In the coating applications, liquid surface tension measurement is critical, which include liquid-air interfacial tension and liquid-substrate (solid) interfacial tension. Contact angle measurement is a common method for the surface tension measurement; however liquid surface tension might not be available for the measurement. Pendant drop method is a good for this purpose.
Theory
The method is based on the calculation derived from the classic Young− Laplace equation.
Where ,
- σ: the surface tension
- R1 and R2: the first and second radius of curvature at point d as shown in the above figure
- R0: the radius of curvature, apex of the drop, usually set as the origin for analysis
- Δρ is the density difference between the liquid drop and continuous phase, e.g. air.
- g: local gravitational acceleration
- z: height of the point d from the horizontal axis.
where beta is form parameter, or also called Bond number (B0), which is a measure of the relative importance of gravitational forces to interfacial forces. The larger bond number, the greater gravitational contribution for the liquid droplet shape.
Measurement tool
Testing procedure
Take a photo of the droplet, image defination, fitting, and get the surface tension data.
Factors for accurate measurement
- Light source must be diffused to avoid optical aberrations and spurious reflection.
- No distortion in camera images
- Needle must be absolutely vertical
- No vibration
- DROPLET size and needle diameter are very critical; try to make Worthington number, W0, close to one.
Worthington number is defined as
Source /Reference
- Source 1: http://dx.doi.org/10.1016/j.jcis.2015.05.012
- Source2: https://doi.org/10.1021/acs.jced.1c00212?rel=cite-as&ref=PDF&jav=VoR
- kruss-scientific.com