Modeling of the Marangoni instability of uniform diffusion through the interphase boundary in weightlessness conditions

Abstract

In this paper, the process of surfactant diffusion through the vertical interphase boundary in the system of two immiscible liquids filling a horizontal channel was studied in a two-dimensional formulation. Densities of the base liquids were initially set equal to the surfactant density. Therefore, all subsequent changes of density in the system were caused only by the effect of contraction. At the nonunifrom diffusion, the interfacial tension is the function of the local surfactant concentration, which gives rise to the Marangoni convection. Since the system contained uncontrolled surface-active impurities, the capillary flow was initiated in a threshold manner. It was shown that at the initial stage, despite the action of the gravitational force, the Marangoni convection occurred in the form of a series of periodic, paired vortices located symmetrically about the channel axis (the same as under zero gravity). As the vertical density difference increased, the number of vortex pairs reduced to a single pair. The results of numerical simulation were verified by performing a full-scale experiment, during which visualization of the flow structure and surfactant concentration fields near the interface was realized. The dynamics of the oscillatory convection mode was studied. The analysis of the results of the numerical and full scale experiments revealed their qualitative agreement. For a few values of the Marangoni and Grashof numbers, the patterns of surfactant concentration fields and stream functions were constructed in addition to the plot of variation of the stream function maximum versus time. It was found that at rather high values of the Marangoni number (Ma≥50000) the diffusion process in the system of immiscible liquids and a soluble surfactant of equal densities leads to the onset of instability even in the absence of the contraction effect.