The drying of liquid droplets is a common phenomenon in daily life, and has long attracted special interest in scientific research. We propose a simple model to quantify the shape evolution of drying droplets. The model takes into account the friction constant between the contact line (CL) and the substrate, the capillary forces, and the evaporation rate. Two typical evaporation processes observed in experiments, i.e., the constant contact radius (CCR) and the constant contact angle (CCA), are demonstrated by the model. Moreover, the simple model shows complicated evaporation dynamics, for example, the CL first spreads and then recedes during evaporation. Analytical models of no evaporation, CCR, and CCA cases are given, respectively. The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model, and they are all subjected to experimental tests. The general model facilitates a quantitative understand...

中文翻译：

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液滴干燥

液滴的干燥是日常生活中的普遍现象，长期以来一直引起科学研究的特殊兴趣。我们提出了一个简单的模型来量化干燥液滴的形状演变。该模型考虑了接触线（CL）与基材之间的摩擦常数，毛细作用力和蒸发速率。该模型演示了实验中观察到的两种典型的蒸发过程，即恒定接触半径（CCR）和恒定接触角（CCA）。此外，简单的模型显示了复杂的蒸发动力学，例如，CL在蒸发过程中先扩散然后后退。分别给出了无蒸发，CCR和CCA情况的分析模型。通过解析模型获得的CL的比例定律或接触角随时间的函数与完整的数值模型一致，并且都经过了实验测试。通用模型有助于定量理解...