dendritic solidification

Here’s a new project we are working on. It is based on a simulation of solidification in supercooled liquids. As the liquid turns to solid, it forms a dendritic structure. This is similar to how snowflakes form, though they have a anisotropic crystalline structure and start from a small, round initial seed. We’ve taken this physical system and modified it to create a non-physical one where both the solid and liquid phase to grow into each other, giving a more symmetric boundary condition where the phases interlock.

The video shows a many of the 10,000 images we generated to explore the system’s parameter space. Warning: This video is extremely repetitive. If you are impatient, skip around to see more pattern diversity.

The simulation is a phase-field model, which treats each phase (eg liquid/solid) as a continuous variable. Instead of having a hard boundary between phases, which can be hard to represent mathematically, there is a thin region where one phase transitions to the other. Properties of the boundary, like the normal, can be represented as the differential properties of the field, like the gradient. Rather than a physical description of solidification, the model uses a potential function to model the dynamics of each phase. The function has two minima, one for each phase. The phase wants to stay in one of these minima, solid or liquid. A temperature variable is used to tip the balance of this potential function. When the temperature is high, the solid phase becomes less stable and tends to transition towards liquid and visa-versa.

This model is very sensitive to initial conditions. The boundary of the phases and initial temperatures can create vastly different results.