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Nonlinear microrheology of active Brownian suspensions

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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 Fext, which causes it to translate at some speed Uprobe. The bath is comprised of a Newtonian solvent with viscosity ηs and a dilute dispersion of active Brownian particles (ABPs) with size a, characteristic swim speed U0, and a reorientation time τR. 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 = Fext/(kBT/a), the ratio of the external force to the thermodynamic restoring force of the suspension. In active suspensions, however, the relevant parameter is Ladv/l = UprobeτR/U0τRFext/Fswim, where Fswim = ζU0 is the swim force that propels the ABPs (ζ is the Stokes drag on a swimmer). When the external forces are weak, Ladvl, the autonomous motion of the bath particles leads to “swim-thinning,” though the effective suspension viscosity is always greater than ηs. When advection dominates, Ladvl, we recover the familiar behavior of the microrheology of passive suspensions. The non-Newtonian behavior for intermediate values of Ladv/l is determined by l/Rc = U0τR/Rc—the ratio of the swimmer's run length l to the geometric length scale associated with interparticle interactions Rc = 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.

Graphical abstract: Nonlinear microrheology of active Brownian suspensions

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Article information

23 Aug 2019
13 Dec 2019
First published
13 Dec 2019

Soft Matter, 2020, Advance Article
Article type

Nonlinear microrheology of active Brownian suspensions

E. W. Burkholder and J. F. Brady, Soft Matter, 2020, Advance Article , DOI: 10.1039/C9SM01713E

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