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

Abstract

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.

Dynamics of thin liquid films on vertical cylindrical fibres

“…This model formulation does not include the nozzle size as a system parameter because we are interested in the flow downstream where the nozzle does not affect the dynamics. Instead, we consider the scales for frequency and mass of the droplets, which depend on the nozzle size (Sadeghpour et al (2017)). We will discuss this dependence later in Appendix B.…”

“…Motivated by the different regimes shown in Figure 9, we review the details of the dependence of bead speeds on its spacing and mass constraint, and their relations to the nozzle diameters. It has been empirically shown in Sadeghpour et al (2017) that when other experimental parameters are fixed, the nozzle diameter determines the spacing and mass constraint for the traveling beads. Typical ranges for the mass constraint and period with increasing nozzle inner diameter are shown in Table 2.…”

“…Such dynamics is an important consideration in various applications (Chinju et al (2000); Zeng et al (2017)) that take advantage of extended interfacial areas afforded by thin liquid films. A recent experimental study (Sadeghpour et al (2017)) observed three distinct regimes of interfacial patterns by simply varying the diameters of the nozzles feeding the fluid. This was quite unexpected because other experimental conditions (flow rate, fiber radius, and fluid), which were thought to primarily govern interfacial dynamics, remained the same.…”

“…In the present paper, we report a combination of experimental and numerical results for flows in the Rayleigh-Plateau regime (regime (b)), in particular under flow conditions where the film thickness is comparable to or larger than the fiber radius. The recent work by Sadeghpour et al (2017) showed that one can observe all three flow regimes under a fixed flow rate and a fixed fiber radius by simply varying the nozzle diameter. We leverage their study to examine the characteristics of nonlinear traveling waves that dominate flow dynamics downstream of the nozzle.…”

Thermohydraulic characteristics of a multi-string direct-contact heat exchanger

“…Most early studies of heat transfer involving liquid films focus on planar surfaces or large diameter tubes [8][9][10][11][12][13][14][15][16][17][18][19]. Liquid films flowing on highly curved surfaces show wavy profiles due to intrinsic flow instability arising from interplay among surface tension, viscous, inertia, and gravitational force [7,20,21]. Two main flow regimes have been observed.…”