Dynamics-dependent density distribution in active suspensions

Abstract

Self-propelled colloids constitute an important class of intrinsically non-equilibrium matter. Typically, such a particle moves ballistically at short times, but eventually changes its orientation, and displays random-walk behavior in the long-time limit. Theory predicts that if the velocity of non-interacting swimmers varies spatially in 1D, $v(x)$, then their density $\rho (x)$ satisfies $\rho (x)=\rho (0)v(0)/v(x)$, where $x=0$ is an arbitrary reference point. Such a dependence of steady-state $\rho (x)$ on the particle dynamics, which was the qualitative basis of recent work demonstrating how to `paint' with bacteria, is forbidden in thermal equilibrium. We verify this prediction quantitatively by constructing bacteria that swim with an intensity-dependent speed when illuminated. A spatial light pattern therefore creates a speed profile, along which we find that, indeed, $\rho (x)v(x)=\mathrm{constant}$, provided that steady state is reached.

References in corpus (8)

• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Differential Dynamic Microscopy: Probing wave vector dependent dynamics with a microscope
• Sedimentation, trapping, and rectification of dilute bacteria
• Towards a 'Thermodynamics' of Active Matter
• Differential Dynamic Microscopy of Bacterial Motility
• Differential Dynamic Microscopy: a High-Throughput Method for Characterizing the Motility of Microorganism
• Dynamics-dependent density distribution in active suspensions
• Correcting artifacts from finite image size in Differential Dynamic Microscopy

Cited by in corpus (2)

• Dynamics-dependent density distribution in active suspensions
• Propagating Density Spikes in Light-Powered Motility-Ratchets