Exact axisymmetric interaction of phoretically active Janus particles

TL;DR

This paper derives an exact analytical solution for the axisymmetric interaction and relative motion of two chemically active Janus particles, revealing complex behaviors including multiple fixed points and stability depending on their properties.

Contribution

It provides a novel exact solution for the full chemical and hydrodynamic interactions of Janus particles, enabling detailed analysis of their relative dynamics.

Findings

The relative velocity can be expressed as a linear sum of geometrical functions.

The system can have up to three fixed points with varying stability.

Regime diagrams illustrate behaviors based on activity and mobility parameters.

Abstract

We study the axisymmetric interaction of two chemically active Janus particles. By relying on the linearity of the field equations and symmetry arguments, we derive a generic solution for the relative velocity of the particles. We show that regardless of the chemical properties of the system, the relative velocity can be written as a linear summation of geometrical functions which only depend on the gap size between the particles. We evaluate these functions via an exact approach which accounts for the full chemical and hydrodynamic interactions. Using the obtained solution, we expose the role of each compartment in the relative motion, and also discuss the contribution of different interactions. We then show that the dynamical system describing the relative motion of two Janus particles can have up to three fixed points. These fixed points can be stable or unstable, indicating that a system of two Janus particles can exhibit a variety of nontrivial behaviour depending on their initial gap size, and their chemical properties. We also look at the specific case of Janus particles in which one compartment is inert, and present regime diagrams for their relative behaviour in the activity-mobility parameter space.