Pattern Formation in Glass Caused by Rayleigh-Taylor Instability

Abstract

Beautiful patterns such as snowflakes, wind ripples, and cloud patterns are ubiquitous in nature. Some of those are formed by interfacial instability. We focus on two pattern formations caused by the Rayleigh-Taylor instability. Rayleigh-Taylor instability is an interfacial instability between two liquids that occurs when a heavier liquid is on a lighter liquid. The first pattern we discuss is a fractal/cell pattern in a coffee cup. If a droplet of coffee solution is placed on milk, the coffee solution spreads on the surface of the milk. Then the Rayleigh-Taylor instability occurs at the interface between the coffee solution and milk, and the coffee solution starts to sink into the milk. We found that the fractal or the cell pattern is formed at the surface of the milk in this process. We showed that an aspect ratio between the radius of the container and the depth of the milk affects vertical flow and it leads to a transition between the fractal pattern and the cell pattern. We also showed that the fractal pattern is formed by a similar mechanism of a viscous fingering. The second pattern is a breakup of a droplet. A sinking droplet in a viscous solution spontaneously deforms to a vortex ring and then breaks up spontaneously. We experimentally investigated relations among breakup number, radii of droplets, viscosities and density differences between two solutions. We also proposed a phenomenological model considering the Rayleigh-Taylor instability. The phenomenological model provides a non-dimensional parameter derived from a radius of a droplet, viscosity and a density difference between two liquids. And, the model states that the breakup number is classified by the parameter. Our experimental results obey the parameter. It means that the competition between a driving force of gravity and the viscosity dissipation at the interface of two solutions determines the breakup number.