Power Law Fitter
Polymer melts are generally shear thinning, meaning that the viscosity decreases with increasing shear rates. Many polymer exhibit a Newtonian plateau at low shear rates, a transition region, and then a power law region as well modeled by the Cross-WLF equation and shown in the following figure.
While the Cross-WLF model is preferred for numerical simulations, power-law models are desirable for quick "back of the envelope" calculations relating material behavior, processing conditions, and geometry. In a power law model, there are two parameters: 1) k, the viscosity at a reference shear rate (often 1/sec), and 2) n, the power law index that is the slope of the viscosity curve with respect to shear rate. As shown in the following figure, different power law models may be appropriate for different shear rate regimes.
This Excel spreadsheet, also accessible by clicking the table below, automatically and interactively calculates the power law coefficients through regression. It is not necessary to use the solver, and the coefficients and graphs are dynamically updated. Two different sets of power law model coefficients are provided as commonly used in the literature.
Two notes on usage. First, the low, medium, and high shear rate regimes have been arbitrarily defined as 1-194, 86-11222, and 4987-99900 reciprocal seconds. You can modify the shear rate regimes by editing column B or deleting/adding cells to the regions of H17:K46 as appropriate. Second, the WLF model coefficients are to be entered in SI units. We commonly use data from the Moldflow material database as shown in the following dialog box.