Question 9.1: Parallel-Disc Rheometer A parallel-disc rheometer is used to......

A parallel-disc rheometer is an instrument used to obtain the rheological properties of non-Newtonian fluids. It consists of a fixed flat surface with another rotating surface held at a fixed elevation above with a sample of the fluid sandwiched between them (Figure 9.2). The rotational speed and distance define the shear rate while the torque to resist the motion defines the shear stress. The surface can be heated or cooled to determine the rheological properties as a function of the temperature.

The shear stress is related to the rotational speed as

\tau=\mu{\frac{2\pi N r}{t}}              (9.1)

where t is the clearance between the disc and plate. For the non-Newonian fluid being tested, the viscosity is therefore found to be

{\mu}={\frac{\tau t}{2\pi N r}}=\displaystyle{\frac{200\times0.001}{2\times\pi\times{\frac{600}{60}}\times0.025}}=0.127\;\mathrm{Nsm}^{-2}          (9.2)

The torque on the shaft is

T={\frac{\mu\omega\pi}{2t}}R^{4} ={\frac{0.127\times\left(2\times\pi\times{\frac{600}{60}}\right)\times\pi}{2\times0.001}}\times0.025^{4}=0.0049\mathrm{~Nm}          (9.3)

It is usual to determine the viscosity of a fluid across a range of shear rates and to measure the shear stress. This is carried out by repeating the measurements at different rotational speeds. The apparent viscosity is then determined as the ratio of the shear stress to shear rate, which can then be used to determine the rheological properties of the fluid across a wide range of shear rates. By controlling the temperature of the plate, the rheological properties can also be linked to the influence of the temperature.