Self-propelled active drops: a history of interaction.

Summary Once immersed in a liquid saturated with surfactants, a microdrop composed of water or oil can self-propel at a speed of a few rays per second. Although the exact physico-chemical origin of this phenomenon is still debated, recent work has shown that it is linked to the solubilization of these drops in their medium. An active drop appears to emit a set of chemical species, called solute, which increases the surface tension. Consequently, an inhomogeneous distribution of solute at the interface of the drop generates a so-called Marangoni flow that propels the drop. The self-propulsion is then explained by an instability resulting from the coupling between the transport dynamics of the solute and the resulting Marangoni flow.This thesis aims to study the interactions between several of these drops or in the presence of confinement. The first chapter introduces general notions of low Reynolds fluid mechanics as well as a description of experimentally studied active droplet systems. The second chapter presents the mathematical framework modeling the self-propulsion of a single drop, and then provides a discussion dealing with the hydro-chemical interactions expected in the presence of several drops or a wall. The third chapter presents an exact derivation of the hydro-chemical interactions between an active drop and a wall in the axisymmetric case. This approach allowed to quantify the influence of the solute advection on the collision dynamics and to raise delay effects occurring at high Peclet number. In the fourth chapter, we study the consequences on the collision dynamics of a size difference between two active drops. It is then shown that even a small difference in radius can lead to very different regimes called rebound, pursuit and pause. The fifth chapter introduces a simplified model of the dynamics of an active drop, used in the study of oblique collisions. If a symmetrical collision tends to align the drops, asymmetrical initial conditions can conversely disperse them. Finally, the sixth chapter brings the conclusion of this manuscript and suggests various perspectives for the further study of active drop interactions.