Unified formulation of particle-size-dependent viscosity for Newtonian dispersions of micro- and nanoparticles

Many different formulations of the viscosity of particle dispersion can be found, even for Newtonian fluids, because of the wide variance in the components of the particle dispersion. In this work, toward the unified formulation, the effects of particle size and concentration were extensively studied. The reported viscosity data of particle dispersions were collected from the literature (10 nm-116 μm, ∼ 20 vol%) as well as the experimental acquisition of the viscosity data of SiO2 dispersion to fulfill the insufficient data range (from tens to hundreds of nanometers). The analysis reveals that the viscosity of the Newtonian dispersion with wide particle concentration and particle sizes cannot be well predicted by conventional equations, particularly for nanoparticles (<100 nm) at high concentrations (>10 vol%). The improved equation including particle size dependency enables the prediction of the viscosity of particle dispersions for a broader range of particle sizes and concentrations with higher accuracy. The formulation provides a holistic understanding of the previous different types of particle dispersions, which leads to a better prediction of their viscosity.