Dynamic Drop Penetration of Horizontally Oriented Fiber Arrays

Rible, Gene Patrick S.; Spinazzola, Michael A.; Jones, Robert E.; Constantin, Rachel U.; Wang, Wei; Dickerson, Andrew K.

doi:10.1021/acs.langmuir.4c00371

Abstract

In this experimental study, we combine drop impact into porous media and onto a single fiber to study drop impact into fiber arrays inspired by mammalian fur coats. In our 3D-printed arrays, we vary the packing density, fiber alignment, strand cross-section, and wettability. Drops impact fibers fixed at both ends, penetrating over short times by momentum and laterally spreading throughout the array. Using image analysis, we measure penetration depth, and wetted width into the array. Impact Weber number and intrinsic porosity define penetration, retraction, and rebound regimes. On average, at an impact Weber number of ≈80, staggered fibers reduce penetration by 24% in hydrophilic fibers and 34% in hydrophobic fibers, and the penetration reduction percentage is expected to increase with increasing Weber number. Our results indicate that as density grows toward the density of mammalian pelts, penetration will reach a maximum value independent of drop impact velocity, thereby providing an effective rain barrier. Hydrophilicity at the densities we test, 50-150 strands/cm², aids fiber array resistance of dynamic penetration by impacting drops through the promotion of lateral drop spreading and inhibition of drop fragmentation. Conversely, hydrophobic fibers best resist low-speed wicking. The fraction of a drop that infiltrates hydrophilic and hydrophobic fibers is nearly identical for a fixed Weber number because lateral spreading restricts the penetration depth into hydrophilic fibers but does not restrict mass infiltration. Above a critical Weber number, the entire drop mass percolates fiber arrays regardless of strand wettability.

Firsts in this work

New experimental tools and observations from this paper.

First drop impacts on 3D-printed fur-mimicking fiber arrays

Drop-impact literature has long been split between three camps: solid surfaces, porous media, and single fibers. This work is the first to drop water on resin-3D-printed multi-fiber arrays sized and packed like mammalian fur, bridging the porous-media and single-fiber camps. Density, alignment, strand cross-section, and wettability are independently controlled.

Hydrophilic fibers resist dynamic penetration better than hydrophobic

Counter to intuition: at the tested densities (50-150 strands/cm²), hydrophilic horizontal arrays best resist raindrop impact. They promote lateral spreading and inhibit drop fragmentation, two mechanisms hydrophobic arrays lack at dynamic velocities.

A critical Weber number marks the wettability crossover

Below We_c, hydrophobic fibers minimize penetration (static / low-speed wicking). Above We_c, hydrophilic takes over (dynamic / raindrop). At ≈5 m/s, hydrophobic fibers shatter and let the drop fully penetrate; hydrophilic fibers stop it at finite depth.

Staggered arrays reduce penetration by up to 34%

At We ≈ 80, staggered hydrophobic fibers cut penetration depth by 34% (24% for hydrophilic), and the benefit grows with Weber number.

Density approaches a dynamic rain-barrier limit

As packing density rises toward mammalian-pelt levels, penetration saturates: drop velocity no longer governs how deep the liquid reaches.

Watch the 10-minute walkthrough

How it works and what we found

Hydrophilic fibers resist dynamic penetration better than hydrophobic

Movie S5: ≈5 m/s impacts, hydrophilic vs hydrophobic

Movie S1: Impact classifications

Figure 5 from the paper: modified fiber aspect ratio versus Weber number, four-panel layout comparing hydrophilic and hydrophobic across two orientations.

Modified fiber aspect ratio (AR*) versus Weber number for hydrophilic (left) and hydrophobic (right) arrays in standard (top) and bottom (bottom) orientations, colored by the number of penetrated layers. AR* is the inter-fiber spacing normalized by the drop diameter; a lower AR* means the impacting drop sees a denser array. The counter-intuitive main finding of the paper: at the tested densities (50-150 strands/cm²), hydrophilic horizontal arrays best resist raindrop impact. They do it by promoting lateral spreading (which redirects kinetic energy out across the array surface) and inhibiting drop fragmentation (which would otherwise let small daughter droplets dive deeply between strands). Hydrophobic fibers do neither; they let the drop fragment and penetrate further at dynamic velocities. In the legend, PDF stands for “penetrated drop fragmentation”: points drawn with a black outline (□) represent drops that fragmented during impact; solid markers (■) are non-fragmenting drops.

