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Updated: Jun 9, 2026

Swimming Performance Assessment in Fishes

Swimming Performance Assessment in Fishes

Published on: May 20, 2011

Purcell swimmer near a wall.

Enrico Micalizio¹, Marco Morandotti¹, Henry Shum²

¹Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, 10129 Italy.

Meccanica

|June 8, 2026

Summary

We analyzed a three-link swimmer near a wall, finding it

Area of Science:

Fluid dynamics
Microswimmer locomotion
Geometric control theory

Background:

Purcell's three-link swimmer model is a fundamental concept in microswimmer research.
Previous studies often simplified hydrodynamic interactions, especially near boundaries.
Understanding wall effects is crucial for realistic microswimmer applications.

Purpose of the Study:

To investigate hydrodynamic interactions between a wall and a three-link swimmer.
To extend theoretical models by incorporating wall-modified drag coefficients.
To determine the conditions for local controllability of the swimmer near a wall.

Main Methods:

Derivation of equations of motion for the swimmer near a no-slip wall.
Application of Geometric Control Theory criteria to assess controllability.

Keywords:

Controllability Microswimmers Resistive force Theory Wall effects

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Last Updated: Jun 9, 2026

Swimming Performance Assessment in Fishes

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Analytical calculations using Lie brackets and numerical simulations for displacement analysis.

Numerical assessment of drag correction approximations and swimmer orientation effects.

Main Results:

The three-link swimmer system is locally controllable in configurations near parallel to the wall.
Controllability is achieved for all values of the length ratio lambda (>0) between the central and outer links.
Analytical and numerical results for horizontal displacement agree, with optimal lambda values identified.
Swimmer orientation relative to the wall influences net displacement components.

Conclusions:

Hydrodynamic interactions with a wall significantly affect microswimmer motion and controllability.
The study provides a theoretical framework and numerical validation for swimmer behavior near boundaries.
Findings offer insights for designing and controlling microswimmers in confined environments.