# The near and far of a pair of magnetic capillary disks

## TL;DR

This paper investigates the complex interactions of magnetic and capillary forces in micro-raft systems, combining theory and experiments to understand their orbital and assembled behaviors at microscopic scales.

## Contribution

It provides a comprehensive model explaining the dynamics of micro-rafts influenced by capillary and magnetic interactions, integrating short and long-range physics.

## Key findings

- Orbital patterns are governed by short-range capillary interactions.
- Static assembled structures are explained by capillary far-field effects.
- A unified model successfully predicts new micro-raft behaviors.

## Abstract

Control on microscopic scales depends critically on our ability to manipulate interactions with different physical fields. The creation of micro-machines therefore requires us to understand how multiple fields, such as surface capillary or electro-magnetic, can be used to produce predictable behaviour. Recently, a spinning micro-raft system was developed that exhibited both static and dynamic self-assembly [Wang et al. (2017) Sci. Adv. 3, e1602522]. These rafts employed both capillary and magnetic interactions and, at a critical driving frequency, would suddenly change from stable orbital patterns to static assembled structures. In this paper, we explain the dynamics of two interacting micro-rafts through a combination of theoretical models and experiments. This is first achieved by identifying the governing physics of the orbital patterns, the assembled structures, and the collapse separately. We find that the orbital patterns are determined by the short range capillary interactions between the disks, while the explanations of the other two behaviours only require the capillary far field. Finally we combine the three models to explain the dynamics of a new micro-raft experiment.