二维Leidenfrost轮的自发动力学
Spontaneous dynamics of two-dimensional Leidenfrost wheels
摘要：
最近的实验表明，莱顿弗罗斯特液滴在平坦的热表面上被其蒸汽悬浮，可以表现出破胶的自发动力学（A。Bouillant等人，Nature Physics，14 1188-1192，2018）。出于这些观察，我们从理论上研究的平移和旋转动力学的Leidenfrost滴的基础上，一个简化的二维模型，专注于近圆形的下降相对于毛细管长度小。该模型耦合的液滴，作为一个刚性的车轮，和薄膜方程的蒸汽流，变形的汽-液界面的轮廓，从而液滴上的水动力和扭矩的运动方程。与以前的分析模型Leidenfrost下降漂浮在一个平面上，它只预测对称的解决方案，我们发现，对称Leidenfrost状态是不稳定的临界滴半径以上：$R_1$为自由滴和$R_2>R_1$为固定滴。在这两种情况下，对称性破缺表现为超临界叉状分叉，进入纯滚动和恒定角速度的稳定状态。与实验进一步定性一致的是，当破裂的固定液滴突然释放时，它最初以加速度$αg$移动，其中$α$是表征液-汽分布斜率的角度，$g$是重力加速度;此外，$α$相对于液滴半径呈现最大值，半径随着表面和液滴之间的温差而增加。
英文摘要：
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., Nature Physics, 14 1188-1192, 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 $αg$, where $α$ is an angle characterizing the slope of the liquid-vapor profile and $g$ is the gravitational acceleration; moreover, $α$ exhibits a maximum with respect to the drop radius, at a radius increasing with the temperature difference between the surface and the drop.
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