Low Reynolds number swimming in two dimensions (Q2724624)

Using a geometrical approach for low Reynolds number swimming introduced by \textit{A. Shapere} and \textit{F. Wilzcek} [J. Fluid Mech. 198, 587--599 (1989; Zbl 0674.76115)], the authors investigate the swimming motion in two dimensions. The outer membrane or the ciliary envelope of a planar organism is represented by conformal image of the unit circle, and power expenditures and velocities are computed using complex variable technique. The calculations for a self-deforming ellipse are presented as an example, and the results show a good agreement with observations for the nematode \textit{Turbatrix aceti}. Using the criterion ``efficiency is equal to velocity/hydrodynamical power'', the authors compute the most efficient swimming stroke. The results show that \textit{ciliary} envelopes emulate high-order geometric modes that optimize the efficiency without extra mechanical power expenditure.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00039].