We experimentally and numerically investigate collective behaviors of oil droplets floating on a surfactant solution in a narrow circular channel. A closed environment where a glass cover is placed on the channel shown that ethyl salicylate droplets on the surface of sodium dodecyl sulfate solution exhibit transient oscillatory dynamics, leading to the formation of a single cluster via the merging of sub-clusters. When the glass cover is removed, oscillatory behavior resumes, and the cluster breaks up. To understand these experimental findings, we introduce a mathematical model that combines equations of motion for droplets with a reaction–diffusion system, where droplet dynamics and the chemical reactions are considered on the one-dimensional surface, and the diffusion of chemicals in the air phase and the water phase is treated in the two-dimensional region. Our model successfully reproduces transient oscillations and the characteristics of cluster formation, and the effect of the glass cover. We argue that the attractive long-range interaction due to the global concentration profile of the solution suffices for the cluster formation.

我们通过实验和数值研究了漂浮在狭窄圆形通道中的表面活性剂溶液上的油滴的集体行为。在通道上放置玻璃盖的封闭环境表明，十二烷基硫酸钠溶液表面上的水杨酸乙酯液滴表现出瞬态振荡动力学，导致通过子簇合并形成单个簇。当玻璃盖被移除时，振荡行为恢复，并且集群分裂。为了理解这些实验结果，我们引入了一个数学模型，该模型将液滴的运动方程与反应扩散系统相结合，其中在一维表面上考虑液滴动力学和化学反应，在二维区域处理化学物质在气相和水相中的扩散。我们的模型成功地再现了瞬态振荡和簇形成的特征，以及玻璃盖的影响。我们认为，由于溶液的全局浓度分布引起的有吸引力的长程相互作用足以形成簇。