Asymptotic transport and dispersion of active particles in periodic porous media

We analyze the long-time transport of active Brownian particles flowing through a doubly-periodic porous lattice using generalized Taylor dispersion theory and Langevin simulations. The asymptotic spreading of a dilute cloud of microswimmers is shown to obey an obstacle-free advection-diffusion equation, which we use to elucidate the effects of motility, lattice geometry and applied fluid flow on transport properties. Our model suggests that the interplay of particle self-propulsion, entropic trapping by the obstacles, and shear-induced dispersion in the flow can be exploited for the control and directional transport of active swimmers through microstructured environments.