Size distribution of cell pattern observed in gravitational instability.

Gravitational instability occurs at the interface of two solutions when a higher-density solution (HDS) is placed on the surface of a lower-density solution (LDS). As the HDS sinks, a cell pattern forms on the surface. We investigate the size distribution of the cells in this pattern. We show that the cumulative size distribution obeys a power law with a power index that is independent of time as long as it is possible to neglect the interactions among the cells. To understand the power law mechanism, a simple model excluding the interactions is proposed, and we demonstrate that this simple model provides the power law measured in experiments. Our results indicate that independent cell generation and growth are key factors to understand the feature of the cell pattern.