The generalized power-law: A new viscosity model

For non-Newtonian inelastic fluids, several models have been proposed to describe the relation between shear viscosity and shear rate. In this work, the simple power-law model is generalized in order to include both shear-thinning and shear-thickening behaviors simultaneously. The model is based on a shear rate dependent consistency index (m) and power-law exponent (n'). As a first approximation, the consistency index is approximated by a sigmoid function while the power-law index is assumed to follow a peak equation. The resulting model has a total of 9 parameters to adjust for the viscosity level, slope of changes and critical shear rates between zero and infinite shear rates values of the viscosity. For the purpose of comparison, the proposed model is fitted to experimental data taken from the literature. Very high level of prediction is obtained over a wide range of shear rates and different theological behaviors can be reproduced showing the usefulness of this generalized model.