  Particles at liquid interfaces have the tendency to cluster due to capillary
forces competing to gravitational buoyancy (i.e., normal to the distorted free
surface). 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
thermally more conductive than water are observed to attract each other and
form clusters once frozen. We call this feature the frozen Cheerios effect,
where interactions are driven by alterations to the direction of the
experienced repelling force (i.e., normal to the distorted isotherm). 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 efficacy 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.
