Systematic parameterisations of minimal models of microswimming

TL;DR

This paper investigates the validity of using averaged parameters in simple microswimmer models by applying multi-timescale analysis to compare their behavioral predictions with more dynamic models.

Contribution

It introduces a systematic asymptotic approach to parameterize minimal microswimmer models accounting for rapid temporal variations.

Findings

A straightforward asymptotic analysis can effectively parameterize non-autonomous models.

Averaged parameter models can qualitatively match behaviors of time-varying models.

The approach provides a systematic way to extend simple models with dynamic features.

Abstract

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multi-timescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we highlight and exemplify how a straightforward asymptotic analysis of these non-autonomous models can result in effective, systematic parameterisations of minimal models of microswimming.