Solutocapillary onset of surface vortices in an air-sheared thin film

A quiescent pure water layer driven by a gentle, radially spreading air jet displays a smooth, axisymmetric outflow. When even a trace of a soluble, non-ionic surfactant is present, that symmetry breaks: after a brief stagnation the interface reorganizes into a persistent pair of counter-rotating vortices centered around the jet axis. Particle-tracking velocimetry reveals three stages — radial expansion, arrest, and dipolar swirl.

We model the phenomenon by coupling Stokes flow in the film to an adsorbed monolayer endowed with a coverage-dependent Marangoni elasticity. Linearization about the base profile of the surfactant concentration yields a non-local eigenvalue problem: the first azimuthal disturbance induces a surface velocity proportional to the surface tension disturbance, converting the transport equation into a reaction–diffusion system. A reaction term of hydrodynamic origin now competes with surface diffusion and bulk viscosity. The resulting dispersion relation highlights two factors that raise the critical air shear required for instability:

• a contrast in surfactant elastic modulus between the dilute core and the nearly saturated outer rim, and
  
  a thin-film geometry that magnifies stresses at the small inner length scale where the air jet first turns parallel to the interface.

Together these ingredients account for the experimentally observed onset and for the exclusive emergence of the dipolar mode. The analysis shows that a non-local Marangoni feedback, modulated by spatial variations in interfacial elasticity, is sufficient to destabilize millimeter-scale thin films and offers a framework for controlling solutocapillary instabilities in coatings, foams, and physiological layers.