# Optimal motion of triangular magnetocapillary swimmers

## TL;DR

This paper numerically investigates the optimal motion of triangular magnetocapillary swimmers at liquid interfaces, revealing how external magnetic field frequency and inter-particle distance influence swimmer speed, supported by simulations and bead-spring models.

## Contribution

It introduces a hybrid simulation approach to analyze magnetocapillary swimmer dynamics and identifies optimal frequencies for maximum speed based on particle relaxation times.

## Key findings

- Maximum swimmer speed depends sharply on magnetic field frequency.
- Optimal frequency is centered around the particle's relaxation time.
- Increasing inter-particle distance reduces maximum speed.

## Abstract

A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the discrete element method. After investigating the equilibrium properties of a single, two and three particles at the interface, we demonstrate a controlled motion of the swimmer formed by three particles. It shows a sharp dependence of the average center-of-mass speed on the frequency of the time-dependent external magnetic field. Inspired by experiments on magnetocapillary microswimmers, we interpret the obtained maxima of the swimmer speed by the optimal frequency centered around the characteristic relaxation time of a spherical particle. It is also shown that the frequency corresponding to the maximum speed grows and the maximum average speed decreases with increasing inter-particle distances at moderate swimmer sizes. The findings of our lattice Boltzmann simulations are supported by bead-spring model calculations.