Chiral propulsion: The method of effective boundary conditions
Abstract
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 propulsionmore »
- Authors:
-
[1];
- Stony Brook Univ., NY (United States)
- Stony Brook Univ., NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
- Stony Brook Univ., NY (United States); Simons Center for Geometry and Physics, Stony Brook, NY (United States)
- Publication Date:
- Research Org.:
- Stony Brook Univ., NY (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1814460
- Alternate Identifier(s):
- OSTI ID: 1822348; OSTI ID: 2280517
- Report Number(s):
- BNL-222158-2021-JAAM
Journal ID: ISSN 1070-6631; TRN: US2213439
- Grant/Contract Number:
- SC0017662; SC0012704; FG02-88ER40388
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Fluids
- Additional Journal Information:
- Journal Volume: 33; Journal Issue: 8; Journal ID: ISSN 1070-6631
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Viscous liquid; Perturbation theory; Navier Stokes equations; Fluid flows; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Korneev, Leonid A., Kharzeev, Dmitri E., and Abanov, Alexandre G. Chiral propulsion: The method of effective boundary conditions. United States: N. p., 2021.
Web. doi:10.1063/5.0058581.
Korneev, Leonid A., Kharzeev, Dmitri E., & Abanov, Alexandre G. Chiral propulsion: The method of effective boundary conditions. United States. https://doi.org/10.1063/5.0058581
Korneev, Leonid A., Kharzeev, Dmitri E., and Abanov, Alexandre G. Tue .
"Chiral propulsion: The method of effective boundary conditions". United States. https://doi.org/10.1063/5.0058581. https://www.osti.gov/servlets/purl/1814460.
@article{osti_1814460,
title = {Chiral propulsion: The method of effective boundary conditions},
author = {Korneev, Leonid A. and Kharzeev, Dmitri E. and Abanov, Alexandre G.},
abstractNote = {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 θm = tan–1(1/√2) ≈ 35.26°.},
doi = {10.1063/5.0058581},
journal = {Physics of Fluids},
number = 8,
volume = 33,
place = {United States},
year = {Tue Aug 17 00:00:00 EDT 2021},
month = {Tue Aug 17 00:00:00 EDT 2021}
}
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Works referenced in this record:
Tensorial hydrodynamic slip
journal, October 2008
- Bazant, Martin Z.; Vinogradova, Olga I.
- Journal of Fluid Mechanics, Vol. 613
Helicoidal particles and swimmers in a flow at low Reynolds number
journal, April 2020
- Ishimoto, Kenta
- Journal of Fluid Mechanics, Vol. 892
Optimization of Chiral Structures for Microscale Propulsion
journal, January 2013
- Keaveny, Eric E.; Walker, Shawn W.; Shelley, Michael J.
- Nano Letters, Vol. 13, Issue 2
Swimming and pumping of rigid helical bodies in viscous fluids
journal, April 2014
- Li, Lei; Spagnolie, Saverio E.
- Physics of Fluids, Vol. 26, Issue 4
Periodic blocking in parallel shear or channel flow at low Reynolds number
journal, April 1993
- Davis, A. M. J.
- Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 4
Chiral Colloidal Molecules And Observation of The Propeller Effect
journal, August 2013
- Schamel, Debora; Pfeifer, Marcel; Gibbs, John G.
- Journal of the American Chemical Society, Vol. 135, Issue 33
Resistance of a grooved surface to parallel flow and cross-flow
journal, July 1991
- Luchini, Paolo; Manzo, Fernando; Pozzi, Amilcare
- Journal of Fluid Mechanics Digital Archive, Vol. 228
Controlled Propulsion of Artificial Magnetic Nanostructured Propellers
journal, June 2009
- Ghosh, Ambarish; Fischer, Peer
- Nano Letters, Vol. 9, Issue 6
Optimal Length of Low Reynolds Number Nanopropellers
journal, June 2015
- Walker, D.; Kübler, M.; Morozov, K. I.
- Nano Letters, Vol. 15, Issue 7
Self-Propulsion at Low Reynolds Number
journal, May 1987
- Shapere, Alfred; Wilczek, Frank
- Physical Review Letters, Vol. 58, Issue 20
Effective slip boundary conditions for arbitrary periodic surfaces: the surface mobility tensor
journal, July 2010
- Kamrin, Ken; Bazant, Martin Z.; Stone, Howard A.
- Journal of Fluid Mechanics, Vol. 658
Life at low Reynolds number
journal, January 1977
- Purcell, E. M.
- American Journal of Physics, Vol. 45, Issue 1
Sedimentation of a rigid helix in viscous media
journal, December 2018
- Palusa, Martina; de Graaf, Joost; Brown, Aidan
- Physical Review Fluids, Vol. 3, Issue 12
Characterizing the Swimming Properties of Artificial Bacterial Flagella
journal, September 2009
- Zhang, Li; Abbott, Jake J.; Dong, Lixin
- Nano Letters, Vol. 9, Issue 10
Helical swimming in Stokes flow using a novel boundary-element method
journal, June 2013
- Liu, Bin; Breuer, Kenneth S.; Powers, Thomas R.
- Physics of Fluids, Vol. 25, Issue 6