We consider a colony of point-like self-propelled surfactant particles(swimmers) without direct interactions that cover a thin liquid layer on asolid support. Although the particles predominantly swim normal to the freefilm surface, their motion also has a component parallel to the film surface.The coupled dynamics of the swimmer density and film height profile is capturedin a long-wave model allowing for diffusive and convective transport of theswimmers (including rotational diffusion). The dynamics of the film heightprofile is determined by three physical effects: the upward pushing force ofthe swimmers onto the liquid-gas interface that always destabilizes the flatfilm, the solutal Marangoni force due to gradients in the swimmer concentrationthat always acts stabilising, and finally the rotational diffusion of theswimmers together with the in-plance active motion that acts either stabilisingor destabilising. After reviewing and extending the analysis of the linearstability of the flat film with uniform swimmer density, we analyse the fullnonlinear dynamic equations and show that point-like swimmers, which onlyinteract via long-wave deformations of the liquid film, self-organise in highlyregular (standing, travelling and modulated waves) and various irregularpatterns for swimmer density and film height.
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