The Effect of Confinement on Active Brownian Particles

Active Brownian Particles (ABPs) are subject to confinement effects when their run or persistence length, l= U₀τ_R, is comparable to the characteristic size of the confining geometry. Here, U₀ is the intrinsic swim speed and τ_R is the reorientation time of the ABPs. Furthermore, ABPs accumulate at no-flux surfaces owing to their persistent swimming. These two effects can produce some unusual and startling effects. For example, it has been seen in simulations (Ray, et al. PRE 2014) that two parallel walls attract each other when placed in a dilute bath of ABPs. In this work, we provide a simple model based on the Smoluchowski equation for the ABPs and an overall macroscopic momentum balance to predict analytically this attractive force. We extend this simple modeling to predict the partitioning of ABPs between a confined channel of width H and an infinite reservoir, showing that the concentration within the channel over that in the bulk increases as l/H. The theoretical results are compared to Brownian dynamics simulations.