Capillary-Driven Rise of Well-Wetting Liquid on the Outer Surface of Cylindrical Nozzles

Abstract

Well-wetting liquids exiting small-diameter nozzles in the dripping regime can partially rise up along the outer nozzle surfaces. This is problematic for fuel injectors and other devices such as direct-contact heat and mass exchangers that incorporate arrays of nozzles to distribute liquids. We report our experimental and numerical study of the rising phenomenon for wide ranges of parameters. Our study shows that the interplay of three dimensionless numbers (the Bond number, the Weber number, and the Ohnesorge number) governs the capillary-driven rise dynamics. In general, as the flow rate or the viscosity increases, the capillary-driven rise height over each dripping period becomes smaller. We identify liquid flow rates below which the temporal evolution of the meniscus positions can be well approximated by a quasistatic model based on the Young–Laplace equation. Our analysis reveals two critical Bond numbers that give nozzle sizes, which correspond to the maximum meniscus rise and the onset of capillary-driven rise cessation. These critical Bond numbers are characterized as a function of the contact angle, regardless of the fluid type. Our study leads to a more efficient and optimized nozzle design in systems using wetting liquids by reducing both the risks of contamination and high pressure drop in such devices.

On weak solutions of a control-volume model for liquid films flowing down a fibre

“…We also approximate v ηε,0 in the H 2 -norm by C 4+γ functions v βηε,0 , satisfying (33), and replace (34…”

“…Thin liquid films flowing down a vertical fibre have attracted many interests in the past decades due to their importance in a variety of engineering applications, including heat and mass exchangers, thermal desalination, and vapor and CO 2 capturing [32,43,42,44,31]. These liquid films are fundamentally driven by Rayleigh-Plateau instability and gravity modulation, spontaneously exhibiting complex interfacial instability and pattern formation [24,25,33,28].Previous experimental works have found that the downstream flow dynamics and pattern formation highly depend on the flow rate, fibre radius, liquid properties, and inlet geometries. Specifically, three typical flow regimes have been extensively studied [22,9,29,14,41].…”

“…Thin liquid films flowing down a vertical fibre have attracted many interests in the past decades due to their importance in a variety of engineering applications, including heat and mass exchangers, thermal desalination, and vapor and CO 2 capturing [32,43,42,44,31]. These liquid films are fundamentally driven by Rayleigh-Plateau instability and gravity modulation, spontaneously exhibiting complex interfacial instability and pattern formation [24,25,33,28].…”

On travelling waves of a control-volume model for liquid films flowing down a fibre

“…Thin liquid films flowing down a vertical fibre have attracted many interests in the past decades due to their importance in a variety of engineering applications, including heat and mass exchangers, thermal desalination, and vapor and CO 2 capturing [27,28,[35][36][37]. These liquid films are fundamentally driven by Rayleigh-Plateau instability and gravity modulation, spontaneously exhibiting complex interfacial instability and pattern formation [20,21,24,29].…”

On-demand ferrofluid droplet formation with non-linear magnetic permeability in the presence of high non-uniform magnetic fields

“…Droplet generation has been utilized in various applications, such as 3D printing 3 , electrosprays 4 , and bioengineering 5 . Droplet formation is performed by passive 6 or active 7 methods, which differ in the absence or presence of an external force. Electrical 8 , magnetic 9 , and acoustic 10 forces have been the most external stimuli in the active methods.…”