Evolution of the size distribution of oil droplets on a water surface: Setup, image processing, and scaling laws

In this thesis, I describe my work towards a novel experiment to study the dynamics of oil droplets on water. It allows following the evolution of the droplet size distribution during a coalescence process with superb statistics. Every experiment run involves more than 20,000 initial droplets coalescing into a few hundred within four to six hours, with droplet sizes ranging from 0.01 cm2 to 1,000 cm2. Data acquisition is built around an LED light source and a shadow image method that exploits the oil droplets’ optical properties. Images of the droplet configuration are taken with a consumer-level DSLR camera and processed with circle detection and morphological methods. I have developed two open-source software frameworks: one facilitates camera remote control at higher frame rates than available in existing software solutions, the other one simplifies the task of batch image processing. The coalescing oil droplets reveal an uncommon characteristic: As the system evolves, the distribution of droplet sizes becomes bimodal. By dividing the droplets into a group of small and a group of large droplets, we are able to identify three regimes in the coalescence process. We introduce a mathematical model in which the distribution decomposes into a superposition of a steady distribution of small droplets and a scaling distribution of larger droplets