Mode instabilities and dynamic patterns in a colony of self-propelled surfactant particles covering a thin liquid layer

TL;DR

This paper models the complex dynamics of self-propelled surfactant particles on a thin liquid film, revealing how their interactions and physical effects lead to diverse pattern formations including waves and irregular structures.

Contribution

It introduces a coupled long-wave model capturing the nonlinear dynamics of self-propelled particles and film height, analyzing pattern formation driven by physical effects and active motion.

Findings

Particles self-organize into regular standing and traveling waves.

The model predicts diverse irregular pattern formations.

Physical effects can stabilize or destabilize the film depending on parameters.

Abstract

We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. Although the particles predominantly swim normal to the free film surface, their motion also has a component parallel to the film surface. The coupled dynamics of the swimmer density and film height profile is captured in a long-wave model allowing for diffusive and convective transport of the swimmers (including rotational diffusion). The dynamics of the film height profile is determined by three physical effects: the upward pushing force of the swimmers onto the liquid-gas interface that always destabilizes the flat film, the solutal Marangoni force due to gradients in the swimmer concentration that always acts stabilising, and finally the rotational diffusion of the swimmers together with the in-plance active motion that acts either stabilising or destabilising. After reviewing and extending the analysis of the linear stability of the flat film with uniform swimmer density, we analyse the full nonlinear dynamic equations and show that point-like swimmers, which only interact via long-wave deformations of the liquid film, self-organise in highly regular (standing, travelling and modulated waves) and various irregular patterns for swimmer density and film height.