Thinning and thickening in active microrheology.

When pulling a probe particle in a many-particle system at a fixed velocity, the probe's effective friction, defined as the average external force over its velocity, γ(eff):=〈F(ex)〉/u, first stays constant (linear response), then decreases (thinning), and, finally, increases again (thickening). We propose a three-time-scale picture to describe the thinning and thickening behavior. There are three distinct time scales for the bath particles: diffusion, damping, and single probe-bath collision. The dominating time scales are controlled by the pulling velocity and determine the behavior of the probe's friction. We test and confirm this description with a Langevin dynamics simulation. Microscopically, we find that for computing the effective friction, the Maxwellian distribution of bath particles' velocities fails in the regime of high Reynolds and Peclet numbers. This can be understood based on the microscopic mechanism of thickening obtained in the T=0 limit. The dynamic regimes defined by the ratio of different time scales can explain several observations of thinning and thickening in literature.