A model has been developed by taking into account the common action of the nucleation, the diffusional growth, the collisions and coagulations of the minority phase droplets and the spatial phase segregation to describe the microstructure evolution in a rapidly directionally solidified immiscible alloy. Numerical solutions have been performed to investigate the microstructure evolution in a directionally solidified hypermonotectic Al - Pb alloy. It has been shown that an undercooled region appears in front of the solid/liquid interface and the liquid-liquid decomposition takes place there. If the solidification velocity is high enough, a steady state of solidification can be established and a fine dispersion of minority phase particles in a hypermonotectic alloy can be obtained.
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