A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as that of a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer with increasing surfactant concentration through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension.

中文翻译：

---

表面张力对紧密堆积的颗粒单层表面活性剂驱动的断裂的影响

相场模型用于捕获颗粒状单分子层中表面活性剂驱动的裂缝模式的形成。该模型适用于密排系统，其中单层的机械响应可以近似为线性弹性固体的机械响应。该模型通过破坏场的演化来估算表面活性剂浓度增加时单层拉伸强度的损失。构造初始边界值问题，并通过位移和表面活性剂破坏场的有限元近似在空间上离散化。基于模型的模拟与现有实验观察结果之间的比较表明，在裂缝模式和裂缝过程的时间尺度上都存在质的匹配。表面张力差异的重要性通过无量纲参数进行量化，揭示了将不同断裂方式分开的阈值。这些发现得到了新执行的实验的支持，这些实验验证了模型并证明了裂缝模式对表面张力差异的强烈敏感性。