Efficient shapes for microswimming: from three-body swimmers to helical flagella

Abstract

We combine a general formulation of microswimmmer 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 swimmer that propels itself 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).

9 pages, 5 figures

References in corpus (5)

• The hydrodynamics of swimming microorganisms
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
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• Modelling the Mechanics and Hydrodynamics of Swimming E. coli
• Can the self-propulsion of anisotropic microswimmers be described by using forces and torques?

Cited by in corpus (5)

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• Dynamic Monte Carlo algorithm for out-of-equilibrium processes in colloidal dispersions
• Reciprocal swimming at intermediate Reynolds number
• Boosting micromachine studies with Stokesian Dynamics
• Parametric Shape Optimization of Flagellated Micro-Swimmers Using Bayesian Techniques