Title: Active particles in periodic lattices,
Abstract: Both natural and artificial small-scale swimmers may often self-propel in
environments subject to complex geometrical constraints. While most past
theoretical work on low-Reynolds number locomotion addressed idealised
geometrical situations, not much is known on the motion of swimmers in
heterogeneous environments. As a first theoretical model, we investigate
numerically the behaviour of a single spherical micro-swimmer located in an
infinite, periodic body-centred cubic lattice consisting of rigid inert spheres
of the same size as the swimmer. Running a large number of simulations we
uncover the phase diagram of possible trajectories as a function of the
strength of the swimming actuation and the packing density of the lattice. We
then use hydrodynamic theory to rationalise our computational results and show
in particular how the far-field nature of the swimmer (pusher vs. puller)
governs even the behaviour at high volume fractions.