Linear viscoelasticity of attractive colloidal dispersions

Abstract

The rheology of a semidilute dispersion of colloids having short-ranged attractions is studied. A depletion potential is chosen as a model for the attractive interaction and arises from nonadsorbing polymer dispersed with the colloids. The complex viscosity of these materials can be calculated by investigating their response to weak oscillatory shear. A first order expansion in small rates of deformation is used to solve for the microstructure and stress in the dispersion. Additionally, the effect of hydrodynamic interactions is studied via the excluded annulus model, which views the radius at which hard-sphere interactions occur as a barrier that resides beyond the hydrodynamic radius of the particles. This treatment allows a continuous variation of the hydrodynamic interaction strength. The viscoelastic response exhibits a sharp transition when going from weak attraction to strong attraction. Below a critical strength, increasing the interparticle attraction reduces the low frequency viscosity. Strong attractions increase the viscous response and delay the onset of an elastic plateau at high frequencies. An asymptotic analysis shows that the stress response is a result of the interplay of two length scales: The range of attraction and the diffusive boundary layer around particles. Independent of the strength of hydrodynamic interactions, the complex viscosity can be described with high accuracy by two well characterized viscoelastic models: At low frequencies, a Maxwell mode; at high frequencies, the purely repulsive hard-sphere response. Our results demonstrate that beyond hydrodynamic interactions the strength and range of the interaction potential between particles plays a central role in setting the viscoelasticity.