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Dynamic contact angle model for resolving low-viscosity droplet oscillations during spreading over a surface with varying wettability

Raghvendra Kumar Dwivedi, Vandana Jain, and K. Muralidhar*

  • Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

  • *Corresponding author: kmurli@iitk.ac.in
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Phys. Rev. Fluids 7, 034002 – Published 15 March, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.034002

Abstract

Droplet oscillations of low-viscosity liquids spreading over textured surfaces arise from pinning of the three-phase contact line that is, in turn, related to hysteresis in the wetting behavior of real surfaces. A dynamic contact angle model proposed in the present work improves the existing models by including the pinning of contact line motion. Experiments are conducted on four substrates of distinct hydrophobicity. The initial Weber number of the drop is deliberately kept small (<0.34) so that surface characteristics dominantly influence spreading. Specifically, a superhydrophobic surface with small hysteresis is shown to display small oscillations, while a hydrophobic surface with large hysteresis has large persistent oscillations. Numerical simulations are subsequently performed with the proposed dynamic contact angle model and compared with experiments. The model is also validated against experiments reported in the literature at a higher Weber number of 31.67. The model successfully predicts the contact angle evolution on the chosen surfaces, including oscillations. Specific experimental trends such as spreading, retraction, pinning of the contact line and underdamped oscillations of the drop height emerge as part of the numerical solution. With the proposed contact angle model, propagation of surface waves at the gas-liquid interface from and toward the apex is revealed as a factor responsible for the observed behavior of drop spreading.

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Phys. Rev. Fluids 7, 034002– Published 15 March, 2022
  • Received 4 December 2021
  • Accepted 2 March 2022
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