Chiral propulsion: The method of effective boundary conditions

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

Automated summary

The paper proposes an effective boundary condition method for chiral propulsion, deriving propulsion coefficients for various helical shapes and showing universal dependence of chiral propulsion on helical angle θ. The method is general, applicable to any helical shape with a small pitch, and achieves maximal propulsion at a universal angle θ(m) around 35.26 degrees.