Tracer diffusion in active suspensions

Eric W. Burkholder; John F. Brady

doi:10.1103/PhysRevE.95.052605

paper

Tracer diffusion in active suspensions

arXiv:1703.10554 · doi:10.1103/PhysRevE.95.052605

Abstract

We study the diffusion of a Brownian probe particle of size $R$ in a dilute dispersion of active Brownian particles (ABPs) of size $a$ , characteristic swim speed $U_{0}$ , reorientation time $τ_{R}$ , and mechanical energy $k_{s} T_{s} = ζ_{a} U_{0}^{2} τ_{R} /6$ , where $ζ_{a}$ is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity $D_{P} = k_{B} T / ζ_{P}$ , where $k_{B} T$ is the thermal energy of the solvent and $ζ_{P}$ is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by $P e_{s} = U_{0} a / D_{P}$ . The active contribution to the diffusivity scales as $P e_{s}^{2}$ for weak swimming and $P e_{s}$ for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale $τ_{R}$ , the active diffusivity scales as $k_{s} T_{s} / ζ_{P}$ : the probe moves as if it were immersed in a solvent with energy $k_{s} T_{s}$ rather than $k_{B} T$ .

5 pages, 3 figures, submitted for publication. Please contact authors regarding supplemental information

Tracer diffusion in active suspensions

Abstract

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