Chiral propulsion: The method of effective boundary conditions

Journal Article · 16 August 2021 · Physics of Fluids

DOI: https://doi.org/10.1063/5.0058581 · OSTI ID:1814460

Korneev, Leonid A.  ^[1]; Kharzeev, Dmitri E. ^[2]; Abanov, Alexandre G. ^[3]

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1. Stony Brook Univ., NY (United States); Stony Brook University
2. Stony Brook Univ., NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
3. Stony Brook Univ., NY (United States); Simons Center for Geometry and Physics, Stony Brook, NY (United States)

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. Here, the proposed method is general and can be applied to any helical shape in the limit of a small pitch. Furthermore, we have established that for a broad class of helical surfaces the dependence of the chiral propulsion on the helical angle θ is universal, x ~ cos θ sin 2θ with the maximal propulsion achieved at the universal angle θ_m = tan^–1(1/√2) ≈ 35.26°.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States); Stony Brook Univ., NY (United States); Stony Brook University, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: FG02-88ER40388; SC0012704; SC0017662
• OSTI ID: 1814460
• Report Number(s): BNL--222158-2021-JAAM
• Journal Information: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 8 Vol. 33; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)Copyright Statement
• Country of Publication: United States
• Language: English