This paper investigates the linear stability of a liquid jet exposed to subsonic crossflow with aluminum particles and surfactant. A dispersion relation for the disturbances at the interface is obtained. The characteristics of metal particle are shown in the expressions of liquid density, viscosity and surface tension. The results reveal that the non-dimensional surface tension gradient and surfactant diffusivity show their strong coupling effects on the instability features. The maximum growth rate and cutoff wavenumber reduce with the increase of the surface tension gradient when the surfactant diffusivity approaches to zero. The maximum growth rate increases while the cutoff wavenumber rarely changes with the enhancement of surfactant diffusivity when the effect of surface tension gradient is ignored. The effect of surface tension gradient or surfactant diffusivity on the instability characteristics also relates to Laplace numbers when the effect of the other one parameter cannot be neglected. In addition, the effects of other non-dimensional physical parameters such as liquid Reynolds number on the instability features at the interface are discussed as well.

中文翻译：

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铝粒子和表面活性剂暴露于亚音速错流的液体射流的线性稳定性分析

本文研究了暴露于亚音速错流下的含铝颗粒和表面活性剂的液体射流的线性稳定性。获得了界面处扰动的色散关系。金属颗粒的特性在液体密度，粘度和表面张力的表达式中显示。结果表明，无量纲表面张力梯度和表面活性剂的扩散率对不稳定性具有较强的耦合作用。当表面活性剂扩散率接近零时，最大增长率和截止波数随表面张力梯度的增加而降低。当忽略表面张力梯度的影响时，随着表面活性剂扩散率的增加，最大生长速率增加而截止波数很少改变。当不能忽略其他一个参数的影响时，表面张力梯度或表面活性剂扩散率对不稳定性的影响也与拉普拉斯数有关。另外，还讨论了其他无量纲的物理参数，例如液体雷诺数，对界面处的不稳定性特征的影响。