Geometrically biased random walks in bacteria-driven micro-shuttles

Micron-sized objects having asymmetric boundaries can rectify the chaotic motions of an active bacterial suspension and perform geometrically biased random walks. Using numerical simulations in a planar geometry, we show that arrow-shaped micro-shuttles, constrained to move in one dimension (1D) in a bath of self-propelled micro-organisms, spontaneously perform unidirectional translational motions with a strongly shape-dependent speed. Relaxing the 1D constraint, a random motion in the whole plane sets in at long times, due to random changes in shuttle orientation caused by bacterial collisions. The complex dynamics arising from the mechanical interactions between bacteria and the object boundaries can be described by a Gaussian stochastic force with a shape-dependent mean and a self-correlation decaying exponentially on the timescale of seconds.