On Modelling the Viscosity of Fullerene-Containing Nanofluids

Abstract

The results of modeling the viscosity of fullerene-containing nanofluids (NFs) in a wide temperature range are presented. Two different models for predicting the viscosity of NFs are proposed. The first one is based on the thermodynamic similarity of the studied NFs with their base fluids. It was established that solutions of fullerene ${\mathrm C}_{60}$ in o-xylene as well as solutions of fullerene ${\mathrm C}_{60}$ in tetralin (1,2,3,4 - tetrahydronaphthalene) are thermodynamically similar with o-xylene and tetralin, respectively. To calculate the viscosity of fullerene-containing NFs, the equations based on the activation theory of viscous flow were used. An analysis of the temperature dependence of the activation energy of the base fluids and corresponding NFs was performed. It was found that the temperature dependences of the activation energy of the base fluids and corresponding NFs are practically equidistant lines. That makes possible to predict the viscosity of the NFs using the obtained temperature dependences of the activation energy of the base fluids and limited information on the NF’s viscosity (one experimental value for a certain concentration). The second model for predicting the viscosity of the NFs is based on the information on a free volume that can be obtained from data on the density of the NFs. In this model, it is proposed to use as the free volume of the studied solutions the inverse quantities to their critical amplitudes calculated by the author’s model of the extended scaling.