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A Linear-Regression-Based Method for Determining Surface Tension from Variation in Interfacial Curvature.

Carrie E Perlman1, Bret A Brandner2, Stephen B Hall2

  • 1Department of Biomedical Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030, United States.

Langmuir : the ACS Journal of Surfaces and Colloids
|August 20, 2025
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Summary
This summary is machine-generated.

A new linear regression method accurately determines surface tension (γ) from interfacial curvature, even with surfactants. This approach simplifies surface tension measurement for fluid interfaces, offering a valuable tool for scientific research.

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Area of Science:

  • Fluid dynamics
  • Surface science
  • Physical chemistry

Background:

  • Surface tension (γ) is crucial for fluid interfaces, balanced by hydrostatic pressure (ΔP) via the Young-Laplace relation.
  • Surfactants can alter interfacial properties, necessitating accurate methods for γ determination.
  • Existing methods may not fully account for surfactant effects on interfacial tension.

Purpose of the Study:

  • To develop a novel linear-regression-based method for determining surface tension (γ) from interfacial curvature.
  • To validate the method using sessile droplets and captive bubbles with dipalmitoyl phosphatidylcholine (DPPC) monolayers.
  • To assess the accuracy of the new method against established techniques like axisymmetric drop shape analysis.

Main Methods:

  • Utilizing the Young-Laplace relation (ΔP = γ (k1 + k2)) and the linear variation of ΔP with elevation.
  • Analyzing images of sessile droplets and captive bubbles to measure interfacial curvature (k1 + k2) at different elevations.
  • Applying linear regression to the plot of ΔP (offset) versus (k1 + k2) to determine γ.

Main Results:

  • Interfacial curvature (k1 + k2) was found to vary linearly with elevation, consistent with the Young-Laplace relation.
  • The developed linear regression algorithm accurately determined surface tension (γ).
  • Comparison with axisymmetric drop shape analysis showed an average absolute difference of 0.30 ± 0.37 mN/m for DPPC monolayers across a γ range of 2-70 mN/m.

Conclusions:

  • The new linear-regression method provides an accurate and accessible means to determine surface tension (γ) from interfacial curvature.
  • The method is robust even in the presence of surfactants like DPPC.
  • The underlying theory is adaptable for 3D imaging, potentially extending its application to complex interfacial geometries.