Linear viscoelastic behavior of dense hard-sphere dispersions

Abstract

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 ${\ensuremath{\omega}}^{\mathrm{\ensuremath{-}}1/2}$ 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 ${\ensuremath{\tau}}_{p}$=${\ensuremath{\tau}}_{1}$ ${p}^{\mathrm{\ensuremath{-}}2}$. The complex shear viscosity scales with the dimensionless relaxation strength ${a}^{2}$${G}_{1}$/${D}_{0}$${\ensuremath{\eta}}_{s}$, the dimensionless relaxation time ${D}_{0}$${\ensuremath{\tau}}_{1}$/${a}^{2}$, and the dimensionless angular frequency ${a}^{2}$\ensuremath{\omega}/${D}_{0}$. The dimensionless groups ${a}^{2}$${G}_{1}$/${D}_{0}$${\ensuremath{\eta}}_{s}$ and ${D}_{0}$${\ensuremath{\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, ${\ensuremath{\eta}}_{\ensuremath{\infty}}^{\mathcal{'}}$, corroborate values calculated by Beenakker [Physica 128A, 48 (1984)].