 
Summary: Optimal Swimming at Low Reynolds Numbers
J. E. Avron,1
O. Gat,2
and O. Kenneth1
1
Department of Physics, Technion, Haifa, 32000, Israel
2
Department of Electrical Engineering, Technion, Haifa, 32000, Israel
(Received 19 April 2004; published 28 October 2004)
Efficient swimming at low Reynolds numbers is a major concern of microbots. To compare the
efficiencies of different swimmers we introduce the notion of ``a swimming drag coefficient'' which
allows for the ranking of swimmers. We find the optimal swimmer within a certain class of two
dimensional swimmers using conformal mapping techniques.
DOI: 10.1103/PhysRevLett.93.186001 PACS numbers: 83.10.y, 45.40.Ln, 83.60.Yz
Motivation. Swimming at low Reynolds numbers is
the theory of the locomotion of small microscopic organ
isms [19]. It is also relevant to the locomotion of small
robots [10]. Although microbots do not yet exist, they are
part of the grand vision of nanoscience [1113] and it is
important to understand the physical constraints that
