Quantifying surface tension measurements of pendant drops

This study aimed to test the robustness of an open-source Axisymmetric Drop Shape Analysis (ADSA) software [paper and software] for measuring surface tension using pendant drop tensiometry. Surface tension, a phenomenon responsible for insects walking on water, trees taking up water through their roots, and droplets forming on a faucet, is caused by molecular attractions. Molecules at the surface experience a pulling force that minimizes the surface area. At equilibrium, a falling drop contracts into a pendant-like shape, balancing surface tension and gravitational force.

 

 

 

 

 

 

 

In this technique, the software acquires the silhouette of an axisymmetric fluid droplet that obeys the Young-Laplace equation. This equation relates Laplace pressure across an interface to the curvature of the interface and the interfacial tension, γ. By providing the initial parameters, the Young-Laplace equation is iteratively fitted to determine a dimensionless quantity called the Bond (or sometimes
Eötvös) number and the drop radius at the apex,. These parameters are then used to calculate the surface tension at the interface.

To obtain the silhouette, the apparatus was set up as shown below, with major differences from previous configurations, including a diffused light source as the backdrop and a high-resolution DSLR camera.

 

 

 

 

 

 

 

Syringes equipped with needles of different gauges, ground to be blunt, were used to create drops. This approach allowed for better control over drop formation, particularly for low-surface-tension liquids that fall easily. The syringe was kept as parallel to gravity as possible, but the manual creation of the drop introduced some rotation and vibrations. These imperfections introduced variability that tested the software’s reliability and accuracy in analyzing pendant drop profiles.

The experiment was conducted on three liquids with known surface tensions – water, ethanol, and kerosene oil – and one liquid with unknown surface tension – Parker Quink. The resulting values were compared with literature values, except in the case of ink for which references were not available.

The graphs of the results also show that as the Bond number increases, the accuracy of the fitting improves, and the spread of measured Bond numbers and surface tension values becomes negligible for each pendant drop analyzed.

This study demonstrates the potential of the ADSA software not only for accurately measuring the surface tension of various liquids but also for exploring relationships between the physical quantities involved, such as Bond number, drop radius, and interfacial tension. Additionally, this technique can be extended to analyze unknown liquids, offering a reliable method for comparative studies. The open-source nature of the software allows it to be further investigated and customized to accommodate advanced techniques, such as measuring surface tension using constrained sessile drops – a novel approach in surface tension analysis.

 

 

 

 

 

 

 

 

Moreover, there is room for improvement in the experimental setup, such as enhancing stability to minimize vibrations and refining the drop formation process to achieve greater precision in future studies.