# Electrophoresis of active Janus particles

## TL;DR

This paper presents a theoretical analysis of active Janus particles' motion under external electric fields, revealing how their trajectories can be controlled and modeled as a pendulum-like system.

## Contribution

It introduces a perturbative scheme to analyze Janus particle dynamics, highlighting the influence of electric fields and surface activity on their orientation and movement.

## Key findings

- Janus particles' orientation dynamics resemble a mathematical pendulum.
- External electric fields can steer Janus particles toward targets.
- Surface activity affects the sensitivity of particle orientation to external fields.

## Abstract

We theoretically consider the dynamics of a self-propelled active Janus motor moving in an external electric field. The external field can manipulate the route of a Janus particle and enforce it to move towards the desired targets. To investigate the trajectory of this active motor, we use a perturbative scheme. At the leading orders of surface activity of the Janus particle and also the external field, the orientational dynamics of the Janus particles behave like a mathematical pendulum with an angular the velocity that is sensitive to both the electric field and surface activity of the motor.