Effective Interactions between Colloidal Particles Suspended in a Bath of Swimming Cells

The dynamics of passive colloidal tracers in a bath of self-propelled particles is receiving a lot of attention in the context of nonequilibrium statistical mechanics. Here we demonstrate that active baths are also capable of mediating effective interactions between suspended bodies. In particular we observe that a bath of swimming bacteria gives rise to a short range attraction similar to depletion forces in equilibrium colloidal suspensions. Using numerical simulations and experiments we show how the features of this interaction arise from the combination of nonequilibrium dynamics (peculiar of bacterial baths) and excluded volume effects.

Figure 1

Images of particles immersed in active baths. On the left, snapshot taken from simulation (self-propelling bacteria are represented by spherocylinders with white head, see inset). On the right, microscopy image from experiment (bacteria are visible in the enlarged image in the inset).

Figure 2

Radial distribution function $g(r)$ measured in simulation (upper panel) and experiment (lower panel). Dashed blue line is the $g(r)$ obtained in simulations with a mixture of $N_p$ species of bacteria each interacting with only one of the $N_p$ particles (no depletion). Typical two-beads configurations corresponding to the two first peaks are also shown in the simulation case. Distances are in unit of particles diameter $d$ (bacteria width is about 0.25 in such a unit).

Figure 3

Example of time evolution of the distance between two nearby particles. Data are from simulation (red line) and experiment (black line, see 34 for the relative video-microscopy movies). Also indicated are the positions of the first peak of the $g(r)$ at $r/d=1.0$ and of the second one (from simulation data) at $r/d=1.28$. Time is in seconds and distances in unit of particles diameter. Inset: Experimental trajectories of the colloidal particles diffusing in the active bath and in the nonmotile bacteria suspension (note that in the latter case diffusivity is suppressed by a factor $\sim {10}^4$).