We describe an experimental test of a new theory of the unidirectional freezing of aqueous colloidal suspensions. At low freezing speeds a planar ice lens completely rejects the particles, forming a steady-state compacted boundary layer in the liquid region. At higher speeds the planar interface becomes thermodynamically unstable and breaks down geometrically to trap bulk regions of colloid within. The theoretical stability threshold is determined experimentally, thereby demonstrating that colloidal suspensions can be treated analogously to atomic or molecular alloys.