Wetting State, Dynamics And Heat Transfer Of Condensed Droplets On Super-hydrophobic Surfaces

Superhydrophobic mirco/nanotextured surfaces for dropwise condensation have recently attracted significant attention due to their potential to enhance heat transfer performance. A drop deposited on a superhydrophobic surface (SHS) can appear in Cassie state with its apparent contact angle (CA) larger than150°and a very small rolling angle. However, drops have different wetting states and behavior in the process of condensation. Most of the literatures reported that the superhydrophobicity of SHS usually lost under the condensation condition. Condensed drops exhibited Wenzel state or combined state of Wenzel and Cassie. On the other hand, a few studies reported that condensed drops could still display Cassie state on a SHS with the drops easily rolling off the surface. The mechanism of this is not clear. In this study, interface free energy (IFE) of condensed drops during their shape changes was calculated to analyze the wetting state and dynamic behavior of condensed drop on a SHS with different structural parameters. And a new model for dropwise condensation heat transfer was proposed to analyze the influence of SHS on heat transfer.Firstly, the Wenzel and Cassie-Baxter equations were derived based on the lowest IFE. Then the volume of a Wenzel drop was considered as two parts, inside and outside micro/nano textures. The CA was calculated and compared with the results obtained by Wenzel equation. And the applicable conditions of Wenzel equation related to the drop volume and the structural parameters were confirmed.Then the driving force and resistance of a condensed drop, which comes from the growth and combination of numerous initial condensation nuclei, was calculated during its shape changes from the early flat shape to a Wenzel or Cassie state. The final state of a condensed drop was determined by whether the resultant force is always greater than0. The calculation results indicate that the condensation drops on the surface only with microroughness display Wenzel state because the resultant force decreases to zero before the basal radius reduces to zero. On a surface with proper two-tier roughness, however, the resultant forces will always be greater than zero. Therefore, a condensed drop on the two-tier surfaces can spontaneously change into Cassie state.Next, the energy increasing rate (EIR) of a condensed droplet was analyzed during its growth in three different modes. And the slowest energy increasing rate corresponding to one of the three routes was used as the criterion to determine the pathway along which a condensed drop will go. The results show that the EIR according to the mode of increasing CA is much smaller than that according to the two other modes during the first period growth of a condensate spot formed within nano-structure, so that it will grow with CA enlarging but base area unchanging until advancing CA. After this, the EIR according to the mode of CA increasing becomes much higher than that according to the two other modes. The three phase contact line (TPCL) of the drop starts to shift and the base area begins to enlarge while CA keeps unchanging. During this second period, the state of increased base area can be wetted, i.e. a Wenzel state droplet or it can be in composite state, i.e. a partially wetted (PW) droplet. The growth mode and its wetted state of a condensed droplet are strongly related to nano-structure. PW condensed drops can appear only on the surfaces with nano-pillars possessing certain height and smaller pitches.Furthermore, the self-propelled jumping mechanism of a coalesced condensed drop on surface was studied. The initial shape of a coalesced drop is determined by the conservation of drop volume and the surface free energy before and after two condensed drops merge. Then the driving force and resistance on TPCL are analyzed during the drop transformation. And the dynamic equation describing the shape conversion of the droplet is proposed and solved. Whether a coalesced condensed drop could jump on a surface is determined by the speed at which the center of gravity moves up when the base radius of the drop reduces to0. The calculation results show that a coalesced droplet on flat surface can transform its shape limitedly. It cannot jump since its transformation stops before it comes to its equilibrium state. A wetted drop on rough surfaces is even more difficult to transform and jump because of the greater TPCL resistance. However, drop on a two-tier surface or a PW drop on nano-structure exhibits a shape transition and possible jumping upon coalescence if the micro and nanostructure parameters are suitable. A too small or too large merged drop will not jump because the obvious viscous dissipation energy or drop gravity respectively dominates the behavior of the drop.Finally, in consideration of the final wetting state of a condensed droplet, its movement behavior and the relative relationship between drop size and structure’s scale, a new model for dropwise condensation heat transfer on superhydrophobic nanotextured surfaces was proposed by estimating the heat flux of a single condensate drop based on thermal resistance analysis and by using the population theory for small and large condensate drops. The calculation results show that nanotextured surface with droplets displaying PW state and jumping after merge has the better heat transfer performance. When droplets depart from a surface by gravity, the overall heat flux will reduce significantly. The overall heat flux will be lower than that of dropwise condensation on the flat surface when droplets display Wenzel state on nanotextured surfaces. However, once the subcooling is high, the condensed droplets on present textured surfaces will quickly merge and flood the nano-structures, which leads to the lower overall heat flux on nanotexture surface than that on flat surface.