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Contact Angle01:13

Contact Angle

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When a solid is dipped inside a liquid, the liquid surface becomes curved near the contact. For some solid–liquid interfaces, the liquid is pulled up along the solid, while for others, the liquid surface is convex or depressed near the solid surface. This phenomenon can be explained using the concept of cohesive and adhesive forces.
The adhesive force is the molecular force between molecules of different materials, that is, between the molecules of the solid and the liquid. The cohesive...
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Related Experiment Video

Updated: Apr 19, 2026

Fabrication of Superhydrophobic Metal Surfaces for Anti-Icing Applications
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An algorithm for selecting the most accurate protocol for contact angle measurement by drop shape analysis.

Z N Xu1

  • 1State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Baoding 071003, China.

The Review of Scientific Instruments
|January 3, 2015
PubMed
Summary

This study compares three static contact angle algorithms, finding they are complementary. A novel combined algorithm improves accuracy across all water drop volumes and contact angles, enhancing static contact angle measurements.

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Area of Science:

  • Surface Science and Engineering
  • Materials Science
  • Physical Chemistry

Background:

  • Accurate static contact angle measurement is crucial for understanding surface properties and material interactions.
  • Existing algorithms like circle-fitting, ellipse-fitting, and axisymmetric drop shape analysis-profile (ADSA-P) have limitations in accuracy and noise resistance.
  • Numerical simulation of water drop profiles provides a reliable basis for error analysis.

Purpose of the Study:

  • To perform an error analysis of widely used static contact angle algorithms using real and numerically generated water drop profiles.
  • To systematically investigate the influence of water drop volume, contact angle, and noise level on algorithm accuracy.
  • To develop and validate a novel, more accurate combined algorithm for static contact angle measurement.

Main Methods:

  • Generated numerous water drop profiles with varying volumes, contact angles, and noise levels using numerical methods based on the Laplace equation.
  • Evaluated the accuracy of circle-fitting, ellipse-fitting, and ADSA-P algorithms against these generated profiles.
  • Developed a new algorithm by combining the strengths of the three investigated algorithms and defined selection rules.

Main Results:

  • Circle- and ellipse-fitting algorithms exhibit low errors and high noise resistance for small/medium volume and contact angle drops.
  • ADSA-P algorithm is accurate for large volume and contact angle drops but sensitive to noise at small volumes/angles.
  • The proposed combined algorithm accurately measures static contact angles across the entire hydrophobicity range, overcoming individual algorithm deficiencies.

Conclusions:

  • The three analyzed algorithms are complementary, each suited for different drop characteristics.
  • A novel combined algorithm significantly improves the precision and reliability of static contact angle measurements.
  • The developed algorithm selection rules ensure accurate evaluation, avoiding common sources of error in static contact angle measurements.