Modeling straight and circle swimmers via immersed boundary methods: from single swimmer to collective motion

TL;DR

This paper introduces a minimal immersed boundary model for microswimmers, capturing both straight and circular swimming behaviors, and explores their interactions and collective dynamics in fluid environments.

Contribution

It presents a novel minimal model of microswimmers using immersed boundary methods, capable of simulating individual and collective swimming behaviors with simple bead-and-link structures.

Findings

Model reproduces straight and circular swimming motions.

Swimmers exhibit complex scattering behaviors upon encounter.

Collective dynamics show emergent patterns driven by hydrodynamic interactions.

Abstract

We propose a minimal model of microswimmer based on immersed boundary methods. We describe a swimmer (either pusher or puller) as a distribution of point forces, representing the swimmer's flagellum and body, with only the latter subjected to no-slip boundary conditions with respect to the surrounding fluid. In particular, our model swimmer consists of only three beads (two for the body and one for the flagellum) connected by inextensible and rigid links. When the beads are collinear, standard straight swimming is realized and, in the absence of propulsion, we demonstrate that the swimmer's body behaves as an infinitely thin rod. Conversely, by imposing an angle between body and flagellum the swimmer moves on circular orbits. We then discuss how two swimmers, in collinear or non-collinear geometry, scatter upon encounter. Finally, we explore the dynamics of a large number of swimmers reacting to one another only via hydrodynamic interactions, and exemplify their complex collective dynamics in both straight and circular swimmers.