Revisiting the modelling of droplets passing through a superhydrophobic orifice

Berce, Jure (author), Jereb, Samo (author), Golobič, Iztok (author)

Precise analytical modeling of droplet size passing through a superhydrophobic orifice is vital for various industrial and scientific applications. The very few published theoretical models rely on spherical droplet assumptions, which proved inaccurate for larger orifices due to gravity-induced droplet deformation. To address this limitation, an analytical model for quasi-static droplet size separation is presented, successfully integrating contact angle hysteresis and gravitational effects. The new model determines the critical separation diameter by analyzing the free-surface droplet profile governed by surface tension, internal liquid pressure, and hydrostatic forces across a toroidal orifice edge. Validation using existing experimental results demonstrated excellent model accuracy (R$^{2}$ = 0.9815, RMSE = 0.0566 mm) and a detailed description of droplet shape evolution. A comprehensive parametric study subsequently revealed that contact angle hysteresis and orifice height have minimal practical influence on the critical droplet volume. Conversely, varying liquid properties significantly affect the separation size. Specifically, the critical droplet volume is mainly governed by the ratio of liquid density to surface tension, which dictates the extent of gravitational deformation. This framework provides a robust theoretical tool for designing passive, gravity-driven separation devices across diverse working liquids.

• Language: English
• Keywords: droplet separation, superhydrophobic surface, orifice, droplet size, force balance, laser-texturing, Young-Laplace equation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 15 str.
• Numbering: Vol. 14, iss. 17, art. 2806
• PID: 20.500.12556/RUL-186416
• UDC: 532.21:544.722.132:621.9.048
• ISSN on article: 2227-9717
• DOI: 10.3390/pr14172806
• COBISS.SI-ID: 289577987
• Publication date in RUL: 01.09.2026

Record is a part of a journal

• Title: Processes
• Shortened title: Processes
• Publisher: MDPI AG
• ISSN: 2227-9717
• COBISS.SI-ID: 523353113

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: separacija kapljic, superhidrofobne površine, reže, velikost kapljice, ravnovesje sil, lasersko teksturiranje, enačba Young-Laplace

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0223
• Name: Prenos toplote in snovi

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J2-50085
• Name: Raziskave medfaznih pojavov kapljic in mehurčkov na funkcionaliziranih površinah ob uporabi napredne diagnostike za razvoj okoljskih tehnologij prihodnosti in izboljšanega prenosa toplote (DroBFuSE)