Effect of fluid viscosity on surface patterns formed by gravitational instability

When a droplet of a higher-density solution (HDS) is placed on the top of a lower-density solution (LDS), the HDS on the surface of the LDS sinks due to gravitational instability. In the sinking process, the HDS draws a fractal pattern or a hole/cell pattern on the surface of the LDS. It is observed that the surface pattern is determined by an aspect ratio of the container and viscosity of the LDS. In the formation of the surface pattern, a time series of the HDS density is analyzed. It is found that the profile of the series for the fractal pattern is different from that for the hole/cell pattern. In order to clarify the difference, we propose a phenomenological model for the time series to obtain fitting functions for both patterns.