Walzel Friedrich, Dijoux Jonathan, Jacomine Leandro, Harle Élodie, Muller Pierre, Charitat Thierry, Drenckhan Wiebke
Institut Charles Sadron, CNRS UPR22 - University of Strasbourg, 23 rue du Loess, BP 84047 67034 Strasbourg Cedex 2, France.
Soft Matter. 2024 Oct 30;20(42):8420-8435. doi: 10.1039/d4sm00919c.
Interactions between bubbles and drops play an important role in many physical phenomena. Whether we consider the interaction between two bubbles (drops) or between many (foams or emulsions), these interactions are complex and still poorly understood. An interesting case arises when two equal- and constant-volume bubbles (drops) interact with each other while being held by two axisymmetrically positioned frames of circular opening - a configuration which is frequently used in characterisation devices. The minimisation of the surface energy of this "double bubble" (or "double drop") configuration, constrained by the fixed volume and the frame boundaries, creates a complex landscape of shape spaces where physically stable shapes are separated by different types of instabilities. Combining experiments, finite element simulations and theory, we provide here for the first time a complete analysis of these shape spaces, considering the adhesive energy between the bubbles and the drops (expressed by the contact angle) as an additional control parameter. We provide the full shape diagrams for different contact angles (0°, 60° and 90°), including a detailed discussion of four types of instabilities. Two of these instabilities break the axisymmetry, while the two others break the connectivity of the ensemble. As far as we are aware, two of these instabilities have never been reported before. We accompany the shape and stability analysis with detailed mechanical characterisation using force and pressure measurements. Experiments, simulations and theory showing excellent agreement. This work will not only be useful in guiding the exploitation of double bubble (double drop) experiments on frames, but it also opens the possibility to exploit these configurations for the characterisation of increasingly complex bubble or drop interactions. Since the contact angle of 90° corresponds to an "imaginary" film separating the two bubbles (drops), our analysis naturally includes the shape and stability of a capillary bridge between two circular frames.
气泡与液滴之间的相互作用在许多物理现象中起着重要作用。无论我们考虑两个气泡（液滴）之间的相互作用，还是多个气泡（泡沫或乳液）之间的相互作用，这些相互作用都很复杂，目前仍知之甚少。当两个体积相等且恒定的气泡（液滴）在由两个轴对称放置的圆形开口框架固定时相互作用时，会出现一个有趣的情况——这种配置常用于表征装置中。在固定体积和框架边界的约束下，这种“双气泡”（或“双液滴”）配置的表面能最小化，产生了一个复杂的形状空间景观，其中物理上稳定的形状被不同类型的不稳定性分隔开。结合实验、有限元模拟和理论，我们首次对这些形状空间进行了全面分析，将气泡和液滴之间的粘附能（由接触角表示）作为一个额外的控制参数。我们给出了不同接触角（0°、60°和90°）下的完整形状图，包括对四种不稳定性类型的详细讨论。其中两种不稳定性会破坏轴对称性，而另外两种则会破坏整体的连通性。据我们所知，其中两种不稳定性以前从未被报道过。我们通过力和压力测量进行详细的力学表征，对形状和稳定性进行分析。实验、模拟和理论结果显示出极佳的一致性。这项工作不仅有助于指导在框架上进行双气泡（双液滴）实验，还为利用这些配置来表征日益复杂的气泡或液滴相互作用开辟了可能性。由于90°的接触角对应于分隔两个气泡（液滴）的“假想”薄膜，我们的分析自然包括了两个圆形框架之间毛细管桥的形状和稳定性。
