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 ω-1/2 to their limiting values. The viscoelastic behavior can be described in terms of one relaxation strength G1 and a series of relaxation times with τp=τ1 p-2. The complex shear viscosity scales with the dimensionless relaxation strength a2G1/D0ηs, the dimensionless relaxation time D0τ1/a2, and the dimensionless angular frequency a2ω/D0. The dimensionless groups a2G1/D0ηs and D0τ1/a2 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, η∞’, corroborate values calculated by Beenakker [Physica 128A, 48 (1984)].