Nanoparticle colloidal system rheology has long been researched, without many concrete conclusions. Literature has been devoted to the viscosity and shear properties of these systems since Einstein’s PhD thesis. However, most models are based on molecular dynamics which are not necessarily applicable to real systems, and most real systems are modeled by empiricism. This report looks to unify these approaches through rheological testing and mathematical analysis in order to achieve several goals using a system composed of hafnium oxide particles suspended in water. The first goal is to have a viscosity model that fits not only empirical data, but also the relevant theory and first principles. By employing the modern techniques of a rhoemeter-on-a-chip to nano-scale particles, the limitations of traditional rheometry are bypassed. The molecular dynamics approaches are converted to zero-shear and infinite-shear viscosities which can be applied to traditional models. A modern model was then derived, applied to new data, and agreement was found to a satisfactory degree. No significant change in viscosity with shear rate was found experimentally or analytically. Traditional research is done with spherical particles, such as polystyrene nanopsheres, as which we are approximating hafnium oxide (HfOx) to be. Polystyrene nanospheres are nominally spherical and commercially available at relatively inexpensive costs. Actual spherical data was required for appropriate comparison, and the findings show that the spherical particles have distinct properties.

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