Determination of shear rate and viscosity from batch mixer data

Abstract

A general analysis allowing the determination of shear rate and viscosity from batch mixer rotor speed and torque data is presented. The batch mixer was represented by two effective adjacent sets of concentric cylinders exerting the same torque as that obtained from the batch mixer. The effective internal radius was determined through a general procedure for calibration using non-Newtonian fluid. The effective equivalent internal radius, Ri, was determined for different polymers and processing conditions. The results revealed that Ri is a universal quantity practically insensitive to the nature and to the rheological behavior of the fluid under mixing. In the case of small gaps, it was found that there is a special position in the gap where the effective internal radius, the shear rate and viscosity are independent of rheological characteristics of the fluid under mixing. This validates the Newtonian approximation previously used by Goodrich and Porter to extract the shear rate-viscosity dependence from batch mixer data. The technique was tested on seven different amorphous and semicrystalline polymers and the results were found to be in reasonable agreement with the data obtained independently with cone-and-plate and capillary rheometers. Contributions of both shear stress between the two cylinders and the stress generated at the wall were evaluated. The latter was found predominant.