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Because of the poor prediction for the larger nanoparticle concentration, a fluid specific correlation is required for the nanolubricant viscosity.4 The resulting correlation of the liquid kinematic viscosity of the base lubricant and the CuO nanolubricants to the liquid density at atmospheric pressure was: where the kinematic viscosity has units of mm2·s-1 while the density (ρ) has units of kg·m-3. The density should be calculated from Eq. (3) and used as input for Eq. (5). Figure 4 shows that the single fit with respect to liquid density, i.e., Eq. (5), results in a slight increase in overpredicted residuals resulting in an approximate range of + 15 % and – 25 %. Equation (5) shows that the kinematic viscosity increases with respect to increasing density, i.e., increasing nanoparticle mass fraction. 6. CONCLUSIONS Liquid kinematic viscosity and liquid density measurements of a synthetic polyolester based copper (II) oxide (CuO) nanoparticle dispersion (nanolubricant) have been presented at atmospheric pressure and for a temperature range from approximately 288 K to 318 K. The CuO particles were approximately 30 nm-diameter, spherical, and well dispersed in the commercially available polyolester chiller lubricant. Viscosity and density measurements were made for the pure base lubricant along with three nanolubricants with differing CuO nanoparticle mass fractions (2.9 %, 5.6 % and 39.2 %). The Stokes-Einstein equation failed to predict the viscosity of the nanolubricant with the largest nanoparticle concentration. For this reason, the liquid kinematic viscosity was correlated with respect to liquid density and temperature. The viscosity of the nanolubricant increased with respect to its density and decreased with respect to its temperature. A linear relationship was developed for liquid specific volume with respect to temperature. The liquid density decreased with respect to temperature and increases with respect to the CuO mass fraction for the temperature range of the study. ACKNOWLEDGEMENTS This work was funded by NIST. Thanks go to the following NIST personnel for their constructive criticism of the first draft of the manuscript: Dr. D. Veronica, and Dr. P. Domanski. The author extends his appreciation to Mr. A. Heckert of the NIST Statistical Engineering Division for his consultations on the uncertainty analysis. In addition, consultations on property measurements and correlations with Dr. A. Laesecke of NIST have had a significant influence on 4 Prasher et al. (2006) also found that the Einstein equation did not adequately predict the viscosity of propylene glycol and ethylene glycol based nanofluids. 3.8 2 -1 -5 ⎛ ρ ⎞ ⎛17.2⎞ v[mm is ]=2.02×10 ⎜ 3 ⎟ exp⎜ ⎟ (5) 1000[kgim ] T Paper No. IIR-177 ⎝⎠⎝r⎠ Figure 4 Residuals between measured nanolubricant kinematic viscosity and single fit with respect to liquid densityPDF Image | VISCOSITY AND DENSITY OF CUO NANOLUBRICANT
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