Chemically active droplets display complex self‐propulsion behavior in homogeneous surfactant solutions, often influenced by the interplay between diffusiophoresis and Marangoni effects. Previous studies have primarily considered these effects separately or assumed axisymmetric motion. To understand the full hydrodynamics, we investigate the motion of a two‐dimensional active droplet under their combined influences using weakly nonlinear analysis and numerical simulations. The impact of two key factors, the Péclet number () and the mobility ratio between diffusiophoretic and Marangoni effects (), on droplet motion is explored. We establish a phase diagram in the space, categorizing the boundaries between four types of droplet states: stationary, steady motion, periodic/quasi‐periodic motion, and chaotic motion. We find that the mobility ratio does not affect the critical for the onset of self‐propulsion, but it significantly influences the stability of high‐wavenumber modes as well as the droplet's velocity and trajectory. Scaling analysis reveals that in the high regime, the Marangoni and diffusiophoresis effects lead to distinct velocity scaling laws: and , respectively. When these effects are combined, the velocity scaling depends on the sign of the mobility ratio. In cases with a positive mobility ratio, the Marangoni effect dominates the scaling, whereas the negative diffusiophoretic effect leads to an increased thickness of the concentration boundary layer and a flattened scaling of the droplet velocity.

中文翻译：

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扩散电泳和马兰戈尼效应联合诱导的液滴自推进

化学活性液滴在均质表面活性剂溶液中表现出复杂的自推进行为，通常受到扩散电泳和马兰戈尼效应之间相互作用的影响。以前的研究主要是单独考虑这些影响或假设轴对称运动。为了了解完整的流体动力学，我们使用弱非线性分析和数值模拟研究了二维活性液滴在其综合影响下的运动。探讨了两个关键因素：佩克莱特数 () 以及扩散电泳效应和马兰戈尼效应之间的迁移率 () 对液滴运动的影响。我们在空间中建立了相图，对四种液滴状态之间的边界进行分类：静止、稳态运动、周期/准周期运动和混沌运动。我们发现，迁移率并不影响自推进的临界点，但它显着影响高波数模式的稳定性以及液滴的速度和轨迹。标度分析表明，在高状态下，马兰戈尼效应和扩散泳动效应分别导致不同的速度标度定律： 和 。当这些效应结合在一起时，速度缩放取决于迁移率的符号。在具有正迁移率的情况下，马兰戈尼效应主导缩放，而负扩散电泳效应导致浓度边界层厚度增加和液滴速度平坦缩放。