Energy analysis of condensate growth on superhydrophobic surfaces with hierarchical roughness

Micro/nano-structured superhydrophobic surfaces can enhance dropwise condensation via coalescence-induced condensate jumping in well-tailored supersaturation conditions. In this paper we report our energy-based analysis of growth dynamics of dropwise condensates on biomimetic surfaces with two-tier micro/nano-textures, which are superior to solely nanotextured surfaces in controlling nucleation density. To understand the role of condensate state transition, i.e., from partially wetting state (PW) to suspended Cassie state (S), in enhancing condensation heat transfer, we considered adhesion energy, viscous dissipation and contact line dissipation as the main portion of resistant energy that needs to be overcome by the condensate droplets formed in surface cavities. By minimizing the energy barrier of the state transition, we optimized first tier roughness on the hierarchically textured surfaces allowing condensates to grow preferentially in the out-of-plane direction. The nanoroughness of the second tier plays an important role in abating the adhesion energy in the cavities and contact line pinning. From the perspective of molecular kinetic theory (MKT), the hierarchically engineered surface is beneficial to remarkably mitigating contact line dissipation. This study indicates that scaling down surface roughness to submicron scale can facilitate self-propelled condensate removal. INTRODUCTION During dropwise condensation on a superhydrophobic surface with micro/nanostructures, condensate droplets can grow and form in three morphologies, i.e., the suspended state (S)1, the wetting state (W)2, or the partially wetting state (PW). 3 A condensate droplet in the suspended state (Cassie droplet), sits on the tips of micro/nanostructures with an air layer filling the structures under the droplet. A Cassie droplet exhibits a large contact angle (> 150o) and a small hysteresis (< 5o) leading to self-propelled rapid removal via coalescence-induced jumping. Consequently Cassie condensates are desired in order to achieve self-purging of the condenser surface. On the contrary, a droplet in the Wenzel state, which is separated by a local energy barrier4, 5 from the Cassie state, fills the structures under the droplet resulting in an immobile droplet due to strong adhesion to the structured surface. By contrast, a droplet in the PW state only partially fills the structures under the droplet. Importantly, recent studies based on droplet morphology analysis have found that condensates in the PW state on structured surfaces can give rise to 56% higher heat transfer than those on flat hydrophobic surfaces, whereas suspended condensates counterintuitively result in 71% degradation in heat transfer because of the low thermal conductivity of the air layer underneath.3 Therefore, PW condensates are preferred to enhance condensation heat transfer and subsequent self-propelled or coalescence-induced PWCassie state transition6,7 is desired for self-purging of the condenser surface, which is essential for sustaining continuous dropwise condensation (CDC) with enhanced heat transfer. Superhydrophobic lotus-leaf-like surfaces can not only allow for easy droplet removal at micrometric length scales during condensation but also promise to enhance heat transfer performance if designed properly. Recently droplet jumping condensation on a nanostructured superhydrophobic CuO surface has been demonstrated to enable about 30% heat transfer enhancement compared to state-of-the-art dropwise condensation.7 However, these condensation experiments were conducted in carefully-tailored and mild thermal conditions with a low supersaturation (< 1.12) and a low critical heat flux (< 8W/cm2), above which condensate flooding on the condenser surface would occur. Therefore nano-engineered surfaces for sustained dropwise condensation require careful control of surface structure length scale and geometry, nucleation density, droplet morphology, and even departure dynamics. Based on interfacial energy analysis, Rykaczewski et al. reported that the growth mechanism of individual water microdroplets on nanotextured surfaces is universal and independent of the surface architecture.8 The key role of the nanoscale topography is confinement of the base area of forming droplets, which allows droplets to grow only through contact angle increase. The nearly spherical droplets formed in this fashion become highly mobile after coalescence. By comparing experimentally observed drop growth with interface free energy calculations, they found that the minimum observed confined microdroplet base diameter depends directly on the nanoscale surface roughness and degree of interfacial wetting. Specifically, the microscale condensation mechanism depends on the height of a liquid film with volume equal to the fill volume between the nanostructures. Through observing condensation on one tier of nanowires in an environmental scanning electron microscope (ESEM), Rykaczewski et al. claimed that the formation of condensate nuclei could be controlled close to the top of the nanostructures.8 But how to form discrete condensate distribution on the surface of nanowires postponing flooding as well as validation of condensation heat transfer enhancement were not systematically studied in this work. 13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics