Date of Award


Document Type

Honors Thesis



First Advisor

David P. Jackson

Second Advisor

Trevor I. Smith




Our research 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). We designed an apparatus to observe, video, and quantify the solidification of 10-μL drops of purified water. By making several simplifications about the freezing process, we used a geometric model to derive a system of differential equations that described the solidification rate and the unfrozen liquid’s volume, radius, and contact angle. Analysis of our equations revealed that the appearance of a singularity was dependent on the density ratio between the solid and liquid. This was also evident in the computer-based simulation that we created to predict frozen droplet shapes. While our model did demonstrate the formation of singularities in liquids with a density ratio <0.75, it inaccurately generated rounded solidified water droplets (density ratio 0.9) that were about 15% greater in volume than those experimentally observed.