Interpretation of the complex viscosity of dense hard-sphere dispersions

Abstract

The complex viscosity of dense hard-sphere dispersions has been determined recently over a large frequency range. If conceived as a homogeneous system with continuously distributed elasticity and viscosity, the complex viscosity can be described theoretically with a constant relaxation strength and relaxation times ${\ensuremath{\tau}}_{p}$=${\ensuremath{\tau}}_{1}$/${p}^{2}$, with p the relaxation number. This is consistent with the empirical analysis of the data. The distributed elasticity can be interpreted microscopically as due to statistical springs acting between the spheres. The springs are modeled as Fraenkel springs to take into account the excluded-volume effect. The relaxation strength has been calculated quantitatively. The resulting deduced relaxation strengths are in fair agreement with the experimentally observed ones. The given interpretation is compared with literature theory.