Calculation of the Critical Shear Rate in a Cylinder Measuring System

This report is about flow instabilities due to the formation of vortices in a fast-rotating concentric cylinder. A formula for calculating the value of the critical shear rate is presented. The comparison with measured data confirms that the calculation predicts the onset of vortices correctly.

All standard models of rheology and the most common analysis of flow curves assume laminar flow of the fluid under investigation. Based on this assumption, the flow curve of a Newtonian fluid shows a constant viscosity plotted versus shear rate. Above a critical value of the angular velocity, a secondary flow, the so called ‘Taylor instability’, occurs in concentric cylinders. These instabilities (or vortices) result in increasing viscosity at higher angular velocity (corresponds to shear rate). This report aims to provide a calculation scheme for predicting the shear rate where Taylor instabilities occur, based on measuring system geometry, density and viscosity.


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