When a water-repellent surface is dunked, a thin film of air (a plastron) stays caught in its texture. Much of this dossier depends on that air holding. The University of Rochester tubes are said to float because air stays trapped inside them, as described in Air-Trapping Buoyancy (Plastron-Based Flotation). This 2025 open-access paper by Md Abir Hasan Jilan, Estefania Solano-Calderon and Shabnam Mohammadshahi is not about Guo's tubes or about metal at all. It asks a narrower question that bears directly on them: in still water, what decides how long a plastron survives before water floods the texture? The paper was received on 26 August 2025, accepted on 10 November 2025, and funded internally by New Mexico State University.
The question and the physics behind it
The paper frames the problem in the standard wetting vocabulary. While air fills the gaps between surface features, water rests on a mix of solid tips and air pockets (the Cassie-Baxter state). Once water fills the gaps and touches the whole surface (the Wenzel state), the surface no longer repels water in the useful sense. The authors treat this switch as the end of the plastron's life.
In water that is not flowing, they argue, the main thing driving that switch is diffusion. If the surrounding water holds less dissolved air than it could at equilibrium, gas slowly passes from the trapped pocket into the liquid. The paper expresses the water's gas content as a saturation level, S. Their Fick's-law model makes the driving force proportional to (1 − S). So the more undersaturated the water, the faster the air pocket should drain.
What was built and how it was watched
The test surfaces were resin squares, 24 mm × 24 mm, covered in cylindrical micro-posts. They were made by masked stereolithography 3D printing and then sprayed three times with a commercial hydrophobic nanoparticle coating (Glaco Mirror Coat Zero), which adds nanoscale roughness on top of the printed posts. There were seven samples, and each one changed a single variable away from a baseline (sample #2) whose diameter, height and gap were all 400 μm:
- Gap g: 200, 400 and 600 μm (samples #1 to #3)
- Height h: 600 and 200 μm (samples #4 and #5)
- Diameter d: 600 and 200 μm (samples #6 and #7)
All seven surfaces had static contact angles of 151–152° and sliding angles of 7–9°. That puts them firmly in the superhydrophobic range. The authors note that features smaller than about 100 µm did not survive printing and coating reliably, so every design used features of 200 µm or more. The printed posts also taper by about 5° from vertical.
Each sample was tested in sealed, still, deionised water at 23 °C and three saturation levels, S = 20%, 40% and 60%. The degassing was done by holding the water under vacuum, and a dissolved-oxygen meter checked the level before each run. The paper reports 42 runs in total. A reflected-light camera viewed the surface from above, where trapped air shows up bright and wetted resin dark. A second camera watched the air–water boundary from the side.
What was measured
Saturation. Every geometry kept its air layer longer as S increased. The longest lifetimes came at 60% and the shortest at 20%. The baseline sample at S = 20% lost its plastron fully in about 120 minutes, with the top and side views agreeing. On a log–log plot of lifetime against (1 − S), the authors report a slope "close to -2", which they say matches their diffusion scaling and earlier work by Bourgoun and Ling and by Nosrati et al.
Geometry. Wider gaps shortened lifetime at all three saturation levels, even though wider gaps hold more air. The paper's explanation is that a wider gap lowers the capillary pressure that pins the water surface at the post tops, and this effect outweighs the extra air. Taller posts lengthened lifetime by holding more air and giving the receding water surface more places to snag. Sample #4, with the tallest posts at 600 μm, lasted longest at every saturation level. Changing the diameter made comparatively little difference over the range tested.
How the air goes. The side camera showed that the water did not drop smoothly. It came down the post walls in steps, pausing at several heights. The authors attribute these pauses to the extra nanoscale roughness from the coating, which is the same layered-texture idea discussed in Hierarchical Micro/Nanoscale Surface Texturing. They also note that some regions flooded before others, even though the texture is regular.
Energy bookkeeping. The authors calculated a dimensionless free-energy difference between the wet and dry states for each sample. It fell from 1.13 to 0.32 as the gap widened (samples #1 to #3) and rose from 0.24 to about 0.9 as the posts got taller (samples #5 to #4). For sample #4 the paper's text gives 0.91 but its Table 2 lists 0.92. They caution that energy alone does not set the time to failure. Diffusion kinetics matter as well. Finally, they fit a response-surface model, which they describe as valid only within the conditions they measured.
What this does and does not show
The study quantifies how the life of a plastron in undersaturated still water depends on the water's dissolved-gas saturation and on the geometry of the texture. In the conditions tested, every plastron was eventually lost to the Wenzel state, and texture only changed how long that took. The agreement the paper reports with Nosrati et al. is not fully independent, since Shabnam Mohammadshahi is a co-author of both papers.
The paper has clear limits on what it can say about the dossier's claims:
- It used 3D-printed resin with sub-millimetre posts, not etched aluminium with micro- and nano-pits.
- It studied the thin air film within surface texture, not a large air pocket held inside a closed-off tube compartment.
- All tests used still deionised water at 20–60% saturation. None used seawater, flow, waves, hydrostatic depth or vibration. The authors themselves name pressure, shear and vibration as future work.
- No saturation level near 100% was tested, so the paper does not measure how long air would last in water at or near equilibrium with air.
For the Rochester claim of no loss of buoyancy over weeks (see Superhydrophobic Metallic Tubes Claims vs. Evidence: The Press Framing, the Paper Abstract and the Patent Abstracts), the paper therefore sets out the physics that any such claim has to deal with: dissolved-gas saturation, gap size and how much air the texture holds. It does not confirm or refute the tube results. Whether the tube's design, such as its mid-tube divider, avoids these limits is a question the tube material would need to answer with its own measurements. The general background is covered in Superhydrophobicity.
Reference
Jilan, M. A. H., Solano-Calderon, E. and Mohammadshahi, S. "Saturation and texture geometry effects on plastron longevity on superhydrophobic surfaces." 2025. DOI 10.1038/s41598-025-28322-w. Open access at https://pmc.ncbi.nlm.nih.gov/articles/PMC12738761/
Source notes & attribution
- https://pmc.ncbi.nlm.nih.gov/articles/PMC12738761/