Question 9.2: Cone-and-Plate Rheometer A viscous liquid is tested using a......
Cone-and-Plate Rheometer
A viscous liquid is tested using a cone-and-plate rheometer that has a radius of 60 mm and cone angle of 2.5° for which the following data are obtained:
Evaluate the type and properties of the non-Newtonian fluid being tested.
A cone-and-plate rheometer is an instrument used to measure the rheological properties of fluids (Figure 9.3). It consists of a fixed flat surface with another cone-shaped surface rotating above with a sample of the fluid sandwiched between them. The cone just touches the flat surface. The rotational speed and tapered gap define the shear rate. The torque on the rotating cone that resists the motion defines the characteristic shear stress. The surface can be heated or cooled to determine the rheological properties as a function of temperature.
For a cone-and-plate viscometer, the shear rate is given by
\gamma=2\pi N c o tφ (9.6)
and the shear stress is given by
\mathbf{{\tau}}={\frac{3 T}{2\pi R^{3}}} (9.7)
From the data, the shear stress and shear rate are calculated to be as follows:
The liquid appears to exhibit pseudoplastic characteristics (Figure 9.4) in which the general power law model for the liquid may be assumed:
\tau = k\dot{\gamma} ^n (9.8)
Linearizing:
\ln\tau=\ln k+n\ln\dot{\gamma} (9.9)
The linearized data are shown in Figure 9.5, which would appear to reasonbly confirm this model, for which n is found to be 0.55, and k is 2.10~(\mathrm{Nsm}^{-2})^{0.55}.
