Sticky-Probe Microrheology

Abstract

We study the strongly nonlinear flow behavior of a sticky colloidal dispersion via active microrheology, where the motion of a Brownian probe driven by an external force through the suspension is tracked to infer material properties. Most prior work has focused on repulsive hard spheres and the influence of Brownian and hydrodynamic forces on rheological behavior. However, in many biological suspensions, particles exert attractive forces on one another; for example, interactions between a probe and structures such as F-actin networks inside eukaryotic cells are suspected to underlie anomalous behavior such as enhanced diffusivity or probe rotation due to slip when investigating network elastic response. Previous attempts to model the effects of particle attractions on flow behavior have shown that for weak flows, interparticle attractions give rise to increased suspension stress and corresponding changes in viscosity. However, these models are limited to weak flows in macroscopically sheared suspensions and cannot be applied to small or locally heterogeneous systems. In active microrheology, a Brownian probe particle interrogates structure as it is driven through the material by an external force. Probe motion distorts particle configuration, allowing interrogation of non-equilibrium behavior. The strength of probe forcing compared to thermal forces defines a P´ clet number, e Pe = F ext /(2kT/a), where kT is the thermal energy and a is the bath particle size, setting the extent of this distortion. The equilibrium microstructure and its distortion under probe forcing are also influenced by the strength of interparticle attractions relative to thermal forces. We formulate a Smoluchowski equation that governs the pair configuration as it evolves with flow strength, interparticle attractions, and Brownian motion. We determine its solution at and far from equilibrium and, from it, compute the microviscosity via a statistical mechanics approach. When probe forcing is weak, microstructural distortion comprises two primary features: a dipolar disturbance set by the weak external force, and an accumulation ring near contact arising from the attractive interparticle force, with thickness set by the range of interparticle attractions. As probe forcing grows strong, particles accumulate in a boundary layer near contact where advective, diffusive, and attractive forces balance. The changes in structure induced by interparticle attractions on particle microstructure lead to corresponding changes in rheology. Attractive forces quantitatively increase the low-Pe Newtonian plateau for viscosity as attractive force increases. The suspension force-thins, but with a slope set by the strength of attractions, where the hindrance of Brownian motion by attractions leads to a steeper decline. The high-Pe plateau found in freely-draining hard-sphere suspensions is recovered, but the value of Pe at which this plateau is achieved increases as attractions grow stronger, indicative of the greater strength of thermal forces.