Steady state propulsion of chemically active drops along a wall

Active drops swim at the micron scale by utilizing the non-linear coupling between the advective transport of a chemical solute they emit, and the Marangoni flows generated by this solute's distribution. This self-propulsion is well studied in an unbounded fluid, where it occurs above a critical advective-to-diffusive transport ratio (i.e., Péclet number). However, the influence of a confining rigid wall on the propulsion of an active drop has remained essentially unexplored, despite its prevalence in experiments. We therefore investigate the steady state propulsion of a model active droplet parallel to a passive rigid wall, to which it is confined by a constant external force (e.g., gravity). Using a numerical framework based on a non-axisymmetric bi-spherical decomposition, we provide critical physical insights on the drop's long-time propulsion as a function of its confinement and the Péclet number.