Viscosity Of Colloidal Suspensions Research Articles

Viscosity of concentrated colloidal suspensions: comparison of bidisperse models

In this paper, recent advances in the study of rheological behavior of concentrated bimodal suspensions are briefly reviewed. The predictive models are divided into two categories, namely, the effective volume fraction (or hard sphere scaling) approach and the separation of contributions approach. Predictions of both approaches are compared with experimental data of electrostatically and sterically stabilized suspensions. It is shown that the predictions of both hard sphere scaling and the scaling method of Zaman and Moudgil (J. Colloid Interface Sci. 212 (1999) 167) to separate the contributions of fine and coarse particles are in good agreement with the experimentally observed results. The approach by Dames, Morrison, Wilenbacher (Rheol. Acta 40 (2001) 434) to separate the hard-sphere and non-hard-sphere contributions is investigated using the aqueous silica and polystyrene suspensions respectively. A good agreement is shown for aqueous silica suspensions. However, significant differences between the predictions and experimental data are found for the sterically stabilized polystyrene suspensions, suggesting a more generalized expression is needed. As an attempt to classify the models on the viscosity of colloidal suspensions, the present study will provide guidelines for interpretation of experimental results and for the development of more comprehensive predictive methodologies for polydispersed colloidal dispersions.

Viscosity of colloidal suspensions

Simple expressions are given for the Newtonian viscosity ${\mathrm{\ensuremath{\eta}}}_{\mathrm{N}}$(\ensuremath{\varphi}) as well as the viscoelastic behavior of the viscosity \ensuremath{\eta}(\ensuremath{\varphi},\ensuremath{\omega}) of neutral monodisperse hard-sphere colloidal suspensions as a function of volume fraction \ensuremath{\varphi} and frequency \ensuremath{\omega} over the entire fluid range, i.e., for volume fractions 00.55. These expressions are based on an approximate theory that considers the viscosity as composed as the sum of two relevant physical processes: \ensuremath{\eta}(\ensuremath{\varphi},\ensuremath{\omega})=${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\infty}}}$(\ensuremath{\varphi})+${\mathrm{\ensuremath{\eta}}}_{\mathrm{cd}}$(\ensuremath{\varphi},\ensuremath{\omega}), where ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\infty}}}$(\ensuremath{\varphi})=${\mathrm{\ensuremath{\eta}}}_{0}$\ensuremath{\chi}(\ensuremath{\varphi}) is the infinite frequency (or very short time) viscosity, with ${\mathrm{\ensuremath{\eta}}}_{0}$ the solvent viscosity, \ensuremath{\chi}(\ensuremath{\varphi}) the equilibrium hard-sphere radial distribution function at contact, and ${\mathrm{\ensuremath{\eta}}}_{\mathrm{cd}}$(\ensuremath{\varphi},\ensuremath{\omega}) the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the P\'eclet time scale ${\mathrm{\ensuremath{\tau}}}_{\mathrm{P}}$, the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity ${\mathrm{\ensuremath{\eta}}}_{\mathrm{N}}$(\ensuremath{\varphi})=\ensuremath{\eta}(\ensuremath{\varphi},\ensuremath{\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 \ensuremath{\omega} is of the form ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\infty}}}$(\ensuremath{\varphi})+${\mathrm{\ensuremath{\eta}}}_{0}$A(\ensuremath{\varphi})(\ensuremath{\omega}${\mathrm{\ensuremath{\tau}}}_{\mathrm{P}}$${)}^{\mathrm{\ensuremath{-}}1\mathrm{/}2}$, in agreement with these experiments, but the theoretical coefficient A(\ensuremath{\varphi}) differs by a constant factor 2/\ensuremath{\chi}(\ensuremath{\varphi}) from the exact coefficient, computed from the Green-Kubo formula for \ensuremath{\eta}(\ensuremath{\varphi},\ensuremath{\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.