Sticky-probe active microrheology: Part 2. The influence of attractions on non-Newtonian flow

Abstract

We derive a theoretical framework for the non-Newtonian viscosity of a sticky, attractive colloidal dispersion via active microrheology by modeling detailed microscopic attractive and Brownian forces between particles. Actively forcing a probe distorts the surrounding arrangement of particles from equilibrium; the degree of this distortion is characterized by the Péclet number, Pe≡Fext/(2kT/a), where kT is the thermal energy and a the probe size. Similarly, the strength of attractive interactions relative to Brownian motion is captured by the second virial coefficient, B2. We formulate a Smoluchowski equation governing the pair configuration as it evolves with external and attractive forces. The microviscosity is then computed via non-equilibrium statistical mechanics. For active probe forcing, the familiar hard-sphere boundary-layer and wake structures emerge as Pe grows strong, but attractions alter its shape: changes in relative probe motion arising from its attraction to the bath particles can lead to a high-Pe, strong-attraction flipping of the microstructure, where an upstream depletion boundary layer forms, along with a downstream accumulation wake. This highly distorted structure is analyzed at the micro-mechanical level, where changes in the time spent upstream or downstream from a bath particle lead to hypo- and hyper-viscosity. When attractions are strong, separating the interparticle microviscosity into contributions from attractions and repulsions reveals an attractive undershoot and a repulsive overshoot, as advection grows strong enough to break interparticle bonds downstream and drain the wake. In contrast to linear-response rheology that is predictable entirely by B2 for short-ranged attractions, here the non-Newtonian viscosity is not, owing to the additional length scale introduced by the boundary layer. The ratio of external to attractive forces eventually supersedes B2 as the relevant predictor of structure and rheology. This behavior may provide interesting connections to active motion in biological systems where attractive forces are present.