Collective behaviors of elastic filaments undulating in close proximity

In order to investigate the collective behaviors of a suspension of active filaments in the limit of a non-dilute regime, we study the interactions relevant to the closely spaced multiple elastic filaments slowly swimming by undulation in a confined viscous fluid. The hydrodynamics and steric interactions between two filaments with an aspect ratio, a/L, critically depend on the separation distance d. We focus on the conditions for the formation of meta-chronal waves of multiple filaments aligned at a wall focusing on the regime of a d L. We consider various tilting angles that possibly break the symmetry in the governing equation and their effects on propulsion efficiency. We quantify the relative importance of the hydrodynamics and the steric interactions to the formation of metachronal waves of undulating bodies as a function of the average separation distance in the suspension.