Single theoretical model for breakup of viscous thread with and without a fiber

IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Physical Review Fluids Pub Date : 2024-08-20 DOI:10.1103/physrevfluids.9.084005
Hyejoon Jun, Hyoungsoo Kim
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Abstract

In this study, we introduce a comprehensive theoretical model for viscous liquid systems exhibiting Rayleigh-Plateau instability, accommodating cases both with and without a solid fiber. Employing the lubrication approach and implementing the hydrodynamic interaction at the solid-liquid interface, we formulate one-dimensional evolution equations for the breakup of viscous liquid threads and films on a fiber. Through several validations, we showed that our model exhibits a good agreement with experimental results in comparison to numerical simulations. Finally, our model, which incorporates the flow effect from the inner boundary condition by reconsidering the ansatz of a conventional long-wave approximation, provides a necessary condition for satellite droplet formation and determines the most unstable mode proportional to k*2, where k* is the most unstable wavenumber. In addition, we observed that the volume of the satellite droplets exponentially decays depending on the wavenumber. Moreover, our single model integrates the findings of Goren's liquid film on a fiber and Rayleigh's viscous liquid thread, demonstrating its versatility and relevance to a wide range of systems.

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有纤维和无纤维粘性线缆断裂的单一理论模型
在本研究中,我们为表现出瑞利-普法不稳定性的粘性液体系统引入了一个全面的理论模型,该模型既适用于有固体纤维的情况,也适用于无固体纤维的情况。我们采用润滑方法和固液界面的流体动力学相互作用,建立了纤维上粘性液丝和液膜破裂的一维演化方程。通过多次验证,我们发现与数值模拟相比,我们的模型与实验结果具有良好的一致性。最后,我们的模型通过重新考虑传统长波近似的剖分,纳入了内边界条件的流动效应,为卫星液滴的形成提供了必要条件,并确定了与 k*2 成比例的最不稳定模式,其中 k* 是最不稳定的波数。此外,我们还观察到卫星液滴的体积随波长呈指数衰减。此外,我们的单一模型综合了戈伦的纤维上液体薄膜和瑞利的粘性液体线的发现,证明了它的多功能性和对广泛系统的相关性。
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来源期刊
Physical Review Fluids
Physical Review Fluids Chemical Engineering-Fluid Flow and Transfer Processes
CiteScore
5.10
自引率
11.10%
发文量
488
期刊介绍: Physical Review Fluids is APS’s newest online-only journal dedicated to publishing innovative research that will significantly advance the fundamental understanding of fluid dynamics. Physical Review Fluids expands the scope of the APS journals to include additional areas of fluid dynamics research, complements the existing Physical Review collection, and maintains the same quality and reputation that authors and subscribers expect from APS. The journal is published with the endorsement of the APS Division of Fluid Dynamics.
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