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The effective viscosity of nanoparticle dispersions has been investigated experimentally quite a lot and various behaviours have been observed. Many models have been proposed to predict the effective viscosity, but these are mainly empirical ones, correlations with a tuning parameter or based on fastidious molecular interactions simulations. In this work, we propose a new fully physics-based analytical expression for the effective viscosity implementing theories from extended thermodynamics, including nano-confinement effects, nanoparticle-fluid interactions, density effects, size effects and nanoparticle volume fraction. We validate this model against several different types of nanoparticle dispersions and emulsions and explain the different behaviours using the same model. It appears that the density ratio of the nanoparticles with respect to the fluid plays a crucial role affecting the viscosity. The nanoparticle-fluid interactions become increasingly important for smaller nanoparticle sizes. From these comparisons, we arrive at a general simplified expression for the effective viscosity of nanoparticle dispersions, where it is observed that there is a direct universal relation between the nanoparticles and fluid densities and the nanodispersion viscosities. The validity of such a relation has been explicitly demonstrated.

Universal relation between the density and the viscosity of dispersions of nanoparticles and stabilized emulsions