Viscoelastic rotating disc

Some rotational viscometers employ a rotating disc, bar, paddle or pin at a constant speed (or series of constant speeds). It is extremely difficult to obtain tme shear stress, and the shear rate usually varies from point to point in the rotating member. In particular, the velocity field of a rotating disc geometry can be considerably distorted in viscoelastic fluids. Nevertheless, because they are simple to operate and give results easily, and their cost is low, they are widely used in the food industry. While they may be useful for quality control purposes, especially Newtonian foods, the reliability of their values should be verified by comparison with data obtained with well defined geometries (capillary/tube, concentric cylinder, and cone-plate). 

To illustrate the plane stress situation let us consider the problem of a viscoelastic cyUnder rotating uniformly around its axis, with special application to flat geometries (discs) (Fig. 16.3). 

In the laboratory, it had been determined that, if you applied a force of 30 Newton-meters to a disc, it would cause failure of the disc in axial rotation. However, the segments were able to withstand these fast pulsations of torque because there were two complimentary mechanisms for transmitting the torque. The first was the facet joint the second, the annulus. In the facet joint, it is the angle of rotation which determined the torque transmission. The more rotation and the more engagement with the facet joint, the greater the torque transferred. However, for the disc, because of the viscoelastic nature of collagen, this is the opposite. So the disc handled the majority of torque in mid-stance when the facet joints were not engaged. 

There are many designs of rheometer for materials with different viscoelasticities. For example, liquids can be examined in the Couette geometry, which consists of vertical concentric cylinders, one of which rotates with the sample between the gap. Cone-and-plate and parallel disc cells are also widely used. For soft solids, oscillatory shearing between vertical parallel plates yields the dynamic shear moduli. 

Dynamic viscoelastic parameters such as the storage modulus and the loss modulus offer another measure of the mechanical properties of hydrogels. The storage and loss moduli represent the stored energy (elastic portion) and the heat dissipated (viscous portion) respectively of a viscoelastic solid. These are determined using a rheometer. The most commonly used set up for these measurements is the rotational rheometer wherein the sample is placed between two discs, the top disc rotates in an oscillatory manner in order to introduce a small strain oscillatory shear, while the torque exerted by the sample on the lower disc is measured. This allows a shear stress-strain relationship to be determined and thus for the moduli in turn to be found. Usually an amplitude sweep will be done to ensure that the sample is in the linear viscoelastic range [73, 75, 79, 80]. 

---