Yaru's Notes

Contact Angle Measurement [part 2]

Understanding how liquids interact with solid surfaces is fundamental to materials science. Contact angle measurement provides a quantitative way to characterize these interactions, revealing whether a surface is hydrophobic or hydrophilic, and enabling precise control of wettability.

I’ve developed a web-based contact angle measurement tool, and in this post, I’ll show you how to use it. You are welcome to contact me for advices and suggestions.

Implementation of Contact Angle Measurement by Polynomial Fitting

Overview of the Method

This software uses a quadratic polynomial fitting approach. Here’s how it works:

  1. Image preprocessing: Enhance contrast, remove noise, detect edges
  2. Contour extraction (optional visual aid): Automatically identify and display the droplet boundary to help guide point selection
  3. Contact point identification: You mark where the droplet touches the surface
  4. Baseline correction: Account for substrate tilt
  5. Fitting point selection: You select points along the droplet profile (these determine the final result)
  6. Polynomial fitting: the software fits a curve to your selected points
  7. Tangent calculation: Calculate slope at the contact point using derivatives
  8. Angle computation: Convert slope to angle, apply baseline correction

Quadratic Polynomial Fitting

The software fits a second-order polynomial (quadratic) to the droplet profile:

y = ax² + bx + c

Why not higher order? A quadratic fitting provides the most consistent results for a range of various droplet shapes.[1]

The 4-10% Rule – Where to Select Points

The optimum domain range for the fittings lies within 4% to 10% of that of the original droplet diameter. In this region, the standard deviation is particularly low.[1]

Using the Software: Step-by-Step Guide

the contact angle measurement tool

  • Step 1: Upload Image: Click “Choose File” and select your droplet image (PNG, JPG, JPEG, or BMP). PNG is recommended for lossless compression. After selecting, click “Upload Image.”

  • Step 2: Detect Contour (Optional Visual Aid): Click “Detect Contour” to run automatic edge detection. If contour detection fails or looks imperfect: Don’t worry! You can still proceed with measurements. As long as you can see your droplet in the original image, you can zoom in and accurately select fitting points along the visible edge. The contour is just an auxiliary feature for user to select fitting points.

  • Step 3: Set Contact Points: Now tell the software where the droplet contacts the surface. Important: Use zoom here! Zoom in using the zoom control for accurate pixel selection.

  • Step 4: Set Baseline

  • Step 5: Select Fitting Points (Left Side then right): Click “Left Points”, select 5-10 points along the left droplet profile, then click “Right Points”, select 5-10 points along the right droplet profile.

  • Calculate Contact Angle: Click “Calculate Contact Angle” and get the result.

References

[1] Quetzeri-Santiago, Miguel A., J. Rafael Castrejón-Pita, and Alfonso A. Castrejón-Pita. “On the analysis of the contact angle for impacting droplets using a polynomial fitting approach.” Experiments in Fluids 61.6 (2020): 143.