Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions

Measurements of the low-shear viscosity ${\eta }_o$ with a Zimm-Crothers viscometer for dispersions of colloidal hard spheres are reported as a function of volume fraction φ up to 0.56. Nonequilibrium theories based on solutions to the two-particle Smoluchoski equation or ideal mode coupling approximations do not capture the divergence. However, the nonhydrodynamic contribution to the relative viscosity $\Delta {\eta }_o$ is correlated over a wide range of volume fractions by the Doolittle and Adam-Gibbs equations, indicating an exponential divergence at ${\phi }_m=0.625\mathrm{}\pm \mathrm{0.015.}$ The data extend the previously proposed master curve, providing a test for improved theories for the many-body thermodynamic and hydrodynamic interactions that determine the viscosity of hard-sphere dispersions.