R. Verberg et al., VISCOSITY OF COLLOIDAL SUSPENSIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(3), 1997, pp. 3143-3158
Simple expressions are given for the Newtonian viscosity eta(N)(phi) a
s 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 bas
ed on an approximate theory that considers the viscosity as composed a
s the sum of two relevant physical processes: eta(phi,omega) = eta(inf
inity)(phi) + eta(cd)(phi,omega), where eta(infinity)(phi) = eta(0) ch
i(phi) is the infinite frequency (or very short time) viscosity, with
eta 0 the solvent viscosity, chi(phi) the equilibrium hard-sphere radi
al distribution function at contact, and eta(cd)(phi,omega) the contri
bution due to the diffusion of the colloidal particles out of cages fo
rmed 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 beh
avior 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 the
oretical coefficient A(phi) differs by a constant factor 2/(chi)(phi)
from the exact coefficient, computed from the Green-Kubo formula for e
ta(phi,omega). This still enables us to predict for practical purposes
the viscoelastic behavior of monodisperse spherical colloidal suspens
ions for all volume fractions by a simple time rescaling.