is calibrated to yield the force. The stretch rate is related in a simple way to the velocities, Vj and V2 in opposite directions, of the two sets of clamps ... 

The rotary clamp consisting of a pair of gears is a basic construction element for the design of various types of extensional rheometer described earlier. The fact that the design is amenable for use in vmiaxial and biaxial extensional rheometry has been shown by Meissner et al. [92]. Other biaxial extensiometers have also been described [93,94] by other researchers. 

Figure 10.21 Sketch showing the principle of operation of the extensional rheometer of Meissner and Hastettler [193], In this elaboration of the rotary clamp concept, a rectangular sample is "clamped" at its ends by sets of ribbed metal belts. The sample is supported by a gas cushion. The commercial version of this apparatus was called the Rheometrics-Melt Extensiometer (RME). A video recording is analyzed to determine the true strain rate. Drawing courtesy of Jen Tiang.

To generate equibiaxial extension, sheet inflation, lubricated squeeze flow, and the rotary clamp technique have all been used [9, p. 261]. The most rehable of these is the one based on the rotary clamp technique, and the latest version of this instrument has been described by Hachman and Meissner [160]. This impressive instrument is presently the only rheometer capable of generating homogeneous biaxial extension, but it is somewhat complex and difficult to use. Lubricated squeeze flow is much simpler, but there are important limitations on its capabilities due the difficulty of maintaining lubrication [220].Isakief a/. [161] used lubricated squeeze flow to carry out stress relaxation experiments for determination of the damping... 

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