Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics [A. Bouillant et al., Nat. Phys. 14, 1188 (2018)]. Motivated by these observations, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and thin-film equations governing the vapor flow, the profile of the deformable vapor-liquid interface, and thus the hydrodynamic forces and torques on the drop. In contrast to previous analytical models of Leidenfrost drops levitating above a flat surface which predict only symmetric solutions, we find that the symmetric Leidenfrost state is unstable above a critical drop radius: $R_1$ for a free drop and $R_2>R_1$ for an immobilized drop. In these respective cases, symmetry breaking is manifested in supercritical pitchfork bifurcations into steady states of pure rolling and constant angular velocity. In further qualitative agreement with the experiments, when a symmetry-broken immobilized drop is suddenly released it initially moves at an acceleration $\alpha g$, where $\alpha$ is an angle characterizing the slope of the liquid-vapor profile and $g$ is the gravitational acceleration; moreover, $\alpha$ exhibits a maximum with respect to the drop radius at a radius increasing with the temperature difference between the surface and the drop.

中文翻译：

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二维Leidenfrost车轮的自发动力学

最近的实验表明，在平坦的热表面上方被蒸气悬浮的液态莱顿弗罗斯特液滴可以表现出破坏对称性的自发动力学[A. Bouillant等。，Nat。物理 14，1188（2018）]。基于这些观察结果，我们在简化的二维模型的基础上理论上研究了莱顿弗罗斯特液滴的平移和旋转动力学，重点是相对于毛细管长度小的圆形液滴。该模型将作为刚性轮流动的液滴的运动方程式与控制蒸汽流动，可变形的气液界面轮廓以及控制液滴上的流体动力和扭矩的薄膜方程式耦合。与以前的仅在对称表面上飘浮的莱顿弗罗斯特液滴分析模型相反，我们发现对称的莱顿弗罗斯特状态在临界液滴半径以上是不稳定的：${\mathrm{[R}}_{\mathrm{1个}}$ 免费放送 ${\mathrm{[R}}_2>{\mathrm{[R}}_{\mathrm{1个}}$固定下来。在这些情况下，对称性破坏表现为超临界干草叉分叉成纯滚动和恒定角速度的稳态。与实验的进一步定性一致，当对称断裂的固定液滴突然释放时，其最初以加速度运动$\alpha G$，在哪里 $\alpha$ 是一个表征液体-蒸汽分布斜率的角度， $G$是重力加速度；此外，$\alpha$ 在表面半径和液滴之间的温度差越大，半径越大，液滴半径越大。