The Dynamics of Flocculated Dispersions

The rheological behavior of Brownian electrorheological (ER) fluids is studied as a model for flocculated colloidal dispersions. The ER fluid has the advantages that the interparticle potential energy can be varied by simply changing the applied field strength, and the microstructure consists of essentially linear chains of particles aligned with the field direction. Studies of the quiescent suspension structure find a dispersed region, an equilibrium flocculated region, and a kinetically flocculated region for low, moderate, and large attractive potential well depths, Umin/kT, respectively. Under simple shear flow, the suspension has a high-shear-rate Newtonian viscosity and a shear thinning viscosity at lower shear rates. For moderate attractive potential well depths the suspension has a low-shear viscosity that scales as exp(Umin/kT). Furthermore, the low-shear limiting behavior is seen at shear rates that scale as exp(-Umin/kT). The first normal stress difference is also presented. It was found that due to the electric field the suspension structure is anisotropic with respect to the compressional axis, and the first normal stress difference does not decay with the shear rate as it does for Brownian hard-spheres, but approaches a low-shear limiting value. A theory is proposed that makes use of the time scale of diffusion for aggregated particles out of their mutual potential well, τ ~ (a2/D)(kT/Umin)exp(Umin/kT), much in the spirit of the Eyring theory, to describe the rheology of the flocculated dispersion. Here a is the particle radius and D is the diffusivity of an isolated particle. When the shear rate is non-dimensionalized by τ, the reduced viscosity data for all field strengths collapse onto a single universal curve. Although we use a relatively small monolayer suspension, our simulation results compare well to the limited experimental and theoretical work on Brownian ER suspensions. The scaling relationship for the low-shear viscosity has also been evidenced in other studies of flocculated dispersions. The model is tested for its general applicability by a study of the rheology of a three-dimensional flocculated dispersion with an isotropic potential by molecular dynamics simulation and by analysis of experimental data obtained independently by Buscall, McGowan and Morton-Jones for a depletion flocculated dispersion. In both cases the suspension has a low-shear viscosity that scales exponentially with the pair potential well depth, and the low-shear limiting behavior was observed at a shear rate that scales inverse exponentially with the pair potential well depth, Umin/kT. The reduced viscosity data collapse onto a single curve when plotted as a function of the shear rate non-dimensionalized by the escape time scale, and the model was found to predict the reduced curves.