Inclined Thin Film Dripping


Long Title: Experimental Investigation of the Rayleigh-Taylor Instability of Thin Films at an Inclined Interface

 

Anyone who has ever painted a ceiling before knows that, if you apply too much paint, the paint will collect and droplets will form. You certainly don’t want droplet formation and neither do any industries that deal with surface coatings. Fortunately, the formation of these droplets from a horizontal surface has been well studied and can be predicted with great accuracy. Not yet studied, however, has been the question of what happens if the surface you are trying to paint is inclined. Will droplets form if the surface is slanted? This was the driving question which led to many long hours watching droplets fall in the Laboratory of Fluid Mechanics and Instabilities at EPFL in Switzerland and which eventually has led to my first published contribution to the scientific community. Publication can be downloaded here.

Image of honey drops and rivulets

Honey dripping from an inclined plane.

From a fluids perspective, this question was an exciting one because the typical method of instability analysis (temporal stability analysis using linear perturbation), failed to answer the question. Instead, a more complex method (absolute-convective instability analysis) was employed and returned results that were at least plausible. I joined this project to design, carry out, and analyze an experiment to asses the validity of the theory that was used.

The experimental design was simple and yet effective in allowing for a wide range of experimental parameters to be tested with minimal uncertainty. In the end, the experimental results agreed surprisingly well with the theory, which is what eventually led to the creation and submission of a publication.

Experimental facility used for RT inclined instability experiments

 

This project was particularly exciting because it allowed me to take a project from the early stages of theory development to the idealized end goal of any project in academia, a full publication. Besides watching droplets fall, there were many experimental questions along the way that needed to be addressed and solved, such as: How can instability best be quantified in this case? How can a 2D model of an infinite domain be assuredly modeled in 3D? What is the surface tension of the fluids we are using?

This last question can be easily answered with instruments that are made for measuring surface tension, however, these instruments were well outside the budget of this project. Fortunately, with the things I had learned in my studies of hydrodynamics, I implemented a method to measure surface tension using only materials that we had in the lab (in fact, the only materials required were a pipette, ruler, and camera). The method relies on the fact that the shape of a suspended droplet must satisfy an equilibrium of hydrostatic pressure and surface curvature pressure at the interfaces. Taking this into account, I wrote a graphical user interface that allows one to reliably measure the surface tension of a liquid just based on the profile of a suspended drop. This program was validated with fluids of known surface tensions and agreed within 2% uncertainty, well within the acceptable range for the experiments.

Pendant Drop Analysis GUI

If this small introduction has left you curious, you are welcome to download the project report by clicking here.