Response to "Comment on 'The swimming of animalcules'" [Phys. Fluids 19, 079101 (2007)]

Abstract

The proof of the statement that a two-bead structure with constant mobilities cannot swim is incorrect. A general expression for the swimming velocity of a two-bead structure with given periodic relative motion is derived in the form of a line integral. The net torque exerted on the fluid is also expressed as a line integral. It is shown that in the example given by Friedman a net torque is exerted on the fluid. Therefore it is not acceptable as a swimming motion. A more complicated periodic relative motion is constructed for which the net torque vanishes, but which leads to a nonvanishing swimming velocity. A dynamical formulation appears to restrict the possibility of swimming. © 2007 American Institute of Physics.