New Models for the Viscosity of Nanofluids

The modeling of viscosity of nanofluids is an unresolved problem. In this article, new viscosity models are developed taking into consideration solvation and aggregation of nanoparticles. At low concentrations of nanoparticles, the nanoparticles are assumed to exist as isolated "solvated" particles. At high concentrations, aggregation of solvated nanoparticles is allowed. The effective volume fraction of dispersed-phase is much larger than the volume fraction of un-solvated nanoparticles due to immobilization of matrix (base) fluid at the surface of the nanoparticles and within the aggregates. The amount of matrix fluid immobilized within the aggregates is dependent on the type of packing of solvated nanoparticles within the aggregates. A model is proposed to relate the effective volume fraction of dispersed-phase to the actual volume fraction. The viscosity models are developed using the effective medium approach taking into account the relationship between effective volume fraction and actual volume fraction of nanoparticles. Six sets of experimental data on the viscosity of nanofluids are used to validate the proposed models. The experimental viscosity data could be described very well with the proposed models.