Numerical Study of a Microscopic Artificial Swimmer

TL;DR

This paper presents a detailed numerical analysis of a microscopic artificial swimmer, modeling its dynamics and efficiency based on physical parameters, and compares the results with experimental observations.

Contribution

It introduces a bead-spring model for the magnetic filament and explores how various parameters affect the swimmer's velocity and efficiency, providing new insights into its operation.

Findings

Velocity depends on shape, magnetic field strength, and oscillation frequency.

Load size affects the trade-off between velocity and efficiency.

Swimmer's direction undergoes a symmetry-breaking transition with increasing oscillation amplitude.

Abstract

We present a detailed numerical study of a microscopic artificial swimmer realized recently by Dreyfus et al. in experiments [R. Dreyfus et al., Nature 437, 862 (2005)]. It consists of an elastic filament composed of superparamagnetic particles that are linked together by DNA strands. Attached to a load particle, the resulting swimmer is actuated by an oscillating external magnetic field so that it performs a non-reciprocal motion in order to move forward. We model the superparamagnetic filament by a bead-spring configuration that resists bending like a rigid rod and whose beads experience friction with the surrounding fluid and hydrodynamic interactions with each other. We show that, aside from finite-size effects, its dynamics is governed by the dimensionless sperm number, the magnitude of the magnetic field, and the angular amplitude of the field's oscillating direction. Then we study the mean velocity and the efficiency of the swimmer as a function of these parameters and the size of the load particle. In particular, we clarify that the real velocity of the swimmer is influenced by two main factors, namely the shape of the beating filament (determined by the sperm number and the magnetic-field strength) and the oscillation frequency. Furthermore, the load size influences the performance of the swimmer and has to be chosen as a compromise between the largest swimming velocity and the best efficiency. Finally, we demonstrate that the direction of the swimming velocity changes in a symmetry-breaking transition when the angular amplitude of the field's oscillating direction is increased, in agreement with experiments.