Simulation of shear thickening in attractive colloidal suspensions

Abstract

The influence of attractive forces between particles under conditions of large particle volume fraction, ϕ, is addressed using numerical simulations which account for hydrodynamic, Brownian, conservative and frictional contact forces. The focus is on conditions for which a significant increase in the apparent viscosity at small shear rates, and possibly the development of a yield stress, is observed. The high shear rate behavior for Brownian suspensions has been shown in recent work [R. Mari, R. Seto, J. F. Morris and M. M. Denn PNAS, 2015, 112, 15326–15330] to be captured by the inclusion of pairwise forces of two forms, one a contact frictional interaction and the second a repulsive force often found in stabilized colloidal dispersions. Under such conditions, shear thickening is observed when shear stress is comparable to the sum of the Brownian stress, kT/a³, and a characteristic stress based on the combination of interparticle force, i.e. σ ∼ F₀/a² with kT the thermal energy, F₀ the repulsive force scale and a the particle radius. At sufficiently large ϕ, this shear thickening can be very abrupt. Here it is shown that when attractive interactions are present with the noted forces, the shear thickening is obscured, as the viscosity shear thins with increasing shear rate, eventually descending from an infinite value (yield stress conditions) to a plateau at large stress; this plateau is at the same level as the large-shear rate viscosity found in the shear thickened state without attractive forces. It is shown that this behavior is consistent with prior observations in shear thickening suspensions modified to be attractive through depletion flocculation [V. Gopalakrishnan and C. F. Zukoski J. Rheol., 2004, 48, 1321–1344]. The contributions of the contact, attractive, and hydrodynamics forces to the bulk stress are presented, as are the contact networks found at different attractive strengths.