Modeling of the Marangoni Instability of Uniform Diffusion through an Interface in Weightlessness Conditions

Resumo

The surfactant diffusion through the vertical interface in a system of two immiscible liquids filling a horizontal channel has been studied in a two-dimensional formulation. The densities of the base liquids were initially set equal to the surfactant density. Therefore, all the subsequent density variations in the system are determined only by the contraction effect. Under nonunifrom diffusion the interfacial tension is a function of the local surfactant concentration, which gives rise to Marangoni convection. Since there are uncontrolled surface-active impurities in the system, the capillary motion is initiated in a threshold manner. It is shown that at the initial stage, despite the presence of gravity, the Marangoni convection is in the form of a series of periodically emerging paired vortices located symmetrically relative to the channel axis (as in weightlessness conditions). As the vertical density difference in the channel increases, the number of vortex pairs is reduced to one. A full-scale experiment, during which the structure of the flows and surfactant concentration fields near the interface was visualized, has been performed to verify the results of numerical simulations. The dynamics of the oscillatory mode of convection has been studied. The results of the numerical and full-scale experiments have been shown to be in qualitative agreement. The pattern of the surfactant concentration fields and stream functions in the channel as well as the time dependence of the maximum value of the stream function are presented for several values of the Marangoni and Grashof numbers. It has been found that at sufficiently large Marangoni numbers (Ma ≥ 50 000) the diffusion process gives rise to instability in the system of immiscible liquids and a soluble surfactant, provided that their densities are equal, even in the absence of contraction.