Frost-free zone on macrotextured surfaces

Abstract

Numerous studies have focused on designing functional surfaces that delay frost formation or reduce ice adhesion. However, solutions to the scientific challenges of developing antiicing surfaces remain elusive because of degradation such as mechanical wearing. Inspired by the discontinuous frost pattern on natural leaves, here we report findings on the condensation frosting process on surfaces with serrated structures on the millimeter scale, which is distinct from that on a conventional planar surface with microscale/nanoscale textures. Dropwise condensation, during the first stage of frosting, is enhanced on the peaks and suppressed in the valleys, causing frost to initiate from the peaks, regardless of surface chemistry. The condensed droplets in the valley are then evaporated due to the lower vapor pressure of ice compared with water, resulting in a frost-free zone in the valley, which resists frost propagation even on superhydrophilic surfaces. The dependence of the frost-free areal fraction on the geometric parameters and the ambient conditions is elucidated by both numerical simulations based on steady-state diffusion and an analytical method with an understanding of boundary conditions independent of surface chemistry. We envision that this study would provide a unified framework to design surfaces that can spatially control frost formation, crystal growth, diffusion-controlled growth of biominerals, and material deposition over a broad range of applications.

Keywords: antifrosting; bioinspiration; condensation frosting; diffusion.

Fig. 1.

Discontinuous frost pattern on (A and B) the natural leaves and (C) the 3D-printed artificial leaf (the area within the red dashed circle in the Left image is magnified in the Right image). The blue and red dashed circles represent the preferred/suppressed frosting on the convex/concave vein features, respectively.

Fig. 2.

Condensation frosting on serrated surfaces inspired by leaves. (A) Schematic of an aluminum serrated surface. The images show an apparent contact angle θ* = 114° on hydrophobic surface, and 18° on superhydrophilic surface. (Scale bars, 1 mm.) Droplet volume is 5 μL. (B) Schematic of the experimental setup for controlled frost growth (not drawn to scale). A humidity sensor connected to an external humidity controller is not drawn, for simplicity. (C) Time lapse images showing the condensation (80 s), fast propagation (200 s), evaporation (910 s), and ice-free (2,270 s) bands. The surface has a vertex angle of 60°. The regime between the yellow dashed lines indicates the frost-free zone. (Scale bars, 1 mm.) (D and E) Micrographs of the frosting process at the (D) peak and (E) valley. The surface has a vertex angle of 90°. (Scale bars, 0.2 mm.) The red and blue dashed lines indicate the relative positions of the peak and valley, respectively. Yellow dashed circles show the distribution of droplet sizes condensed near the peak and valley regions. Both surfaces are hydrophobic. The ambient humidity is 25% at T = 23.5 °C, and surface temperature is −12 °C. (F) Schematic of the frosting mechanism. (G) Boundary conditions for simulating the diffusion of water vapor during the condensation stage. The schematic is not to scale. (H) The concentration field of water vapor and (I) the normalized flux magnitude, both near the serrated surface features.

Fig. 3.

Formation of the frost-free band. Increasing (A) the vertex angle of the serrated features α or (B) the ambient humidity RH results in a wider areal frost coverage. Experimental measurements of the frost coverage (crosses) agree with the predictions made by simulations using the evaporation model (open circles) and the no-condensation model (open diamonds). (C) Boundary conditions for simulating evaporation of droplets in the valley. (D) Diffusion flux in the valley is positive (water vapor diffuses onto the wall) when frost coverage is low (50%), and negative (water vapor diffuses out from the wall) when frost coverage is high (62%). The arrows indicate directions and do not represent their magnitudes. (E) Boundary conditions for simulating diffusion of water vapor after evaporation. (F) Water vapor in the valley is supersaturated when frost coverage is low (42%), and undersaturated when frost coverage is high (58%). S, L, and Dry stand for solid, liquid, and dry domain, respectively.

Fig. 4.

Analytical model with the boundary conditions for predicting the areal frost coverage on the serrated surface. (A) Boundary conditions in each phase regime between two peaks. (B) Scaling relation that connects the concentration at the boundary of the vapor and solid domain (c_b, defined in A) with the geometric parameter (α, defined in Fig. 2A) and the ambient water vapor concentration (c₀, defined in A). (C) Scaling relation between the frost-free zone (1 − f, defined in Fig. 2F) and the combined parameter composed of c_b and α. Simulated data points are based on the evaporation model using 20° ≤ α ≤ 90°, and 20% ≤ RH ≤ 100%. (D) Map of frost-free zone as a function of the vertex angle (α) and ambient relative humidity (RH) with experimental results. While state-of-the-art microtextured/nanotextured surfaces show no frost-free zone (i.e., 100% frost coverage), the vein of the artificial leaf (α = 45°) in Fig. 1C and a serrated surface with α = 40° show the predicted frost-free zone (i.e., 50% frost coverage) for 5 h (SI Appendix, Fig. S3G) under a similar frost condition (RH = 25 to 50%, surface temperature is <−10 °C). The Inset shows the frost-free coverage on the veins of an artificial leaf. The frost coverage that corresponds with vertex angle and ambient humidity further corroborates the results of the map.