Two floating camphor particles interacting through lateral capillary force

TL;DR

This paper models the interactions of two floating camphor particles on water, incorporating capillary forces and chemical concentration gradients, revealing six motion modes and bifurcation-based mode transitions.

Contribution

It introduces a novel mathematical model including lateral capillary forces and analyzes mode transitions via bifurcation theory.

Findings

Six distinct modes of particle motion identified.

Mode transitions explained through bifurcation analysis.

Capillary forces significantly influence particle dynamics.

Abstract

We consider a mathematical model for a two-particle system driven by the spatial gradient of a concentration field of chemicals with conservative attractive interactions in one dimension. This setup corresponds to an experimental system with floating camphor particles at a water surface. Repulsive interaction is introduced, as well as self-propelling force, through the concentration field of camphor molecules at the water surface. Here we newly adopt the attractive lateral capillary force due to the deformation of the water surface. The particles experience competing dissipative repulsion and conservative attraction. We numerically investigated the mathematical model, and found six different modes of motion. The theoretical approach revealed that some of such mode transitions can be understood in terms of bifurcation.