水平圆柱间的液桥：重力与电场的影响
Liquid bridges between horizontal cylinders: effects of gravity and electric fields
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中文总结 AI 辅助
本文结合实验、建模与模拟，研究水平圆柱间液桥的形状与动力学，揭示电场抵消重力使液桥变扁平的规律，所建降阶模型可准确预测其稳态与过阻尼动力学。
中文摘要 AI 辅助
本文通过实验、降阶数学建模和数值模拟研究了悬浮于两个平行水平圆柱间的液桥，考虑了带电与不带电两种构型，圆柱作为电极可施加电势差。初始研究聚焦于平衡态液桥形状，仅在不带电情形下分析动力学。实验中研究了变压器油液桥，将其建模为理想电介质。电场可抵消重力效应，使液桥上升并变得更扁平，其形状可通过含非局域电场贡献的Young-Laplace型方程很好地描述，该方程的电场贡献采用边界元法计算。通过伪弧长延拓构造这些解的分岔图，以表征液桥形状对液体体积和电场强度的依赖关系。在无电场时，基于Onsager变分原理开发的降阶模型分析向平衡态的瞬态弛豫过程，并与直接数值模拟结果对比。在宽参数范围内，降阶模型预测的稳态与完整公式的稳态吻合度高，且在过阻尼 regime 下能很好地捕捉动力学行为。
英文摘要
Liquid bridges suspended between two parallel horizontal cylinders are studied using experiments, reduced-order mathematical modelling and numerical simulations. Both non-electrified and electrified configurations are considered, with the cylinders acting as electrodes between which a potential difference can be applied. The initial focus is on equilibrium bridge shapes, while the dynamics is examined only in the non-electrified case. In the experiments, transformer-oil bridges are investigated and modelled as perfect dielectrics. The electric field counteracts the gravitational effects and causes the bridges to rise and become flatter, with shapes that are well described by Young--Laplace-type equations containing non-local electric-field contributions evaluated using a boundary-element method. Bifurcation diagrams of these solutions are constructed by pseudo-arclength continuation to characterise the dependence of bridge shapes on liquid volume and electric-field strength. In the absence of an electric field, the transient relaxation to equilibrium is analysed using a reduced-order model developed using Onsager's variational principle, with comparison to direct numerical simulations. The steady states predicted by the reduced-order model agree closely with those of the full formulation over a wide parameter range, and the dynamics is well captured in the overdamped regime.
