Linear viscoelastic behavior of dense hard-sphere dispersions

The complex shear viscosity of sterically stabilized colloidal dispersions of different-sized silica particles (radius a=28–76 nm) was measured with torsion resonators and a nickel-tube resonator between 80 Hz and 200 kHz. The volume fraction of the samples was varied from 0.10 to 0.60. In the intermediate-frequency region, the real and the imaginary parts of the complex shear viscosity decay as ${\omega }^{\mathrm{-}1/2}$ to their limiting values. The viscoelastic behavior can be described in terms of one relaxation strength $G_1$ and a series of relaxation times with ${\tau }_p$=${\tau }_1$ $p^{\mathrm{-}2}$. The complex shear viscosity scales with the dimensionless relaxation strength $a^2$ $G_1$/$D_0$ ${\eta }_s$, the dimensionless relaxation time $D_0$ ${\tau }_1$/$a^2$, and the dimensionless angular frequency $a^2$ω/$D_0$. The dimensionless groups $a^2$ $G_1$/$D_0$ ${\eta }_s$ and $D_0$ ${\tau }_1$/$a^2$ are a function of the volume fraction only. At higher volume fractions the high-frequency limiting values of the real part of the complex shear viscosity, ${\eta }_{\infty }^{\mathcal{’}}$, corroborate values calculated by Beenakker [Physica 128A, 48 (1984)].