Approximation for determining the effective nanolayer thickness in nanofluids of spherical nanoparticles through permittivity

• Nanolayer permittivity is higher than that of nanoparticles and base fluid. • The model relates nanolayer thickness with nanofluid permittivity. • It is shown how to calculate thickness and other nanolayer properties. • Generalized Maxwell Garnett’s equation for spherical geometry coincides with that from the Steeman-Maurer’s model. In this study, a novel approach is introduced to determine nanolayer thickness knowing nanofluid permittivity. The nanoparticles are assumed to be spherical, and the generalized Maxwell Garnett model for spherical inclusions with a single layer is applied under the hypothesis that nanolayer permittivity is significantly higher than that of both the nanoparticles and the base fluid. It is shown that the equation derived from the generalized Maxwell Garnett model coincides with that from the Steeman-Maurer model, despite the fact that the two models are based on different premises. The proposed approximation is tested on two nanofluids with the same base fluid but different nanoparticle sizes. The hypothesis is deemed highly plausible, supported by the findings of both Leong et al.’s model (when translated into permittivity) and the generalized Maxwell Garnett model for the nanofluids studied. Results show that nanolayer thickness decreases as nanoparticle concentration increases and increases with rising temperature. Additionally, the ratio of nanolayer thickness to nanoparticle radius is larger for the nanofluid containing smaller nanoparticles. Building upon this, the nanolayer density is calculated following the Iglesias et al.’s model. It is observed that this increases with increasing temperature and decreases with increasing nanoparticle concentration. Furthermore, the nanolayer density is smaller or greater than that of the base fluid depending on whether the molar volume of mixing is positive or negative. These findings lead to the hypothesis that a positive increment of nanofluid density (or a negative molar volume of mixing) could provide insights into the stability of nanofluids prepared without surfactants.