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Related Experiment Video

Updated: Apr 26, 2026

Measuring the Interaction Force Between a Droplet and a Super-hydrophobic Substrate by the Optical Lever Method
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A finite-element method model for droplets moving down a hydrophobic surface.

Øistein Wind-Willassen1, Mads Peter Sørensen

  • 1Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800, Kongens Lyngby, Denmark, oiww@dtu.dk.

The European Physical Journal. E, Soft Matter
|August 1, 2014
PubMed
Summary

This study models droplet descent on hydrophobic surfaces using the Finite-Element Method (FEM). The model accurately predicts droplet velocity and energy dissipation, aiding in hydrophobic surface characterization.

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Area of Science:

  • Fluid dynamics
  • Computational physics
  • Surface science

Background:

  • Understanding droplet behavior on hydrophobic surfaces is crucial for applications like microfluidics and anti-fouling coatings.
  • Previous models often simplified fluid dynamics or surface interactions, limiting predictive accuracy.

Purpose of the Study:

  • To develop a comprehensive 2D computational model for droplet descent on inclined hydrophobic substrates.
  • To investigate the influence of slip length on droplet velocity and energy dynamics.
  • To validate the model against experimental data and explore its utility in characterizing hydrophobic surfaces.

Main Methods:

  • A 2D Finite-Element Method (FEM) model was established to solve the Navier-Stokes equations within the droplet.
  • The arbitrary Lagrangian-Eulerian (ALE) method was employed to track the dynamic droplet surface.
  • Frennet-Serret equations were used to incorporate contact angle effects.
  • Energy components (translation, internal motion, dissipation) and tracer particle trajectories were quantified.

Main Results:

  • The model accurately predicts droplet velocity as a function of slip length, showing good agreement with experimental results.
  • Quantification of energy associated with center-of-mass translation, internal fluid motion, and local energy dissipation was achieved.
  • Predicted tracer particle trajectories within the droplet align with observed sliding motion of accelerating droplets.

Conclusions:

  • The developed FEM model provides a robust framework for simulating droplet dynamics on hydrophobic surfaces.
  • The model successfully describes the sliding motion and energy dissipation of accelerating droplets.
  • This computational approach can be utilized to determine characteristic slip parameters and assess drag reduction for hydrophobic surfaces.