# A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

## TL;DR

This paper introduces a versatile perturbative method for analyzing bead-based microswimmers, revealing complex self-propulsion behaviors and extending understanding beyond existing models through validation and broad applicability.

## Contribution

A general perturbative calculation scheme for bead-based microswimmers driven by arbitrary forces, incorporating hydrodynamic interactions, and validated against numerical and analytical models.

## Key findings

- Identified qualitative differences in far-field flow patterns.
- Revealed richer swimmer behaviors than previous models predicted.
- Validated approach with 3-bead assemblies and existing geometries.

## Abstract

Studies of model microswimmers have significantly contributed to the understanding of the principles of self-propulsion we have today. However, only a small number of microswimmer types have been amenable to analytic modeling, and further development of such approaches is necessary to identify the key features of these active systems. Here we present a general perturbative calculation scheme for swimmers composed of beads interacting by harmonic potentials, driven by an arbitrary force protocol. The hydrodynamic interactions are treated using the Oseen and Rotne-Pragner approximations. We validate our approach by using 3 bead assemblies and comparing the results with the numerically obtained full-solutions of the governing equations of motion, as well as with the existing analytic models for a linear and a triangular swimmer geometries. While recovering the relation between the force and swimming velocity, our detailed analysis and the controlled level of approximation allow us to find qualitative differences already in the far field flow of the devices. Consequently, we are able to identify a behavior of the swimmer that is richer than predicted in previous models. Given its generality, the framework can be applied to any swimmer geometry, driving protocol and beads interactions, as well as in many swimmers problems.