We investigate the growth of aggregates made of adhesive frictionless oil droplets, piling up against a solid interface. Monodisperse droplets are produced one by one in an aqueous solution and float upward to the top of a liquid cell where they accumulate and form an aggregate at a flat horizontal interface. Initially, the aggregate grows in 3D until its height reaches a critical value. Beyond a critical height, adding more droplets results in the aggregate spreading in 2D along the interface with a constant height. We find that the shape of such aggregates, despite being granular in nature, is well described by a continuum model. The geometry of the aggregates is determined by a balance between droplet buoyancy and adhesion as given by a single parameter, a “granular” capillary length, analogous to the capillary length of a liquid.

中文翻译：

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连续体模型应用于液滴和水坑的颗粒类似物

我们研究了由粘附性无摩擦油滴制成的聚集体的生长，堆积在固体界面上。单分散液滴在水溶液中一个接一个地产生，并向上漂浮到液池的顶部，在那里它们聚集并在平坦的水平界面处形成聚集体。最初，聚合以3D方式增长，直到其高度达到临界值为止。超过临界高度，添加更多的液滴会导致聚集体以恒定的高度沿界面以2D方式扩散。我们发现，这种聚集体的形状尽管本质上是颗粒状的，但可以通过连续模型很好地描述。聚集体的几何形状由液滴浮力和附着力之间的平衡决定，该平衡由单个参数“类似于液体的毛细管长度”的“颗粒”毛细管长度给出。