Hierarchical Condensation

Xiao Yan, Feng Chen, Soumyadip Sett, Shreyas Chavan, Hang Li, Lezhou Feng, Longnan Li, Fulong Zhao, Chongyan Zhao, Zhiyong Huang, Nenad Miljkovic

Research output: Contribution to journalArticlepeer-review


With the recent advances in surface fabrication technologies, condensation heat transfer has seen a renaissance. Hydrophobic and superhydrophobic surfaces have all been employed as a means to enhance condensate shedding, enabling micrometric droplet departure length scales. One of the main bottlenecks for achieving higher condensation efficiencies is the difficulty of shedding sub-10 μm droplets due to the increasing role played by surface adhesion and viscous limitations at nanometric length scales. To enable ultraefficient droplet shedding, we demonstrate hierarchical condensation on rationally designed copper oxide microhill structures covered with nanoscale features that enable large (∼100 μm) condensate droplets on top of the microstructures to coexist with smaller (<1 μm) droplets beneath. We use high-speed optical microscopy and focal plane shift imaging to show that hierarchical condensation is capable of efficiently removing sub-10-μm condensate droplets via both coalescence and divergent-track-assisted droplet self-transport toward the large suspended Cassie-Baxter (CB) state droplets, which eventually shed via classical gravitational shedding and thereby avoid vapor side limitations encountered with droplet jumping. Interestingly, experimental growth rate analysis showed that the presence of large CB droplets accelerates individual underlying droplet growth by ∼21% when compared to identically sized droplets not residing beneath CB droplets. Furthermore, the steady droplet shedding mechanism shifted the droplet size distribution toward smaller sizes, with ∼70% of observable underlying droplets having radii of ≤5 μm compared to ∼30% for droplets growing without shading. To elucidate the overall heat transfer performance, an analytical model was developed to show hierarchical condensation has the potential to break the limits of minimum droplet departure size governed by finite surface adhesion and viscous effects through the tailoring of structure length scale, coalescence, and self-transport. More importantly, abrasive wear tests showed that hierarchical condensation has good durability against mechanical damage to the surface. Our study not only demonstrates the potential of hierarchical condensation as a means to break the limitations of droplet jumping, it develops rational design guidelines for micro/nanostructured surfaces to enable excellent heat transfer performance as well as extended durability.

Original languageEnglish (US)
Pages (from-to)8169-8184
Number of pages16
JournalACS Nano
Issue number7
StatePublished - Jul 23 2019


  • coalescence
  • condensation
  • diverging
  • hierarchical surfaces
  • jumping
  • self-transport
  • superhydrophobic

ASJC Scopus subject areas

  • Materials Science(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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