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.

中文翻译：

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在失重条件下通过界面对均匀扩散的 Marangoni 不稳定性进行建模

在二维配方中研究了在填充水平通道的两种不混溶液体系统中通过垂直界面的表面活性剂扩散。基液的密度最初设定为等于表面活性剂的密度。因此，系统中所有随后的密度变化仅由收缩效应决定。在非均匀扩散下，界面张力是局部表面活性剂浓度的函数，这会引起 Marangoni 对流。由于系统中存在不受控制的表面活性杂质，毛细管运动以阈值方式启动。结果表明，在初始阶段，尽管存在重力，Marangoni 对流的形式是一系列周期性出现的成对涡旋，它们相对于通道轴对称（如在失重条件下）。随着通道中垂直密度差异的增加，涡旋对的数量减少到一个。为了验证数值模拟的结果，进行了全尺寸实验，在该实验期间，界面附近的流动结构和表面活性剂浓度场被可视化。已经研究了振荡对流模式的动力学。数值和全尺寸实验的结果已被证明在定性上是一致的。对于 Marangoni 和 Grashof 数的几个值，给出了通道中表面活性剂浓度场和流函数的模式以及流函数最大值的时间依赖性。已经发现，在足够大的马兰戈尼数 (Ma ≥ 50 000) 下，扩散过程会导致不混溶液体和可溶性表面活性剂的系统不稳定，只要它们的密度相等，即使没有收缩。