Cooperative dynamics and self-propulsion of active matter at interfaces

Active particles, and more generally active matter, are known for their ability to move in a given medium by harnessing energy in their surrounding or by carrying their own energy reservoir. A large field of interest regarding active particles is their collective behaviour due to the interactions between individual components of the active system. Examples can be found in biology, medicine, microfluidic or chemistry. In this thesis, the role of individuals in active matter is investigated
in two peculiar systems: walking droplets and magnetocapillary microswimmers. Each system lies at an liquid-air interface and relies on the deformation of the liquid surface in their dynamics.
Walking droplets are known to propel themselves thanks to the standing capillary waves they generate at each impact on the liquid interface. The persistence time of those waves can be controlled which allows to keep images of the droplet on the interface and to alter the particle motion. This is the memory of the walking droplets. Changing this persistence time allows to change the number of images of the droplet and to explore different dynamics. The limit of extremely large persistence time is considered in this manuscript. In free space, this unique wave
memory dynamics allows to generate the first example of deterministic run and tumble dynamics widely encountered in biology. This behaviour finds its origin in the wavefield which traps temporarily the walking droplets. The properties of this run and tumble dynamics are shown to by directly related to the memory stored in the wavefield. If placed in an harmonic potential, the walking droplet is forced to continuously interact with this own wavefield. It is shown that the
waves self-organise. In this case, the energy stored in the wavefield mimics an equipartition of energy as well as a minimisation principle. Magnetocapillary microswimmers use the liquid interface in order to self-assemble and the liquid underneath in order to move thanks to hydrodynamic interactions and non-reciprocal deformation. This thesis models two different experimental microswimmers: the linear microswimmer better known as the NajafiGolestanian
microswimmer and the triangular magnetocapillary microswimmer. In each case, the non-reciprocal deformation required for the swimming dynamics is at the centre of the discussion. For the linear structure, non-reciprocity is produced by breaking the spatial symmetry of the swimmer. We also discuss the importance of the particles inertia in this low Reynolds dynamics. For the triangular structure, a new swimming mechanism is highlighted where the particles rotation and the structure deformation act cooperatively to generate the translation of the swimmer along the interface. This findings constitute the first step towards the modelisation of larger structures and more efficient swimmers for application in microfluidic.