Particle trapping and banding in rapid solidification

Solidification of suspensions of small particles, from nanometer to colloidal (sub-micrometer) sizes, produces biomimetic materials with novel microstructure and expanding applications in microfluidics, nanotechnology and tissue engineering. To facilitate understanding and control of the solidification process, a thermodynamically consistent theory is here developed. We use the Boltzmann particle velocity distribution to determine the probability a particle is engulfed by an advancing solid-liquid interface and obtain the resulting kinetic phase diagram. We demonstrate use of the theory by predicting the formation of bands in rapidly solidified alumina suspensions, in quantitative agreement with experiment.