How Dr. Malcom M. Cross may have tackled the development of " An apparent viscosity function for shear thickening fluids"

A new apparent viscosity function for shear thickening fluids has been recently published [1], which is able to cover the three characteristic regions typically exhibited by these materials (thinning/thickening/thinning). The proposed function was shown to provide an excellent fitting to several independent data sets used. However, although its formulation has the Cross model as a starting point, the K_i-parameter time constants were enforced to be negative, which is counter-intuitive. In the light of the original work of Cross [2], the present short communication introduces small changes to the viscosity function developed in [1] to make the fitting parameters more natural. The original microstructural ideas of Cross are also considered in order to provide additional intuition and interpretation. Finally, the fitting values of the model parameters for all of the curves considered in the original manuscript are included here so that results can be reproduced or used for numerical simulations.