title: Efficient shapes for microswimming: From three-body swimmers to helical flagella.
abstract: We combine a general formulation of microswimmer equations of motion with a numerical bead-shell model to calculate the hydrodynamic interactions with the fluid, from which the swimming speed, power, and efficiency are extracted. From this framework, a generalized Scallop theorem emerges. The applicability to arbitrary shapes allows for the optimization of the efficiency with respect to the swimmer geometry. We apply this scheme to "three-body swimmers" of various shapes and find that the efficiency is characterized by the single-body friction coefficient in the long-arm regime, while in the short-arm regime the minimal approachable distance becomes the determining factor. Next, we apply this scheme to a biologically inspired set of swimmers that propel using a rotating helical flagellum. Interestingly, we find two distinct optimal shapes, one of which is fundamentally different from the shapes observed in nature (e.g., bacteria).
authors.affiliation: Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
authors.forename: Bram
authors.initials: B
authors.lastname: Bet
authors.affiliation: Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands.
authors.forename: Gijs
authors.initials: G
authors.lastname: Boosten
authors.affiliation: Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands.
authors.forename: Marjolein
authors.initials: M
authors.lastname: Dijkstra
authors.affiliation: Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
authors.forename: René
authors.identifier: 000000022221294X
authors.initials: R
authors.lastname: van Roij
mesh_terms: D003198:Computer Simulation; D004926:Escherichia coli / Q000502:physiology*; D005407:Flagella / Q000502:physiology*; D057446:Hydrodynamics; D008954:Models, Biological; D009038:Motion; D013550:Swimming