Marangoni FractalMingjun FanAward: Top 100
School: beijing national day school When artists are creating a painting, they sometimes deposit drops of ink-alcohol mixture onto diluted acrylic paint. The droplets will then spread in a fractal manner, creating a sense of both chaos and order in their artwork and demonstrating the intertwining relationship between scientific rationality and artistic sensibility. In order to better understand the process, the formation of such pattern can be divided into two parts: the stable spreading stage and the fractal stage. In the former stage, the interfacial tension gradient due to alcohol evaporation will cause the ink-alcohol mixture to expand in the direction of higher surface tension on the periphery, which is actually called the Marangoni effect. In the latter stage at the initial moment of fractal formation, it has been proposed that the evaporation of alcohol will cause a small gradient in the interfacial tension at the boundary, and this gradient will amplify the originally small perturbation at the interface. The analysis reveals that there is a special wave that is amplified most violently, which corresponds to first-layer bifurcation number. Such amplifying of perturbation continues after each branch experiences the above two stages, thus forming a fractal pattern. The phenomenon itself is highly repeatable across variables depending on the type of ink, thickness, viscosity, and so on. It shares similarity with the well-known viscous finger phenomenon and countless other fractals in nature. However, systematic research into the mechanism behind this particular phenomenon is still to be continued in the future. 
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