Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer

Abstract

We propose simple formulas for calibration of rheological parameters of Bingham fluid using a co-axial cylinder rheometer, in which the inner cylinder rotates at a constant speed, and the outer cylinder is stationary. A critical rotational speed exists due to existence of yield stress. If rotation speed exceeds the critical value, all fluid is fully sheared between the concentric cylinders. Plug flow exists only when rotation speed is less than the critical value. The effects of radius ratio and Bingham number are discussed. The rheometer with radius ratio very close to unity is discussed as a limiting case, and the result confirms previous research. Formulas for calibration are derived using Least Squares and perturbation methods for all values of radius ratio, based on measured rotation speed and torque. Two sets of experimental data are used for verification. The validation shows that the formulas derived here yield reasonable and accurate estimates of rheological parameters.