A new mathematical model to predict cavern diameters in highly shear thinning, power law liquids using axial flow impellers

Abstract

An axial force model is described for predicting cavern diameters in highly shear thinning liquids using axial flow impellers. The model has been verified experimentally by measuring cavern sizes in viscous and shear thinning Carbopol solutions with SCABA 3SHP1 impellers. The proposed force model considers the total momentum imparted by the impeller as the sum of both tangential and axial components and assumes a torus-shaped cavern. It combines torque and axial force measurements with the simple power-law equation to predict the cavern diameter with the cavern boundary defined by a limiting velocity. The proposed new model is capable of predicting the measured cavern diameters for Re > 20 and is valid for sizes greater than the impeller diameter but less than the vessel diameter. This approach is also shown to be superior to the traditional Elson and Nienow yield stress model in extremely shear thinning fluids whose flow curve can be well-fitted by the power-law equation. In principle, the model can also be applied to caverns generated by radial flow impellers.