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Effects of Nozzle Geometry on the Fluid Dynamics of Thin Liquid Films Flowing down Vertical Strings in the Rayleigh–Plateau Regime


Thin-liquid films flowing down vertical strings undergo instability, creating wavy film profiles and traveling beads. Previous studies assumed that the liquid film thickness and velocity profiles within the healing length from a nozzle were specified by the Nusselt solution, independent of the nozzle geometry. As a result, the influence of the nozzle diameter on the flow characteristics, such as the liquid bead size, spacing, and traveling speed, was largely overlooked. We report an experimental and numerical simulation study on liquid-film flows in the Rayleigh-Plateau regime while systematically varying the nozzle diameter from 0.5 to 3.2 mm at different mass flow rates (0.02, 0.04, 0.06, and 0.08 g/s). We find that the nozzle diameter does have a strong influence on the flow regime and the flow characteristics. We identify the thickness of a nearly flat portion of a liquid film that precedes the onset of instability, which we term the preinstability thickness, as a critical flow parameter that governs the size, spacing, and frequency of liquid beads that develop downstream. By defining the liquid film aspect ratio α in terms of the preinstability thickness, we capture a flow transition from the Rayleigh-Plateau (RP) instability regime to the isolated droplet regime. Improved understanding of the flow regimes and characteristics assists in the systematic design and optimization of a wide variety of processes and devices, including fiber coating and direct contact heat and mass exchangers.

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