  In this work we address the "smoking ring" propulsion technique, originally
proposed by E. M. Purcell. We first consider self-locomotion of a
doughnut-shaped swimmer powered by surface tank-treading. Different modes of
surface motion are assumed and propulsion velocity and swimming efficiency are
determined. The swimmer is propelled against the direction of its outer surface
motion, the inner surface having very little affect. The simplest swimming mode
corresponding to constant angular velocity, can achieve propulsion speeds of up
to 66% of the surface tank-treading velocity and swimming efficiency of up to
13%. Higher efficiency is possible for more complicated modes powered by
twirling of extensible surface. A potential practical design of a swimmer
motivated by Purcell's idea is proposed and demonstrated numerically. Lastly,
the explicit solution is found for a two-dimensional swimmer composed of two
counter-rotating disks, using complex variable techniques.
