Hydrodynamics of a rotating torus

摘要

The hydrodynamics of a torus is important on two counts: firstly, most stiff or semiflexible ring polymers, e.g. DNA miniplasmids are modeled as a torus and secondly, it has the simplest geometry which can describe self propelled organisms (particles). In the present work, the hydrodynamics of a torus rotating about its centerline is studied. Analytical expression for the velocity of a force free rotating torus is derived. It is found that a rotating torus translates with a velocity which is proportional to its internal velocity and to the square of the slenderness ratio, epsilon, similar to most low Reynolds number swimmers. The motion of a torus along a cylindrical track is studied numerically and it is observed that a force free torus changes its direction of motion (from a propelled state (weak wall effects) to a rolling state (strong wall effects)) as the diameter of the inner circular cylinder is increased. The rolling velocity is found to depend only on epsilon when the inner cylinder diameter approaches that of the torus.