Abstract
Simple expressions are given for the Newtonian viscosity (φ) as well as the viscoelastic behavior of the viscosity η(φ,ω) of neutral monodisperse hard-sphere colloidal suspensions as a function of volume fraction φ and frequency ω over the entire fluid range, i.e., for volume fractions 0<φ<0.55. These expressions are based on an approximate theory that considers the viscosity as composed as the sum of two relevant physical processes: η(φ,ω)=(φ)+(φ,ω), where (φ)=χ(φ) is the infinite frequency (or very short time) viscosity, with the solvent viscosity, χ(φ) the equilibrium hard-sphere radial distribution function at contact, and (φ,ω) the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the Péclet time scale , the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity (φ)=η(φ,ω=0) agrees very well with the extensive experiments of van der Werff et al., [Phys. Rev. A 39, 795 (1989); J. Rheol. 33, 421 (1989)] and others. Also, the asymptotic behavior for large ω is of the form (φ)+A(φ)(ω, in agreement with these experiments, but the theoretical coefficient A(φ) differs by a constant factor 2/χ(φ) from the exact coefficient, computed from the Green-Kubo formula for η(φ,ω). This still enables us to predict for practical purposes the viscoelastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.
- Received 13 June 1996
DOI:https://doi.org/10.1103/PhysRevE.55.3143
©1997 American Physical Society