Chiral propulsion: The method of effective boundary conditions

We propose to apply an "effective boundary condition" method the problem of chiral propulsion. For case a rotating helix moving through fluid at low Reynolds number, amounts replacing original (in limit small pitch) by cylinder, but with special kind partial slip conditions non-slip on helix. These are constructed reproduce far-field velocities problem, and defined few parameters (slipping lengths) that can be extracted from in planar rather than cylindrical geometry. derive propulsion coefficients for spirals, helicoids, helically modulated cylinders, some their generalizations using introduced method. In we compare our results ones derived Lighthill find very good agreement. The proposed is general applied any helical shape pitch. have established broad class surfaces dependence angle $\theta$ universal, $\chi\sim \cos\theta\sin 2\theta$ maximal achieved universal $\theta_m = \tan^{-1}(1/\sqrt{2})\approx 35.26^\circ$.