Active particles in the presence of obstacles

We consider active particles (microswimmers) moving in an environment with obstacles. These are treated using the Active Brownian Particle model (ABP), where particles move forward at constant speed but in a randomly-varying direction. We use homogenisation theory to predict their coarse-grained dynamics at long times. We present numerical solutions that describe their spatial distribution and effective diffusivity as a function of the strength of swimming and area fraction occupied by the obstacles. We then use matched asymptotic approximations to explain our numerical results in the dilute limit corresponding to small obstacle area fraction and in the dense limit, when the obstacles are nearly touching.