Viscosity of colloidal suspensions

Simple expressions are given for the Newtonian viscosity eta(N)(phi) as well as the viscoelastic behavior of the viscosity eta(phi,omega) of neutral monodisperse hard-sphere colloidal suspensions as a function of volume fraction phi and frequency omega over the entire fluid range, i.e., for volume fractions 0 < phi < 0.55. These expressions are based on an approximate theory that considers the viscosity as composed as the sum of two relevant physical processes: eta(phi,omega) = eta(infinity)(phi) + eta(cd)(phi,omega), where eta(infinity)(phi) = eta(0) chi(phi) is the infinite frequency (or very short time) viscosity, with eta 0 the solvent viscosity, chi(phi) the equilibrium hard-sphere radial distribution function at contact, and eta(cd)(phi,omega) the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the Peclet time scale tau(P), the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity eta(N)(phi) = eta(phi, omega = 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 omega is of the form eta(infinity)(phi) + eta(0)A(phi)(omega tau(P))(-1/2), in agreement with these experiments, but the theoretical coefficient A(phi) differs by a constant factor 2/(chi)(phi) from the exact coefficient, computed from the Green-Kubo formula for eta(phi,omega). 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.