Theoretical description of repeated surface-tension auto-oscillations

A mathematical model is proposed to follow the behavior of a system where a droplet of a surfactant with limited solubility on the tip of a capillary under the free liquid surface dissolves in a container with a unity aspect ratio. Numerical simulations show that instability repeatedly arises and fades in the system, resulting in auto-oscillations of the surface tension in agreement with the experimental data. The system evolution during the oscillation is discussed in detail. It is established that the presence of a boundary in the radial direction is a necessary precondition for the appearance of the second and following oscillations.