An empirical equation for shear viscosity of shear thickening fluids

Quantitative modelling of the rheology of non-Newtonian fluids requires significant empirical input due to very complex behaviour of the bulk fluid as a result of particle-scale physics of fluids. The existing rheology models are mainly limited to certain fluid dynamics conditions such as shear rate, shear stress, etc. Adopting Doolittle's free volume theory approach, we have proposed an empirical equation to describe the relative free volume-dependent viscosity, the shear stress-dependent viscosity, the shear rate-dependent viscosity, and the dimensionless Peclet number-dependent relative viscosity of shear thickening fluids. The proposed formulae predict all rheologically different behaving Newtonian, intermediate shear thinning, shear thickening and extreme shear thinning regimes of shear-thickening fluids. The proposed formulae have been validated against the experimental rheological data of various shear thickening fluids over a range of pH, volume fraction, electrolyte concentration, temperature, and magnetic field. The results suggest that the predicted threshold material parameters of shear thickening fluids help to quantitatively evaluate the effect of varying physico-chemical conditions on the rheology of shear thickening fluids. We simulated the flow of a shear thickening fluid, modelled using proposed shear rate-dependent equation, in a 2D staggered porous medium. We observed bimodal distribution of pore-scale shear rate, shear viscosity and velocity in a porous medium.