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Optimization and small-amplitude analysis of Purcell's three-link microswimmer model
1Faculty of Mechanical Engineering , Technion - Israel Institute of Technology , Haifa 32000, Israel.
Proceedings. Mathematical, Physical, and Engineering Sciences
|September 13, 2016
Summary
This study analyzes Purcell
Area of Science:
- Fluid dynamics
- Microswimmer locomotion
- Biophysics
Background:
- Purcell's three-link microswimmer is a model system for understanding locomotion at low Reynolds numbers.
- Previous studies on microswimmer dynamics often relied on numerical simulations.
Purpose of the Study:
- To analytically investigate the motion of a three-link microswimmer in viscous flow.
- To derive explicit expressions for displacement and energetic efficiency.
- To explore the effect of stroke amplitude on movement direction.
Main Methods:
- Perturbation expansion of microswimmer dynamics.
- Analysis of square and circular gaits in joint angle space.
- Derivation of leading-order and next-order correction terms.
Main Results:
- Explicit expressions for microswimmer displacement were obtained.
- Correction terms revealed movement direction reversal at large amplitudes.
- Asymptotic expressions for Lighthill's energetic efficiency were derived.
Conclusions:
- Analytical approximations allow for predicting microswimmer behavior, including direction reversal.
- The findings enable optimization of stroke amplitude and swimmer geometry for enhanced performance.
- This work provides a theoretical framework for designing efficient microswimmers.
