服从达西定律的流体中的液滴聚并
Droplet coalescence in fluids obeying Darcy's law
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中文总结 AI 辅助
研究限域在Hele-Shaw单元中服从达西定律的液滴聚并，识别出桥半径演化的两种时间 regime，揭示其标度律及转变机制，确定该类流体液滴聚并的新普适 regime。
中文摘要 AI 辅助
在液滴聚并过程中，由于表面张力，会形成连接液滴的流体桥并迅速扩张。对于球形液滴，这种动力学在粘性和惯性 regime 中已被充分理解。然而，在强限域条件下，流体运动受几何约束的根本改变，导致小尺度上的耗散。我们研究了限域在Hele-Shaw单元（两块由窄间隙分隔的平行板）中的液滴聚并。在该几何结构中，深度平均流动服从达西定律，而表面张力驱动界面运动。我们在桥半径（R_b）的演化中识别出两种不同的时间 regime。在早期，桥的增长满足R_b ~ t^(1/2)，这源于与限域相关的弯月面不稳定性，该不稳定性决定了桥形成前液滴接触的起始。在后期，桥的增长显著放缓，满足R_b ~ t^(1/5)，与近期关于达西控制聚并的理论预测一致。我们表明，这些 regime 之间的转变由多个几何长度尺度控制。特别地，当界面曲率半径与板间距相当，流动完全限域时，达西 regime 开始。利用边界积分公式，我们发现R_b的两种标度律均由桥宽决定。这些结果共同确定了一大类服从达西定律的流体中液滴聚并的新普适 regime。
英文摘要
During drop coalescence, a connecting bridge of fluid forms and rapidly expands due to surface tension. For spherical drops, these dynamics are well understood in both the viscous and inertial regimes. However, under strong confinement, fluid motion is fundamentally altered by geometric constraints, leading to dissipation on small lengthscales. We investigate the coalescence of drops confined in a Hele-Shaw cell (two parallel plates separated by a narrow gap). In this geometry, the depth-averaged flow is governed by Darcy's law while surface tension drives the interface motion. We identify two distinct temporal regimes in the evolution of the bridge radius that evolves as a power law ($R_b$). At early times, the bridge grows as $R_b \sim t^{1/2}$, which results from a confinement-dependent meniscus instability that determines the initiation of contact between droplets prior to bridge formation. At later times, the bridge growth slows substantially and follows $R_b \sim t^{1/5}$, consistent with recent theoretical predictions for Darcy-governed coalescence. We show that the transition between these regimes is controlled by several geometric lengthscales. In particular, the onset of the Darcy regime occurs when the interface radius of curvature becomes comparable to the plate spacing, such that the flow becomes fully confined. Using a boundary integral formulation, we find that both scaling laws for $R_b$ are determined by the bridge width. Together, these results identify a new universal regime of drop coalescence in a broad class of fluids obeying Darcy's law.
