Out-of-Plane Biphilic Surface Structuring for Enhanced Capillary-Driven Dropwise Condensation

Abstract

Rapid and sustained condensate droplet departure from a surface is key toward achieving high heat-transfer rates in condensation, a physical process critical to a broad range of industrial and societal applications. Despite the progress in enhancing condensation heat transfer through inducing its dropwise mode with hydrophobic materials, sophisticated surface engineering methods that can lead to further enhancement of heat transfer are still highly desirable. Here, by employing a three-dimensional, multiphase computational approach, we present an effective out-of-plane biphilic surface topography, which reveals an unexplored capillarity-driven departure mechanism of condensate droplets. This texture consists of biphilic diverging microcavities wherein a matrix of small hydrophilic spots is placed at their bottom, that is, among the pyramid-shaped, superhydrophobic microtextures forming the cavities. We show that an optimal combination of the hydrophilic spots and the angles of the pyramidal structures can achieve high deformational stretching of the droplets, eventually realizing an impressive "slingshot-like" droplet ejection process from the texture. Such a droplet departure mechanism has the potential to reduce the droplet ejection volume and thus enhance the overall condensation efficiency, compared to coalescence-initiated droplet jumping from other state-of-the-art surfaces. Simulations have shown that optimal pyramid-shaped biphilic microstructures can provoke droplet self-ejection at low volumes, up to 56% lower than superhydrophobic straight pillars, revealing a promising new surface microtexture design strategy toward enhancing the condensation heat-transfer efficiency and water harvesting capabilities.

Figure 1

(a) Cross section of the microelements. H = 56 μm and P = 81 μm are kept constant. The half-opening angle is denoted by the Greek letter β. Comparison between superhydrophobic (b) and biphilic (c) microcavities. The biphilic structures induce controlled droplet pinning at the bottom, enabling pressure gradients within the droplet. Detachment from the hydrophilic spot results in conversion of surface energy into kinetic energy, causing surface clearing droplet jumping.

Figure 2

(a) Single droplet growing at the center of the computational domains. Five different microgeometries have been simulated, including uniform superhydrophobic surface in all cases with θ = 166.9°, θ_r = 165.9°, and θ_a = 167.8°. The number following the text “Pyramids” or “Pillars” indicates the angle β. For the β = 7° case, the droplet barely clears the microtexture, while for pillars, the droplet jumps out of the computational domain. (b) The same as (a), but with a hydrophilic spot (θ = 20°, A = 85 μm²) at the center of the domain. Surface clearing jumping events are observed in all cases. The inset figure illustrates the top view of the texture along with location of the hydrophilic spot. Each four-frame sequence shows the growth of the droplet, representing the detachment and/or ejection of the droplet.

Figure 3

(a) Calculated geometrical aspect ratio h/(2R₀) as a function of the droplet volume for biphilic (green) and superhydrophobic (red) surface (for 20° pyramids). h represents the distance from the lowest to the highest point of the droplet, while R₀ represents the radius of a perfectly spherical droplet at the given volume. (b) Volume at which the droplet clears the surface (loses contact) represented for five different microgeometries with biphilic surface (green) and superhydrophobic surface (red). An “X” instead of a bar indicates that the droplet was not completely ejected from the surface. Inset figure illustrates the moment of detachment from the substrate, which was taken as an ejection condition. (c) Vertical force on, and (d) vertical acceleration of the droplet from the moment of detachment from the hydrophilic spot to complete lift off from the surface.

Figure 4

Comparison between two double domains of (a) 20° pyramids and (b) straight-walled pillars, both equipped with hydrophilic spots. The three-frame sequence shows the effect of increasing droplet volume. In the case of the 20° pyramids, the droplets are stretched inside the microcavity, similar to what is observed on the single-droplet domain. The droplets are self-ejected, without interacting with the neighboring droplet. On the pillar domain, coalescence with the neighbor droplet results in ejection at lower individual volume compared to what was observed on the single-droplet domain.

Figure 5

Geometry and boundary conditions. A rectangular computational domain composed of solid and fluid subdomains is used. The base material is shown in blue, while the liquid–vapor interface is depicted in green.