Numerical study of the Marangoni instability resulting in surface tension auto-oscillations: general regularities of...

Theoretical studies are performed to explain the mechanism of surface tension auto-oscillations recently found. The Marangoni instability in a system containing a surfactant droplet under the air-water interface is investigated numerically. The simulations, based on the equations of fluid mechanics, take into account convective diffusion and adsorption of the surfactant. The behavior of the system is determined by nonstationary concentration gradients that are nonuniform on the surface as well as in the normal to the surface direction. Initially a slow diffusion dissolution of the drop material takes place. The convective transfer of the surfactant is negligible, the surface tension remains nearly constant and the system parameters change rather slowly during the induction period. With the increase of the concentration gradients the system becomes unstable, resulting in a jump in the convection velocity, surface tension, and adsorption on the surface. The concentration and velocity distributions in the bulk and on the surface are obtained from the numerical solution of the problem. The contributions of different mechanisms of the mass transfer are compared in different stages of the process.