[论文解读] Effect of velocity, fluid properties and drop shape on coalescence and neck oscillation

Manas Ranjan Behera, Hiranya Deka+2 more|arXiv (Cornell University)|Feb 7, 2026

Fluid Dynamics and Heat Transfer被引用 0

一句话总结

该论文使用轴对称仿真来绘制 Weber、Ohnesorge 与 Bond 数以及液滴形状共同作用下，在落入深水池时对局部共聚与完全共聚及颈部振荡的控制关系。

ABSTRACT

We perform axisymmetric numerical simulations to investigate the coalescence dynamics of a liquid drop in a deep liquid pool. This study aims to generalize the mechanisms of partial coalescence across a range of drop shapes, elucidate the underlying mechanism of neck oscillations, and examine the roles of inertial, viscous and gravitational forces, quantified by the Weber, Ohnesorge, and Bond numbers, in governing the coalescence behavior. A phase diagram is constructed to delineate the boundaries between partial and complete coalescence regimes based on these dimensionless parameters. Our analysis of the height-to-neck ratio shows that, upon contact with the pool, the primary drop forms an upward liquid column that ultimately pinches off due to inwardly directed horizontal momentum. Additionally, the study suggests that as the dimensionless numbers increase, the effect of the vertical collapse rate plays a significant role in the outcome of the coalescence process. Notably, the Rayleigh-Plateau instability is found to be insignificant in driving partial coalescence within the explored parameter space. We identified a transition regime between partial and complete coalescence, characterized by multiple neck oscillations that delay the pinch-off of secondary droplets. The formation of secondary droplets is most prominent for prolate drops, followed by spherical and oblate drops of comparable volume. Furthermore, we observe that the tendency to form multiple droplets from elongated liquid columns diminishes with an increase in the impact velocity of the primary drop.

研究动机与目标

• 在深水池中研究在一系列 We、Oh、Bo 范围内的液滴共聚动力学。
• 在球形与非球形液滴形状下推广部分共聚机制。
• 阐明颈部振荡机制及其在夹断与二次液滴形成中的作用。
• 构建工作域图，以区分部分与完全共聚随无量纲量的变化关系。

提出的方法

• 在轴对称（r,z）几何中，使用 Gerris（VoF 方法）求解带表面张力的不可压 Navier–Stokes 方程。
• 对两种牛顿流体（液滴/池与空气）进行密度与黏度变量化；通过体积分数 c 跟踪界面。
• 改变液滴长宽比 AR，以表示扁平、球形和长圆形状，同时保持液滴体积不变。
• 计算无量纲数 We = ρl V^2 Deq / σ、Oh = μl / sqrt(ρl σ Deq)、Bo = ρl g Deq^2 / σ，以探索不同的流动域。
• 进行网格收敛性验证，并与现有实验（如 Blanchette & Bigioni）比较，用于部分共聚与气泡夹带的对比。

Figure 1 : (a) Schematic diagram illustrating the initial configuration of a drop impacting a liquid pool. (b) Depiction of various shapes of drops. The aspect ratios, ${\it AR}=b/a<1$ , ${\it AR}=1$ , and ${\it AR}>1$ , correspond to oblate, spherical, and prolate shapes, respectively.

实验结果

研究问题

• RQ1 We、Oh 与 Bo 如何共同控制部分共聚与完全共聚的转变？
• RQ2 液滴形状（AR）对部分共聚的可能性与特征以及二次液滴形成有何影响？
• RQ3 在转变区域的共聚过程，颈部振荡的机制及其在夹断中的作用是什么？

主要发现

• 一个由 We–Oh–Bo 三参数组成的势能面将部分共聚与完全共聚区分开来，在给定 AR 时，Wec 依赖 Oh 与 Bo。
• 较高的 Oh 或 Bo 通过抑制毛细波或增加重力排水来促进完全共聚。
• 增大 We 会加速垂直排水并降低顶点高度，从而有利于转变为完全共聚。
• 长圆形液滴在相同体积下更易出现部分共聚并比球形或扁平液滴更容易形成二次液滴。
• 转变区域附近的颈部振荡可能延迟夹断并促使形成多重二级结构，形状和落差速度会调制这一行为。

Figure 2 : (a) Variation of the normalized neck radius $(r_{D}/D_{eq})$ with normalized time $(\tau=t/\sqrt{\rho_{l}D_{eq}^{3}/8\sigma})$ for different mesh sizes $\Delta x$ , with ${\it AR}=1.4$ , ${\it We}=40$ , ${\it Bo}=0.5$ , and ${\it Oh}=0.003$ . (b) Variation of normalized pinch-off time $(\