Question 9.3: Couette Rheometer Rheological test data for a polymer fluid......
Couette Rheometer
Rheological test data for a polymer fluid using a Couette rheometer involves gradually increasing the shear rate to 200 s^{–1} (1) and measuring the shear stress, followed by gradually decreasing the shear rate and measuring the new stress (2). Identify the type and properties of the non-Newtonian fluid.
\begin{matrix} \text{Shear rate, } \dot{γ} (s^{-1}) & 5 & 18 & 45 & 72 & 99 & 113 & 139 & 180 & 200\\ \text{Shear stress}, τ_1 (Nm^{–2}) & 116 & 225 & 440 & 598 & 747 & 817 & 948 & 1114 & 1181 \\ \text{Shear stress}, τ_2 (Nm^{–2}) & 74 & 203 & 392 & 474 & 684 & 750 & 874 &1065 & 1172 \end{matrix}
A Couette rheometer is an instrument used to measure the rheological properties of fluids and consists of a cup that fits into a cylindrical bob (Figure 9.6). A sample of the fluid being tested is sandwiched between the bob and the cup. It is operated with either the cup being held and the bob rotated or, more rarely, the bob being held and the cup rotated. The rotational speed and distance between the cup and bob define the shear rate. The torque to resist the motion defines the characteristic shear stress. By heating or cooling the cup, the rheological properties of the fluid can be determined as a function of the temperature.
The apparent viscosity of the fluid is the ratio of the measured shear stress to shear rate:
{\mu}_{a p p}={\frac{\tau}{\dot\gamma}} (9.10)
The complete range of data is therefore
The data are shown in Figure 9.7
\begin{matrix} \text{Shear rate, } \dot{γ} (s^{-1}) & 5 & 18 & 45 & 72 & 99 & 113 & 139 & 180 & 200\\ \text{Viscosity } \mu_{app1} (Nsm^{–2}) & 23.2 & 14.2 & 8.8 & 8.3 & 7.5 & 7.2 & 6.8 & 6.2 & 5.9 \\ \text{Viscosity } \mu_{app2} (Nsm^{–2}) & 14.8 & 11.3 & 8.0 & 7.6 & 6.9 & 6.6 & 6.3 &5.9 & 5.9 \end{matrix}
