Evaluation of spherical shapes swimming efficiency at low Reynolds number with applications to some biological problems

Swimming spherical shapes at low Reynolds number have been used as a model to describe locomotion of several microorganisms such as cyanobacteria. Other examples of biological interest include the motion of vesicles within eucaryotic cells which persists even in the absence of microtubules [Eur. J. Cell. Biol. 60 (1993) 217]. The role of tangential deformation has been pointed out as a reasonable mechanism for self-propulsion of shapes lacking appendages such as cilia or flagella [BMC Microbiol. 1 (1) (2001) 4] and even ranges of wave parameter values have been predicted consistently with its average speed [R. Proc. Natl. Acad. Sci. 93 (1996) 8340] in the case of Synechococcus. Here we re-evaluate the strategy of tangential deformations of a sphere as compared to radial ones in terms of their efficiencies. We confirm under this criterion of optimality that tangential waves are more efficient than radial waves at least within the same range of parameters.