On the engulfment of spherical particles by a moving ice-liquid interface

Second phase particles suspended in a liquid undergoing solidification are either repelled and swept along by the advancing solid-liquid interface or, beyond a critical velocity of the solidification front, engulfed and encapsulated into the solid phase. In this study critical encapsulation velocities were determined for spherical latex particles at an advancing ice-water interface by means of a gradient freezing stage attached to a light microscope. The influence of the particle radius, the temperature gradient at the planar solidification interface, and the viscosity of the melt has been investigated. The experimental data confirm the theoretically predicted 1/R relationship between the particle radius and the critical growth velocity V_c. The effect of the temperature gradient can be described by a power law (V_c ∝ G^1/4), but its influence on V_c may be even weaker. The inverse proportionality between V_c and the dynamic viscosity of the melt may also be weaker than it would result from Stokes' law. The critical distance between particle and solidification interface was calculated to be in the range of 0.76 to 16.3 nm depending on the theoretical model applied. The resulting Hamaker constant of the system ice/polystyrene/water is -1.7 x 10^-21 J.