Frozen Cheerios effect: Particle-particle interaction induced by an advancing solidification front

Particles at liquid interfaces have the tendency to cluster due to long-range capillary interactions. This is known as the Cheerios effect. Here we experimentally and theoretically study the interaction between two submerged particles near an advancing water-ice interface during the freezing process. Particles that are more thermally conductive than water are observed to attract each other and form clusters once frozen. We call this feature the frozen Cheerios effect. On the other hand, particles less conductive than water separate, highlighting the importance of thermal conduction during freezing. Based on existing models for single particle trapping in ice, we develop an understanding of multiple particle interaction. We find that the overall strength of the particle-particle interaction critically depends on the solidification front velocity. Our theory explains why the thermal conductivity mismatch between the particles and water dictates the attractive/repulsive nature of the particle-particle interaction.