Axisymmetric Pushing of a Spherical Cargo using an Active Spherical Janus Motor

TL;DR

This paper develops a numerical approach to analyze the axisymmetric flow interactions between a self-propelling Janus sphere and an inert cargo, revealing regimes of hovering and synchronized motion.

Contribution

It introduces an analog to the twin multipole approach for flow analysis and explores the effects of size and separation on cargo-motor interactions.

Findings

Identification of a hovering regime at finite separation distance.

Conditions for equal velocity translation of both spheres.

Validation of the numerical approach with literature and COMSOL.

Abstract

We analyze the interaction between a self-diffusiophoretic spherical Janus motor and an inert spherical cargo particle in an axisymmetric configuration in the Stokes regime. To study the different configurations of the two spheres and their motions, we develop an analog to the twin multipole approach to numerically determine the axisymmetric stream function for the flow field. We verify the validity and accuracy of this approach using existing literature and COMSOL Multiphysics. We study the effects of the size of the Janus cap, the relative ratio of sizes of the two spheres, and their separation distance on their interactions. For the case of a stationary cargo, we identify the existence of a distinct regime where the Janus motor hovers at a finite separation distance from the cargo and summarize the results using a phase diagram. In the presence of a freely moving cargo, we analyze the steady terminal velocities of the Janus motor and the cargo to identify distinct conditions at which the two spheres can translate with equal velocities while maintaining a finite separation distance.