Three-dimensional Phase-field Modelling of Droplet Evolution on Patterned Substrates

  • Krishnan, Aravind (Indian Institute of Technology Kanpur)
  • Kumar, Rajan (Indian Institute of Technology Kanpur)
  • Bandyopadhyay, Soumya (University of Florida)
  • Mukherjee, Rajdip (Indian Institute of Technology Kanpur)

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Wetting phenomena and the mechanisms that control them have been the subject of scientific interest for decades. Inspired by natural surfaces such as lotus leaves and rose petals, extensive efforts have been devoted to mimicking their superhydrophobic properties. Controlled dewetting plays a crucial role in nanopattern generation or solid-state device fabrication. While wetting is classically described by Young’s equation, practical wetting behaviour is influenced by surface geometry, contamination, roughness, deformation, and external fields such as pressure, gravity, and electromagnetic forces. In this work, we employ the classical Cahn–Hilliard equation with a modified free-energy functional to model the purely physical interaction of a liquid droplet with a solid substrate in three dimensions, excluding chemical effects. We first investigate the evolution of the spherical droplet on planar substrates and subsequently extend the analysis for varying shapes and sizes. The model is then applied to textured substrates with regular patterns, where transitions between Wenzel and Cassie–Baxter wetting states are observed, and their dependence on substrate parameters is quantified. The results are compared with existing experimental and numerical studies for validation. The interplay between hydrophobic and hydrophilic states, the stabilisation of the Cassie–Baxter state, and the simultaneous evolution of multiple droplets with equal volumes but different radii of curvature are analysed.