[論文レビュー] 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被引用数 0

ひとこと要約

要約: 本論文は、Weber数、Ohnesorge数、Bond数と滴の形状が、深い液体プールに滴が衝突した際の部分共融と完全共融および頸部振動をどう支配するかを、軸対称シミュレーションでマッピングする。

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.

研究の動機と目的

• Investigate coalescence dynamics of a liquid drop in a deep liquid pool across a range of We, Oh, and Bo.
• Generalize partial coalescence mechanisms across spherical and nonspherical drop shapes.
• Elucidate the neck oscillation mechanism and its role in pinch-off and secondary-droplet formation.
• Construct regime maps to delineate partial and complete coalescence as functions of dimensionless groups.

提案手法

• Solve the incompressible Navier–Stokes equations with surface tension using Gerris (VoF method) in axisymmetric (r,z) geometry.
• Model two Newtonian fluids (drop/pool) and air with variable densities and viscosities; track interface via volume fraction c.
• Vary drop aspect ratio AR to represent oblate, spherical, and prolate shapes while keeping drop volume constant.
• Compute non-dimensional numbers We = ρl V^2 Deq / σ, Oh = μl / sqrt(ρl σ Deq), Bo = ρl g Deq^2 / σ to explore regimes.
• Perform grid-convergence validation and compare with existing experiments (e.g., Blanchette & Bigioni) for partial coalescence and bubble entrainment.

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.

実験結果

リサーチクエスチョン

• RQ1 How do We, Oh, and Bo jointly control the transition between partial and complete coalescence?
• RQ2 What is the influence of drop shape (AR) on the likelihood and characteristics of partial coalescence and secondary-droplet formation?
• RQ3 What mechanisms govern neck oscillations and their role in pinch-off during coalescence at the transition regime?

主な発見

• A three-parameter We–Oh–Bo regime surface separates partial from complete coalescence regimes, with Wec dependent on Oh and Bo for given AR.
• Higher Oh or Bo promote complete coalescence, by damping capillary waves or increasing gravitational drainage, respectively.
• Increased We accelerates vertical drainage and reduces apex height, favoring transition to complete coalescence.
• Prolate drops are more prone to partial coalescence and form secondary droplets more readily than spherical or oblate drops at comparable volumes.
• Neck oscillations near the transition regime can delay pinch-off and facilitate multiple secondary structures, with shape and impact velocity modulating this behavior.]
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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 $(\