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Issue 4, 2020
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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, 2020,16, 1034-1046
Article type

Nonlinear microrheology of active Brownian suspensions

E. W. Burkholder and J. F. Brady, Soft Matter, 2020, 16, 1034
DOI: 10.1039/C9SM01713E

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