Eur. Phys. J. B 60, 325-336 (2007)
https://doi.org/10.1140/epjb/e2007-00358-1

Hydrodynamics of a rotating torus

¹ Department of chemical engineering, Indian Institute of Technology, Bombay, Mumbai, 400076, India
² Instituut-Lorentz, Universiteit Leiden, Leiden, Postbus, 9506, 2300, RA, The Netherlands
³ School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA

Corresponding author: ^a rochish@che.iitb.ac.in

Received: 23 July 2007
Revised: 2 November 2007
Published online: 22 December 2007

Abstract

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, ϵ, 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 ϵ when the inner cylinder diameter approaches that of the torus.