Emergent rheotaxis of shape-changing swimmers in Poiseuille flow

TL;DR

This paper analytically investigates how shape-changing swimmers in Poiseuille flow exhibit emergent rheotaxis, revealing that nonlinear interactions between oscillatory speed and shape determine their long-term drift behavior.

Contribution

It provides a formal asymptotic analysis identifying the causal factors behind the emergent rheotactic behavior of deforming swimmers in flow.

Findings

Long-term drift is governed by a swimmer-dependent constant.

The sign of this constant determines attraction or repulsion to flow.

Nonlinear interactions between speed and shape drive rheotactic behavior.

Abstract

A simple model for the motion of shape-changing swimmers in Poiseuille flow was recently proposed and numerically explored by Omori et al. (2022). These explorations hinted that a small number of interacting mechanics can drive long-time behaviours in this model, cast in the context of the well-studied alga Chlamydomonas and its rheotactic behaviours in such flows. Here, we explore this model analytically via a multiple-scale asymptotic analysis, seeking to formally identify the causal factors that shape the behaviour of these swimmers in Poiseuille flow. By capturing the evolution of a Hamiltonian-like quantity, we reveal the origins of the long-term drift in a single swimmer-dependent constant, whose sign determines the eventual behaviour of the swimmer. This constant captures the nonlinear interaction between the oscillatory speed and effective hydrodynamic shape of deforming swimmers, driving drift either towards or away from rheotaxis.