The rheology of suspensions of charged rigid spheres

Abstract

The rheology of particulate dispersions which are strongly influenced by particular types of non-hydrodynamic forces is analysed within the framework of suspension mechanics. Interactions between particles in a homogeneous shear flow without inertia are governed by viscous, electrostatic, London-van der Waals and Brownian forces. The balance among these provides the fluid with a microstructure described quantitatively at dilute concentrations by a pair distribution function and qualitatively by a characteristic interaction length. The bulk rheology follows from the microstructural variables through suitable averaging. In dilute electrostatically stabilized suspensions of small rigid spheres for which London-van der Waals attractions and hydrodynamic interactions can be ignored, the theory predicts a Newtonian low-shear limit. The analytic expression for the viscosity contains a ϕ 2 -coefficient which can be quite large and agrees well with experimental data. At higher flow strengths a scale analysis of the pair conservation equation indicates a shear-and strain-thinning rheology, representing a breakdown of the fluid microstructure. Without flow the interaction length attains a maximum determined by the balance between Brownian motion and electrostatic repulsion. A weak shear merely perturbs this balance but generates stresses proportional to the fifth power of the length. With increasing shear rate this length and consequently the shear viscosity are reduced until viscous interactions completely dominate. Asymptotic solutions for an intermediate regime in which Brownian motion and hydrodynamic interactions are both negligible reveal power-law extensional and shear viscosities with non-zero normal stresses.