Nonlinear microrheology of active Brownian suspensions

The rheological properties of active suspensions are studied via microrheology: tracking the motion of a colloidal probe particle in order to measure the viscoelastic response of the embedding material. The passive probe particle with size R is pulled through the suspension by an external force F^ext, which causes it to translate at some speed U^probe. The bath is comprised of a Newtonian solvent with viscosity η_s and a dilute dispersion of active Brownian particles (ABPs) with size a, characteristic swim speed U₀, and a reorientation time τ_R. The motion of the probe distorts the suspension microstructure, so the bath exerts a reactive force on the probe. In a passive suspension, the degree of distortion is governed by the Péclet number, Pe = F^ext/(k_BT/a), the ratio of the external force to the thermodynamic restoring force of the suspension. In active suspensions, however, the relevant parameter is L^adv/l = U^probeτ_R/U₀τ_R∼F^ext/F^swim, where F^swim = ζU₀ is the swim force that propels the ABPs (ζ is the Stokes drag on a swimmer). When the external forces are weak, L^adv≪l, the autonomous motion of the bath particles leads to "swim-thinning," though the effective suspension viscosity is always greater than η_s. When advection dominates, L^adv≫l, we recover the familiar behavior of the microrheology of passive suspensions. The non-Newtonian behavior for intermediate values of L^adv/l is determined by l/R_c = U₀τ_R/R_c-the ratio of the swimmer's run length l to the geometric length scale associated with interparticle interactions R_c = R + a. The results in this manuscript are approximate as they are based on numerical solutions to mean-field equations that describe the motion of the active bath particles.