A note on swimming using internally generated traveling waves

In this note we bring together two ideas related to modeling the dynamics of swimming microorganisms: (1) as in Ajdari et al. [C. R. Acad. Sci. Paris, Ser. II 319, 861 (1994)], we consider fluid transport from one end of an organism to the other using an internal deformable canal along which a traveling peristaltic deformation propagates at speed V; (2) as described in Stone and Samuel [Phys. Rev. Lett. 77, 4102 (1996)], the swimming speed U(t) of an organism may be simply related to the velocity of the surface. Thus, we obtain an explicit relation between the average swimming velocity 〈U〉 and V, as well as a more detailed picture of the time-varying flow in the canal and of the instantaneous swimming speed of the organism.