Micropolar effects on the effective shear viscosity of nanofluids

Abstract

The modified size-dependent Einstein's and Brinkman's solutions are established for the effective shear viscosity of rigid particle suspensions taking into account the micropolar effects in the base fluid. Solutions are obtained based on the homogenization approach and allow us to take into account the influence of the particle size. Two non-classical parameters arise in the considered micropolar solutions: the length scale parameter and the coupling (micropolarity) number of the base fluid. The solutions developed are validated using tests performed with polydimethylsiloxane based TiO2 nanofluids as well as other published data on the size-dependent shear viscosity of different nanofluids. Good agreement between the predictions and the experimental data is established across a wide range of volume fractions and size of nanoparticles. The possibility for unique identification (at given temperature) of the micropolar parameters of the base fluids is shown. Temperature-dependent values of non-classical rotational and spin viscosities of polydimethylsiloxane, ethylene glycol, and water are evaluated.