# Superfast collective motion of magnetic particles

## TL;DR

This paper demonstrates that magnetic particles at water-air interfaces can form complex, fast-moving aggregates called flotillas, whose speed scales with the square root of the number of particles, enabling rapid magnetic delivery systems.

## Contribution

It introduces a theoretical model explaining the superfast collective motion of magnetic particle flotillas, surpassing the speed of individual chains or spindles.

## Key findings

- Flotillas move faster than single chains or spindles.
- Speed scales with the square root of particle number.
- Theoretical insights guide magnetic delivery system design.

## Abstract

It is well-known that magnetic forces can induce a formation of densely packed strings of magnetic particles or even sheafs of several strings (spindles). Here we show that in a sufficiently strong magnetic field, more complex aggregates of particles, translating with a much faster speed than would be for a single particle or even a spindle, can be assembled at the water-air interface. Such a superfast flotilla is composed of many distant strings or spindles, playing a role of its vessels, and moves, practically, as a whole. We provide theoretical results to interpret the effect of a collective motion of such magnetic vessels. Our theory shows that, in contrast to an isolated chain or spindle, which velocity grows logarithmically with the number of magnetic particles, the speed of the interface flotilla becomes much higher, being proportional to the square root of their number. These results may guide the design of magnetic systems for extremely fast controlled delivery.