Collective surfing of two self-propelled swimmers laden liquid-air interface with the aid of self-induced Marangoni flow *

Some bacterial species such as Bacillus subtilis, Flavobacteria, etc. are known to produce a certain type of chemical (surfactin), which lowers the surface tension of the carrier fluid and creates a surface tension-driven Marangoni flow. We have studied the motion of two hydrodynamically coupled force-free, swimmers (pushers) confined to move along a planar liquid-air interface without and with the presence of self-induced Marangoni flow. In the absence of the Marangoni flow, we reported a closed analytical form of two types of linearly unstable planar rotational equilibria. In type 1 orbit, the pushers follow a unique circular trajectory, where the swimmers are always oriented head-to-head. In type 2 orbit, the pushers are moving along circles with different radii. In both cases, the relative orientation between the pushers and their distance remains constant. Our numerical results reveal the possibility of a persistent stable orbiting motion of two pushers in the presence of self-induced Marangoni flow. All simulations were performed at low Reynolds number and non-zero Peclet number.