Analyzing the Singularities of Freezing Sessile Water Droplets
Department of Physics & Astronomy, Dickinson College (Carlisle, PA)
M.E. Bonomo, C. Caslin, D. Lifschitz, T.I. Smith, & D.P. Jackson
Senior Capstone Research Project, Fall 2012 – Spring 2013
A singularity is a system’s attempt to confine opposing forces to a single point. There are quite a few intriguing occurrences of singularities in nature. The swirl of a baby’s cowlick is the point at which all differently oriented hairs meet. The air is completely still in the eye of a hurricane, whereas there are strong winds blowing in every direction outside of this point. Or, more abstractly, consider what time it would be if we were standing in the very center of the North pole — the place at which all time zones converge. In fluid mechanics, we often see the emergence of singularities at the point between two fluid phases. For example, sessile water droplets (immobile on a flat surface), that freeze from the bottom to the top, form a cusp at the very end of the transformation.
We experimentally, mathematically, and computationally investigated the singularity that forms at the tip of water droplets freezing on a flat surface (Snoeijer and Brunet, AJP 2012). The pointy tip appears to be a result of the opposing forces of the liquid’s surface tension and the solid’s expansion while freezing, such that in the final moments of the solidification process, the liquid is forced to self-focus to a point. Our geometric model predicted solidified drops about 15% greater in volume than those experimentally observed.
- M. E. Bonomo, “Analyzing the Singularities of Freezing Sessile Water Droplets.” Dickinson College Honors Theses (4), 2013.