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

Tiny suspended particles are moved ahead of a freezing front, leaving behind pure ice. Yet, if particles are big or freezing occurs rapidly, they can get trapped in ice. Here, we investigate this phenomenon, focusing on the behavior of spherical objects, near the critical entrapment speed. Through experiments and theory we quantify how far particles travel before becoming entrapped. Moreover, we observe that two nearby particles either attract or repel during freezing, depending on their thermal conductivities. Our findings help to understand cluster formation during solidification, which we show to be analogous to clustering of particles at liquid interfaces, known as the Cheerios effect.