Proceedings of the 7th World Congress on Mechanical, Chemical, and Material Engineering (MCM'21)
Prague, Czech Republic Virtual Conference – August, 2021
Paper No. HTFF 137
DOI: 10.11159/htff21.137

Growth and Self-Ejection of Single Condensate Droplet on
Nanostructured Microcones
Nicolò G. Di Novo1,2, Alvise Bagolini2, Nicola M. Pugno1,3
1

Laboratory of Bio-Inspired, Bionic, Nano, Meta, Materials & Mechanics, Department of Civil, Environmental andMechanical Engineering, University of Trento, Via Mesiano, 77, 38123 Trento, Italy
2Sensors and Devices Center, FBK, Via Sommarive 18, 38123 Trento
3
School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS,United Kingdom
nicolo.dinovo@unitn.it; bagolini@fbk.eu; nicola.pugno@unitn.it

Extended Abstract
In the last decade, the phenomenon of coalescence-induced droplet jumping has been studied in depth because of theadvantages it brings in applications such as anti-frosting, anti-icing, condensation heat transfer, water harvesting, thermal
diodes for electronics cooling and self-cleaning [1]. In this work we theoretically and experimentally show that surfaces
structured with micro truncated cones covered with highly hydrophobic nanostructures exhibit a recurrent self-ejection ofsingle condensate droplets in addition to the common coalescence-induced jumps. We analytically modelled the external
forces acting both on a droplet of condensate slowly growing in conical pores (a simplification of the growth between
truncated cones) and during the following rapid transient for two possible cases of self-ejection: 1) rapid swelling out of thestructures and 2) detachment from a pinning site (a less hydrophobic defect or the nucleation site). Viscous and adhesion
dissipations were included in the modelling. We described the shape of the growing droplet as a function of the tapering (𝛽)and of dynamic contact angles (𝜗𝑎𝑑𝑣 and 𝜗𝑟𝑒𝑐 ). For both cases, the minimum requirement for self-ejection is that the receding
𝑝𝑖𝑛𝑛𝑖𝑛𝑔
angle of the walls (𝜗𝑟𝑒𝑐 ) and any pinning site (𝜗𝑟𝑒𝑐) are greater than 90°+𝛽. In the first case, as the volume increases,
the upper meniscus moves towards the apex of the cones and the lower one follows it as soon as it reaches 𝜗𝑟𝑒𝑐 ; when thedroplet reaches the apex of the structures it self-ejects because the superior meniscus expands rapidly and a Laplace pressure
gradient is generated between the menisci. In the second case, the superior meniscus grows towards the apex and when thelower one recedes from the pinning site, the droplet self-ejects due to the Laplace pressure gradient generated by the abruptchange in wettability, as recently reported for relatively large droplets (radius > 50 μm) in diverging grooves [2]. Describing
growth and self-ejection with a system of forces requires a careful distinction between external and internal forces. The
modelling with forces, unlike the energetic one [2], allowed us to describe the ejection transient dynamics and to derive theejection velocity while maintaining the dependence on the dynamic contact angles of the superhydrophobic walls and of aneventual pinning site, fundamental quantities for the design of real surfaces. The analytical results relative to the case of the𝑝𝑖𝑛𝑛𝑖𝑛𝑔pinning site foresee that, at a fixed contact angle hysteresis of the superhydrophobic walls and 𝜗𝑟𝑒𝑐, the ejection velocity
𝑝𝑖𝑛𝑛𝑖𝑛𝑔
increases with 𝛽 (until the limit 𝛽 = 𝜗𝑟𝑒𝑐− 90°, beyond which there cannot be ejection); in addition, the velocity isgreater as the droplet size decreases if viscous dissipations are not considered while a peak trend is observed with thedissipations included.
We fabricated silicon truncated micro cones arranged in square and hexagonal patterns and covered with nanostructures.
Through condensation experiments in a controlled environmental chamber we observed for the first time the self-ejection of
the drops that nucleate and grow between the cones (in the case in question the droplet diameter ≈ 11 𝜇𝑚). By fabricating
cones of different sizes, we have also studied the self-ejection rate per unit area as a function of the droplet size. Furthermore,
we performed preliminary condensation frosting experiments. Future investigations of this new class of jumping droplet
surfaces may show important advantages in the mentioned applications.

References[1] Chuntian Liu et al., Langmuir 2021 37 (3), 983-1000, doi: 10.1021/acs.langmuir.0c02758[2] Xiao Yan et al., “Laplace Pressure Driven Single-Droplet Jumping on Structured Surfaces,”ACS Nano 2020 14 (10),12796-12809, doi: 10.1021/acsnano.0c03487

HTFF 137-1