Single Particle Motion in Active Matter

Abstract

Active matter refers to a broad class of materials in which the constituent particles or organisms are able to self-propel (swim) by some internal physicochemical mechanism. Though the origin of this self-propulsive motion is a rich area of study, we are primarily interested in the collective effects of this motion on the physical properties — and in particular, the rheology — of the active material as a whole. As such we model self-propulsive motion using the minimal active Brownian particle (ABP) model: a particle of size a , swims in a direction q with a speed U0, and the direction of its motion changes randomly over some time scale τR. On a macroscopic scale, active motion leads to unique hydrodynamic and mechanical stresses exerted by the particles on their embedding medium. These stresses arise from the microscopic force associated with particle locomotion — the swim force F swim. Though the idea of the swim force is widely recognized in the abstract, little attention has been given to the characterization and mechanical consequences of this force. In this work we are particularly interested the role of the swim force in the effective motion of passive constituents in active environments, and how the swim force affects long-ranged hydrodynamic interactions (HI) in active suspensions. We examine these issues through the lens of microrheology: tracking the motion of a colloidal probe particle through an active medium, and using its motions to infer the effective viscoelastic properties of the suspension. Using generalized Taylor dispersion theory, we find an activity-driven enhancement to the diffusion of the probe in an active medium. This first-principles theory unites many experimental observations of tracer diffusion, and provides simple physical descriptions of the problem that do not rely on the specific self-propulsion mechanism of the swimmer. This same framework is then used to compute the suspension microviscosity (as measured by the drag on the probe particle), and the fluctuation-dissipation relation in an active system. We find that activity reduces the drag on the probe, but the drag is still larger than it would be in a Newtonian fluid; this stands in contrast to experimental measurements of reduced shear viscosities. We show that the microviscosity of a suspension is reduced — and may even become negative! — due to HI, and that this effect is not due to the fluid velocity disturbance associated with the swimmers' self-propulsion.