Eccentric rotating disks

Gent (1960) first published an ERD experiment using vulcanized rubber. He reports that his inspiration came from Maxwell s rotating cantilever rod experiments. Mooney (1934) also tried the geometry on gum rubbers. Maxwell and Chartoff (1965) carried out the first tests on polymer melts. Maxwell s (1967) experiments caused the geometry to become known as the Maxwell orthogonal rheometer. 

If an elastic rubber sample is placed between ERD, a force in the xz direction will be necessary to maintain the offset a. Any 

Eccentric rotating disks, (a) Cross section of the experimental geometry, (b) Top view showing particle paths, (c) Relative displacements of particles in a coordinate system rotating with the lower disk. 

Exercise 1.10.7 derived this result from the neo-Hookean model. 

Comparison of ERD to other rheometers for a poly, dimethylsiloxane melt. Prom Macosko and Davis (1974), 

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Relaxation times were determined with a Rheometrlcs Mechanical Spectrometer Model RMS-7200 by the use of the eccentric-rotating-disk mode. 

Eccentric Rotating Disks (Macosko and Davis, 1974 Walters, 1975 see also Section 5.7)... 

Example 2.3.1 Flow Between Eccentric Rotating Disks... 

Consider again the flow between eccentric rotating disks pictured in Exercise 1.10.7. 

Figure 5.7.2a illustrates the eccentric rotating disk (ERD) geometry (recall Exercise 1.10.7 and Example 2.3.1). A sample is placed between two disks that rotate at the same angular velocity but about offset or eccentric axes. Surface tension holds the sample between the disks. The flow between these eccentric rotating disks results in a shearing motion, with material elements moving in circular paths with respect to each other. A coordinate system r, j, z that rotates with the lower disk (Figure 5.7.2b) can describe the relative motion between particles (Figure 5.7.2c). The deformation is seen to be of constant magnitude, but continually changing direction.

Note that in the literature this geometry js called the Maxwell orthogonal rheometer or eccentric rotating disks, ERD (Macosko and Davis, 1974 Bird, et al., 1987, also see Chapter 5). Usually, the coordinates X2 = > and X3 = z are used. 

Figure 6.6 Comparison of viscosities calculated from tensile measurements with dynamic shear viscosities for a sample of poly iso butylene. Shear viscosity, eccentric rotating disk...

The rotating disk is secured to the motor shaft with a collet, which ensures an eccentricity of less than 4%. The mercury contactor which allows the current to be measured, has a very low contact resistance due to its large wetted area ( cm2) and so provides a cleaner signal than usual solid-solid contactors. 

Eccentric rotating cylinders can give accurate and G data but only at rather small strains (Broadbent and Walters, 1971). At larger deformation, cavitation or extrusion of the sample from the gap can occur. This also seems to be the problem for such other eccentric geometries as the tilted rotating disks or cone and plate (Davis and Macosko, 1973 Walters, 1975). 

External cylindrical lapping is used to process external surfaces of cylindrical parts. Therefore, the workpieces are moxmted radially on a workpiece holder on a two-face machine, whereby the parts scroll with an eccentric motion between the lapping disks. This process is used to reach very high shape precision, required, for instance, for jet needles in injection pumps. Cylindrical lapping of drilled holes is realized with cylindrical bushes, which describe rotating and lifting movements. Because of this kinematic, high surface qualities are reached, which are unable to be accomplished by other processes (Paulmann 1991). 

Blancard et al. [3] proposed a new type of viscous micropump which uses rotational movement of disks instead of an eccentric rotor. In this concept, fluid is either on one disk or is sandwiched between two disks while the viscous stresses induces by the rotation of the disk(s) drives the flow. Maximum flow rates of 1.0 ml/min for the single-disk and 2.1 ml/min for the double-disk micropumps have been achieved. 

Figure 3.2 Schematic diagram showing the principal features of parallel eccentric disks rotational viscometer.

Frame with thumbscrews supports substrate Strain increases with each turn of the screw Quasi-static stretch applied Eccentric disks rotated axially by a motor Translates rotary motion into oscillatory linear motion Dynamic stretch applied... 

Figure 1.10.1 shows two parallel disks rotating at velocity 2. The disks are separated by a distance h and their axes of rotation are eccentric or displaced by an amount a. 

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