Abstract

A thin viscous film flowing down a fiber is subject to Plateau–Rayleigh instability leading to temporal beading patterns, characterized by the bead spacing \(S_b\), bead velocity \(V_b\), and bead diameter \(D_b\). In this study, experiments are performed to document the beading pattern as it depends upon the flow rate Q, nozzle diameter \(D_n\), fiber diameter \(D_f\) and liquid viscosity \(\mu\). The large experimental data set collapses upon scaling with the Nusselt solution for gravity-driven thin film flow with viscous time scale showing the dimensionless bead diameter scales with the capillary number. The dimensionless bead frequency and bead spacing are similarly related and characterize the dispersion relationship.

Graphic abstract

中文翻译：

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薄膜流下光纤中的高原-瑞利不稳定性的缩放分析

摘要

沿着纤维流动的粘性薄膜受到高原-瑞利不稳定性的影响，导致时间串珠图案，其特征在于珠粒间距\(S_b\)、珠粒速度\(V_b\)和珠粒直径\(D_b\)。在这项研究中，进行实验以记录成珠图案，因为它取决于流速Q、喷嘴直径\(D_n\)、纤维直径\(D_f\)和液体粘度\(\mu\). 大型实验数据集在使用 Nusselt 解决方案缩放时崩溃，用于具有粘性时间尺度的重力驱动薄膜流，显示无量纲珠直径尺度与毛细管数。无量纲珠频率和珠间距类似地相关并且表征色散关系。

图形摘要