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ABSTRACT
The Gibbs free energy barrier for heterogeneous nucleation of a condensed droplet on a rough surface changes significantly with changes of humidity content in the condensing environment. The influence of environmental factors (ambient temperature and relative humidity) and substrate characteristics (topology, surface chemistry, and substrate temperature) on atmospheric condensation phenomenon is very important to elucidate the condensed droplet wetting state and condensate harvesting applications. Condensation from the humid air has been reported for plain silicon and fabricated nanopillar surfaces to facilitate condensate harvesting. Droplet growth and size distributions were recorded for 90 min. Spherical droplets condensed on the silicon surfaces and irregular-shaped droplets were observed on the nanopillar surfaces due to the pinning effect of the pillars. The effect of droplet pinning on coalescence events has been described based on the energy balance for the condensed droplets. A mathematical model reveals that certain dimensional combinations (pillar pitch, pillar diameter, and pillar height) of the nanopillar geometry are required to exhibit the pinning mechanism for condensed droplets. Regeneration of droplets was observed at void spaces generated from coalescence events. The growth of individual droplets was tracked over multiple time and length scales, starting from nucleation to get further insight into the direct growth and coalescence mechanisms.
Abbreviation: ESEM: Environmental Scanning Electron Microscope; HCP: Hexagonal Closed-Packed; MPL: Microsphere Photolithography; RH: Relative Humidity
Nomenclature
| A | = | contact area of a droplet, µm2 |
| d | = | diameter of droplet, µm |
| E | = | partial pressure of water vapor, Pa |
| es | = | pressure of water vapor at saturation, Pa |
| ΔG | = | Gibbs free energy, J |
| h | = | pillar height, µm or nm |
| hfg | = | latent heat of vaporization, J/Kg |
| kw | = | thermal conductivity of water, W/m.K |
| r | = | pillar radius, µm |
| rb | = | droplet cap base radius, µm |
| R | = | droplet radius, µm |
| Rm | = | the gas constant, J/kg K |
| Rd | = | droplet conduction resistance, m2 K/W |
| S | = | droplet cap height, µm |
| t | = | time, s or min |
| T | = | temperature, K |
| Ts | = | surface temperature, K |
| Tsat | = | saturation temperature, K |
| Tl | = | liquid droplet temperature, K |
| V | = | volume of water in a gap, µm3 |
| Vs | = | spherical cap volume, µm3 |
| X,Y | = | defined variable |
Greek Symbols
| α | = | pillar density, number of pillars/µm2 |
| β | = | constant |
| γLV | = | surface tension of water in air, mN/m |
| γPL | = | surface tension of water with pillar, mN/m |
| γSL | = | surface tension of water with substrate, mN/m |
| γPV | = | surface tension of pillar, mN/m |
| γSV | = | surface tension of substrate, mN/m |
| ε | = | surface coverage % |
| θ0 | = | equilibrium contact angle, degree |
| θ′ | = | apparent contact angle of droplet on pillar, degree |
| θ1 | = | pinning angle of droplet by the pillar edge, degree |
| ρd | = | droplet density, Kg/m3 |
| ρG | = | water vapor density, Kg/m3 |
Acknowledgments
The authors would like to thank Dr. Steve Eckels and the Institute for Environmental Research (IER) for the use of the environmental chambers. The authors also acknowledge their gratefulness to Rachel Bohm for her support in experimentation and both of the Universities for providing the required funding and facilities.
Supplementary Material
Supplemental data for this article can be accessed here.
Supporting Information
Additional information regarding the importance of relative humidity on heterogeneous nucleation energy barrier (S1), interfacial force balance (S2) to estimate the apparent contact angle (θ′) considering the pinning from the pillar edge, contact angle on silicon surface (S3), unit calculation for energy equations (S4) as well as three videos showing the microscale droplet growth process (Video S5, S6), the pinning of droplets (Video S7) have been provided.
