A simple method of correcting the parallel plate rim shear stress for non-Newtonian behavior

In the rheological characterization of non-Newtonian fluids in a steady torsional shear flow using a parallel-plate geometry, there is a need to correct the shear stress at the rim for non-Newtonian behavior. Solving the governing torsional flow equation inversely by Tikhonov regularization using experimental torque vs. rim shear rate data is the most scientific method for obtaining the model independent shear stress. In this short communication, a simple empirical method based on using the derivative of the polynomial fit to torque vs. rim shear rate to correct for the shear stress is presented. This method can be applied to any fluid behavior. The accuracy of this method was confirmed by the outstanding agreement of between the shear stress results of the two methods of polynomial and the inverse problem for magnetorheological fluids. The performance of other correction methods was also discussed.