Collisions and rebounds of chemically active droplets

Active droplets swim as a result of the nonlinear advective coupling of the distribution of chemical species they consume or release with the Marangoni flows created by their non-uniform surface distribution. Most existing models focus on the self-propulsion of a single droplet in an unbounded fluid, which arises when diffusion is slow enough (i.e. beyond a critical Peclet number, $Pe_{c}$ ). Despite its experimental relevance, the coupled dynamics of multiple droplets and/or collision with a wall remains mostly unexplored. Using a novel approach based on a moving fitted bi-spherical grid, the fully coupled nonlinear dynamics of the chemical solute and flow fields is solved here to characterise in detail the axisymmetric collision of an active droplet with a rigid wall (or with a second droplet). The dynamics is strikingly different depending on the convective-to-diffusive transport ratio, $Pe$ : near the self-propulsion threshold (moderate $Pe$ ), the rebound dynamics is set by chemical interactions and is well captured by asymptotic analysis; in contrast, for larger $Pe$ , a complex and nonlinear combination of hydrodynamic and chemical effects set the detailed dynamics, including a closer approach to the wall and a velocity plateau shortly after the rebound of the droplet. The rebound characteristics, i.e. minimum distance and duration, are finally fully characterised in terms of $Pe$ .