Continuous phenomenological modeling for the viscosity of shear thickening fluids

In general, shear thickening fluids show a marked increase in viscosity beyond a critical shear rate, which can be attributed to the hydrodynamic clustering effects, where in any external energy acting on a shear thickening fluid is dissipated quickly. However, there is a lack of theoretical modeling to predict the viscosity curve of shear thickening fluids, which changes continuously with the increasing shear rate. In this article, a phenomenological continuous viscosity modeling for a class of shear thickening fluids is proposed. The modeling predicts shear thickening and thinning behaviors that are naturally exhibited by shear thickening fluids for high and high enough values of the shear rate. The result shows that the phenomenological modeling provides a very good fit for several independent experimental data sets. Therefore, the proposed modeling can be used in numerical simulations and theoretical analysis across different engineering fields.