A critical Weber number marks the wettability crossover

Figure 9 from the paper: six-panel comparison of hydrophobic vs hydrophilic penetration depth with vertical dashed lines marking the critical Weber number for each density.

Normalized maximum penetration depth in hydrophobic fibers versus the same quantity in hydrophilic fibers, panel by panel for each density. Vertical lines mark the critical Weber number (We_c) at which hydrophobic penetration starts exceeding hydrophilic. Below We_c the hydrophobic case penetrates less (the static / low-speed wicking regime where hydrophobicity helps). Above We_c the hydrophilic case takes over and resists better (the dynamic / raindrop regime). The per-density We_c values are printed on each panel. At raindrop velocities (≈5 m/s, see Movie S5 below), hydrophobic arrays shatter the drop and let it fully percolate the array; hydrophilic arrays still stop it at a finite depth.

3D-printing fur-inspired fiber arrays

Figure 1 from the paper: 3D-printed fiber array. Oblique view, top view, and schematic comparison of aligned vs staggered configurations.

Drop-impact literature has historically split into three camps: solid surfaces, porous media, and single fibers. This work bridges the porous-media and single-fiber camps by producing resin-3D-printed fiber arrays sized and packed like mammalian fur (50-150 strands/cm²) and then dropping water on the whole array rather than on a single strand. Fixing each fiber at both ends eliminates cantilever beam dynamics, isolating the wetting physics. Density, alignment, strand cross-section, and wettability are all independently controlled. Two configurations are tested: aligned (square grid) and staggered (every other row shifted by half a cell). Staggered arrangements consistently reduce penetration relative to aligned arrays of identical density, by up to 34% at We ≈ 80.

Penetration saturates with density

Figure 7 from the paper: normalized max penetration depth vs Weber number, six panels showing the saturation behavior with density and the aligned vs staggered comparison.

Normalized maximum penetration depth versus Weber number for hydrophilic (left) and hydrophobic (right) arrays at three densities (about 50, 100, and 144 strands/cm squared), aligned vs staggered. As density rises toward the density of natural pelts, the curves flatten: a dynamic ceiling on penetration that natural pelts already exploit.

Supplementary videos

Watch all of them as a playlist on YouTube →

Movie S1: Impact classifications

Image sequences of all eight observed impact classifications, paired with the normalized temporal heat maps from Figure 3.

Movie S2: Aligned, 144 strands/cm², U ≈ 0.5 m/s

Drops impact aligned fiber arrays at packing density 144 strands per square centimeter, at an impact velocity of about 0.5 m/s.

Movie S3: Aligned, 144 strands/cm², U ≈ 0.3 m/s

Same array as Movie S2, lower impact velocity (about 0.3 m/s), for contrast in the impact regime.

Movie S4: Aligned, 144 strands/cm², U ≈ 0.5 m/s

Movie S2 with time annotations overlaid for readers tracking each impact phase.

Movie S5: ≈5 m/s impacts, hydrophilic vs hydrophobic

The climax of the paper: at raindrop velocities (≈5 m/s), hydrophobic fibers (right) shatter the drop into many fragments that deeply penetrate the array, whereas the hydrophilic case (left) stops the drop at finite depth. Counter to intuition, hydrophilic horizontal fibers win at raindrop speeds.

Citation

@article{rible2024horizontal,
  author  = {Rible, Gene Patrick S. and Spinazzola, Michael A. and Jones, Robert E. and Constantin, Rachel U. and Wang, Wei and Dickerson, Andrew K.},
  title   = {Dynamic Drop Penetration of Horizontally Oriented Fiber Arrays},
  journal = {Langmuir},
  volume  = {40},
  number  = {26},
  pages   = {13339--13354},
  year    = {2024},
  doi     = {10.1021/acs.langmuir.4c00371}
}

Acknowledgments

This research was partially funded by the National Science Foundation (CMMI 1825801 and CBET 2153740). We thank undergraduate research assistants at the Fluids and Structures Laboratory, Visalsaya Chakpuang, David Job Dooley, and Agustin Soto for bespoke code contributions, Rachel Robinette for video analysis, and Syed Jaffar Raza for editing the supplementary videos. We also give special thanks to Mohammad Alipanahrostami for coating our hydrophobic fibers.

Discussion

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