Periodic trajectories of rotating micro-cylinders in a confining geometry

Cylindrical-shaped structures are ubiquitous in nature. Many micro-swimmers such as bacteria and algae utilize the microtubule-based flagella and cilia for locomotion. These cylindrical organelles almost never live in free space, yet their motions in a confining geometry can be counter-intuitive. For example, one of the intriguing (yet classical) results in this regard is that a rotating cylinder next to a plane wall does not generate any net force in Newtonian fluids and therefore does not translate. In this work, we employ both numerical and analytical tools to investigate the motions of micro-cylinders under prescribed torques in a confining geometry. We start by studying the self-induced translations of a single cylinder bounded by a circular confinement. We then show that a cylinder pair can form a variety of periodic trajectories depending on the relative position to the confinement. Potential physical mechanisms will be discussed at the end of the talk.