Pattern formation in bubbles emerging periodically from a liquid free surface.

Patterns formed by centimeter scale bubbles on the free surface of a viscous liquid are investigated in a cylindrical container. These bubbles emerge periodically at the surface and interact with each other in the central zone. Their radial emission, due to interaction and radial surface flow, leads to the formation of a variety of patterns. Different star-like and spiral patterns appear spontaneously by increasing the bubble emergence frequency. It is found that these patterns are due to a constant angular shift in the bubble emission direction. Measurements of this angular shift show a supercritical bifurcation accompanied by a transition from a pattern of two opposed straight arms to spiral patterns. By applying the tools and concepts from the study of leaf arrangement in botany (phyllotaxis), the recognized patterns and the mechanism of the pattern formation are discussed. Close similarities to the leaf arrangement are found in the behavior of the angular shift and the patterns. These findings suggest that the observed patterns are formed by a packing mechanism of successively appearing elements (bubbles), which is similar to that of the leaves at the earliest stage of phyllotaxis.