液滴在倾斜纤维上的聚并

中文摘要 AI 辅助

沿圆柱表面输送液滴是一个新兴的研究领域，具有广泛的实际应用，如雾收集和过滤。Feng等人（2024）最近的实验研究揭示了预润湿圆柱纤维上大量新的液滴聚并动力学，表明需要更先进的理论。本文研究了倾斜圆柱纤维上液滴聚并的早期和晚期动力学。在早期阶段，当连接两个液滴的液桥最小厚度较小时，我们提出一个基于润滑的模型来分析液桥的毛细驱动自相似动力学。我们的理论预测了液桥的生长速率，并表明相邻接触角的不对称性有助于合并液滴的迁移，与实验观察结果吻合良好。在晚期阶段，随着液滴合并的进行，惯性效应变得显著并导致快速的质量传递。为了捕捉这一状态，我们开发了一个用于在倾斜预润湿圆柱上流动的液膜加权残差模型，纳入了重力、低至中等惯性、表面张力和分子间力等关键物理效应。该模型解释了实验观察到的液滴聚并过程中的定向自推进输运，其中较大的液滴向较小的液滴迁移。基于该模型的数值模拟进一步支持了这些发现，预测的聚并诱导液滴迁移与实验观察结果之间显示出良好的一致性。

英文摘要

Transporting droplets along cylindrical surfaces is an emerging area of research with a wide range of practical applications such as fog collection and filtration. Recent experimental studies by Feng et al. (2024) have revealed a wealth of new droplet coalescence dynamics on a pre-wetted cylindrical fibre, illustrating the need for more advanced theory. In this paper, we study both the early-stage and late-stage dynamics of droplet coalescence on a sloped cylindrical fibre. In the early stage, when the minimum thickness of the liquid bridge connecting two droplets is small, we propose a lubrication-based model to analyze the capillary-driven self-similar dynamics of the liquid bridge. Our theory predicts the bridge growth rate and demonstrates that asymmetry in the adjoining contact angles contributes to the migration of the merged droplet, showing good agreement with experimental observations. In the late stage, as droplet merging progresses, inertia effects become significant and lead to rapid mass transfer. To capture this regime, we develop a weighted residual model for liquid films flowing on a sloped pre-wetted cylinder, incorporating key physical effects such as gravity, low-to-moderate inertia, surface tension, and intermolecular forces. This model explains the experimentally observed directional self-propelled transport during droplet coalescence, where the larger droplet migrates toward the smaller one. Numerical simulations based on this model further support these findings, showing good agreement between the predicted coalescence-induced droplet migration and experimental observations.

发表机构

• North Carolina State University（北卡罗来纳州立大学）
• Northwestern University（西北大学）

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