We discuss a simple experiment investigating the shrinkage of surface soap bubbles sitting on a thin solid plate with a circular orifice located under the apex of the bubble. We identify three different shrinking regimes, the occurrence of which depends on a combination of key parameters that include the ratio between initial bubble and orifice sizes and physicochemical properties of the fluid system. For low-viscosity liquids and/or large ratios, a bubble remains quasi-hemispherical as shrinking proceeds. In contrast, for liquids with sufficiently large viscosities and/or small geometric ratios, a bubble seeks the shape of a spherical cap while the air inside it escapes through the orifice. In this case, shrinking proceeds with a bubble foot that either recedes over time or does not move for the largest viscosities and/or smallest ratios. We use basic physical arguments to rationalize the three identified regimes and to explain the shrinking dynamics. Specifically, this model which captures observations and measurements is based on Bernoulli's principle for the air flow, volume conservation, and a friction law that accounts for viscous dissipation at the moving bubble foot.

中文翻译：

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缩小表面肥皂泡的不同方案

我们讨论了一个简单的实验，该实验研究的是坐在一块薄实心板上的表面肥皂泡的收缩情况，该固体板上有一个位于气泡顶点下方的圆形孔。我们确定了三种不同的收缩方式，其发生取决于关键参数的组合，这些参数包括初始气泡和孔口尺寸之间的比率以及流体系统的理化性质。对于低粘度液体和/或大比例液体，随着收缩的进行，气泡仍保持准半球形。相反，对于具有足够大的粘度和/或小的几何比的液体，气泡寻找球形帽的形状，而其内部的空气则通过孔逸出。在这种情况下，气泡会随着时间的推移而缩回，或者在最大粘度和/或最小比率下不会移动，从而导致缩孔。我们使用基本的物理论据来合理化三个确定的制度并解释不断缩小的动力。具体来说，该模型捕获了观察和测量结果，是基于伯努利的空气流动原理，体积守恒原理和考虑到运动气泡脚处的粘性耗散的摩擦定律。