On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform

TL;DR

This paper compares various numerical models of flagellated microswimmers, highlighting the limitations of simplified approaches and emphasizing the importance of long-range forces and accurate flagellum waveforms for reliable predictions.

Contribution

It evaluates the accuracy of simplified models against benchmark solutions, revealing their limitations in predicting swimmer dynamics and the significance of long-range hydrodynamic interactions.

Findings

Simplified models lack robustness in predicting head shape effects.

Long-range forces significantly influence swimmer behavior.

Benchmark models provide more accurate predictions.

Abstract

For a sperm cell-like flagellated swimmer in an unbounded domain, several numerical models of different fidelity are considered based on the Stokes flow approximation. The models include a Regularised Stokeslet Method and a 3D Finite Element Method, which serve as the benchmark solutions for several approximate models considered. The latter include the Resistive Force Theory versions of Lighthill and Gray and Hancock as well as a simplified approximation based on computing the hydrodynamic forces exerted on the head and the flagellum separately. It is shown how none of the simplified models is robust enough with regards to predicting the effect of the swimmer head shape change on the swimmer dynamics. For a range of swimmer motions considered, the resulting solutions for the swimmer force and velocities are analysed and the applicability of the Stokes model for the swimmers in question is probed.